Transcript
Ultrasonic irradiation and its mixing and nucleation consequences Master Thesis Salah Shawaz September 2012
Faculty of Applied Sciences Mechanical Engineering Department: Process & Energy, Faculty 3mE Section: Intensified Reaction & Separation Systems
Graduation Committee Dr. ir. H.J.M. Kramer Prof. dr. ir. A.I. Stankiewicz Dr. M. Tummers
Ultrasonic irradiation and its mixing and nucleation consequences
Summary This project aim to determine the macro streaming, the heat input and crystal nucleation induced by ultrasonic irradiation of a vessel containing solutions at different power input and irradiation time. First, experimental determination of the mixing induced by the ultrasound irradiation at different power input was studied using a high speed, high resolution camera. The particle image velocimetry (PIV) technique was used for these studies. The experiments showed that when increasing the power of the ultrasound processor, the velocity increased subsequently. Also, when power was increased, vorticity was increased. After, the heat input given by the sonotrode was studied using high speed camera and liquid crystals which change the color with temperature. The particle image thermometry (PIT) method was used to determined 2D temperature profiles. From the 2D temperature measurement 2D supersaturation profiles was determined. Experiments showed that when temperature increases, supersaturation decreases. The distribution of supersaturation and temperature were assessed at the same moment. Lastly crystal nucleation was performed at power inputs of 50% and 75% and different insonation time from 30 to 120 seconds. The solution used in these experiments was lactose. It was found that when power input increases, the amount of lactose crystals formed was also increasing. With higher power input and increased insonation time, the number of the crystals increased as well as the mean diameters. However there were exception. Above a certain level of insonation time the volume based diameter did not correspondently grow.
2
Ultrasonic irradiation and its mixing and nucleation consequences
Contents Summary ................................................................................................................................................. 1 1. Introduction......................................................................................................................................... 5 2. Theory.................................................................................................................................................. 7 2.1 Crystallization .............................................................................................................................. 7 2.1.1 Supersaturation ...................................................................................................................... 7 2.1.2 Nucleation .............................................................................................................................. 7 2.1.3 Crystal Growth ........................................................................................................................ 8 2.1.4 Characterization of Crystal Size Distribution ......................................................................... 9 2.2 Lactose ........................................................................................................................................ 11 2.2.1 Isomeric forms and solubility of lactose .............................................................................. 12 2.2.2 Lactose in the solid state ...................................................................................................... 14 2.3 Ammonium sulphate ................................................................................................................. 16 2.4 Ultrasound .................................................................................................................................. 17 2.4.1 Ultrasonic cavitation............................................................................................................. 17 2.4.2 macro streaming................................................................................................................... 18 2.4.3 Local temperature rise ......................................................................................................... 19 2.5 Sonocrystallization .................................................................................................................... 19 2.6 Particle image velocimetry (PIV) ............................................................................................. 20 2.7 Particle Image Thermometry (PIT) .......................................................................................... 21 2.8 Combined Particle Image Thermography (PIT) and Velocimetry ......................................... 22 3. Experiments and Methods ................................................................................................................ 23 3.1 Materials ..................................................................................................................................... 23 3.2 Experimental set-up and method ............................................................................................. 25 4 Experimental procedures ................................................................................................................... 28 4.1. Ammonium sulfate crystallization.............................................................................................. 28 4.2. Lactose crystallization ................................................................................................................ 28 4.3. PIV analysis ................................................................................................................................ 29 4.4. PIT analysis ................................................................................................................................ 29 5 Results ................................................................................................................................................ 32 5.1 Ammonium sulfate crystallization results ................................................................................... 32 5.2 Lactose crystallization results...................................................................................................... 32 5.2.1. Initial experiments ............................................................................................................... 32 5.2.2. Results ................................................................................................................................. 33 3
Ultrasonic irradiation and its mixing and nucleation consequences
5.3 PIV measurements ...................................................................................................................... 36 5.4 PIT measurements....................................................................................................................... 39 5.4.1. Power output of the ultrasound.......................................................................................... 41 Discussion and Conclusions ................................................................................................................... 43 References ............................................................................................................................................. 46 MATLAB function and files: ................................................................................................................... 48
4
Ultrasonic irradiation and its mixing and nucleation consequences
1. Introduction Crystallization is the process of formation of a solid from a liquid phase. This separation method is based on the difference between chemical potential of the liquid phase compared to the solid phase. Supersaturation is defined as a difference between the actual concentration and the solubility concentration of a solute. (S.N. Herreilers, 2007)
Crystallization is a highly selective process. It operates at lower temperatures when compared to a separation by distillation for the same material. (J. Ulrich and M.J. Jones) There are many factors why there is a growing importance of crystallization as an industrial separation process. For instance, many products are solids under ambient conditions, in particular in the specialty chemicals sector, the pharmaceutical industry and the manufacture of foods. On the other side, the ability to minimally manipulate the macroscopic properties of crystals such as shape and size by choice of crystallization conditions makes the technique a very attractive option. Especially, in the above mentioned industry sectors , where reproducible product quality with well defined properties (flow properties, color, dissolution characteristics, polymorphic form etc.) are essential. The processes of crystallization are therefore promising. However, there are also some disadvantages. Batch crystallization from a solution is generally started by a decrease in temperature or an increase in concentration, until primary nucleation starts and proceeds over an often not well-defined period of time. In this way primary nucleation is very difficult to control and obtaining reproducible crystal size distributions in batch crystallization is therefore considered difficult. (Virone et al. 2006) It is claimed that ultrasound irradiation of a solution stimulates primary nucleation in a controlled way at low supersaturation, and reduce the induction time as well. (Lakerveld et al, 2011) In addition, the nucleation rate can be manipulated by varying power input and irradiation time of the ultrasound, the control of nucleation rate would give a much better control of the crystallization process. The induction of the nucleation by ultrasound is however not well described. Moreover, in literature it is not rare that authors merely report positive results are reproducible. In practice the effects of ultrasound might not always predictable nor reproducible. The effects very strongly depend on the geometry of the vessel in which the insonation takes place and the type of sonotrode used. It can postulated that the theory is not able to predict the results, because not much is known about the exact mechanism of the ultrasound. Some reports (Verzijden, 2008 and van der Graaf, 2011) have therefore questioned the reproducibility of ultrasound induced crystal nucleation. Also, it has been hypothesized that the geometry of the sonotrode and the reactor have large influence on the amount of nuclei which are formed. (Lakerveld et al. 2011). Furthermore, questions remain about the influence of macro streaming which is also induced by ultrasound.
5
Ultrasonic irradiation and its mixing and nucleation consequences
The objective of this project was to investigate the macro streaming, power input and crystal nucleation induced by ultrasonic irradiation. The experiments were conducted in a vessel containing a supersaturated solution which was irradiated with different powers and for different periods of time. In this study, to our knowledge, the crystallization, flow, temperature, and supersaturation profiles measurements were combined for the first time. Particle image velocimetry (PIV) technique was used to measure the velocity field associated with the acoustic streaming in the crystallizer. The average velocity and vorticity were measured at different power input. To determine the heat input, a particle image thermometry (PIT) technique was used. By this technique the temperature difference was measured for different power input to calculate the heat input. A temperature and supersaturation (SS) field at a certain insonating time for different power input were also determined using PIT technique.
6
Ultrasonic irradiation and its mixing and nucleation consequences
2. Theory 2.1 Crystallization Crystallization is a solid-fluid separation operation in which crystalline particles are formed from a homogeneous fluid phase. (J. D. Seader) This separation method is based on the difference between chemical potential of the liquid phase compared to the solid phase. This difference is the driving force for the formation of crystals. Many interactive mechanisms are involved in crystallization process, such as supersaturation, nucleation, crystal growth, attrition and agglomeration. These concepts are described below. 2.1.1 Supersaturation The driving force for crystallization can be expressed in terms of supersaturation which can be defined as a difference between the actual concentration and the solubility concentration of a solute. There are mainly four ways to create supersaturation:
i. The first method is cooling crystallization, where supersaturation is created by cooling the solution; ii. The second method is evaporative crystallization, where supersaturation is created by evaporation of the solvent; iii. Anti-solvent crystallization is the third main crystallization method. Here supersaturation is created by adding an additional component which influences the solubility; iv. The fourth method is reactive crystallization, in which a very large supersaturation is created by adding two streams containing separate reactants that form a product with a very low solubility.
In this thesis, crystalline particles are formed from a solution using cooling crystallization, where supersaturation is created by cooling the solution to a desired temperature. The supersaturation can be written in terms of the supersaturation ratio, which depends on the concentration ( C ) and the solubility ( C sat ).
SS =
C C sat
2.1.2 Nucleation Nucleation is the formation of new crystalline particles. As discussed above, although there are different methods for crystallization, the basic principle which leads to solidification is the difference in chemical potential in favor of the solid state. (Richardson et al.2002) This difference is normally shown in the following equation:
∆µ = µsolid (T ) − µliquid (T ) 7
Ultrasonic irradiation and its mixing and nucleation consequences
Nucleation can be divided in primary and secondary nucleation. Primary nucleation is the spontaneous formation of crystal nuclei. Primary nucleation can be divided in homogeneous and heterogeneous nucleation.
In homogeneous the nuclei are spontaneously formed without external stimulus. In
heterogeneous nucleation formation of nuclei is initiated due to the presence of foreign bodies. The region of supersaturation that does not result in primary nucleation is referred to as the metastability zone. During secondary nucleation nuclei are thought to be formed or due to nucleation in the vicinity or on the surface of crystals. (Bernstein, 2002) The rate of homogeneous nucleation is given by the following expression ( Seader et al, 1998) ;
2 3 − 16 π v σ N s s , L a B o = A exp 2 3v 2 (RT )3 ln( C ) C sat Where ;
B o = rate of homogeneous primary nucleation, number of nuclei/ cm 3 .s A = frequency factor. (theoretically A = 1030 nuclei / cm 3 .s )
N a = Avogadro number = 6,022* 1026 molecules/kmole v s = molar volume of the crystal
σ s ,L = interfacial tension v = number of ions/molecule of solute C = supersaturation ratio C sat In practice, nucleation frequently occurs heterogeneously. For heterogeneous primary nucleation the same expression can be applied , where A is determined experimentally and may be many orders of magnitude different from the theoretical value. A value of 1025 is often quoted. ( Seader et al, 1998) 2.1.3 Crystal Growth Similar to nucleation, crystal growth only occurs if there is a driving force as a result of nonequilibrium thermodynamic conditions. The crystal growth rate is a physical property of a given material. However growth rates not only depend on the temperature, pressure and composition of the mother liquor. It also depend on parameters such as supersaturation (under cooling), fluid flow conditions, history of the crystals, the nature of the surfaces of crystals and the presence or absence of additives (impurities) in the mother liquor.
8
Ultrasonic irradiation and its mixing and nucleation consequences
Crystal growth rates are very important to the engineer since they determine the residence time. This in turns determines the size of the crystallizer which is related to the investment costs.( J. Ulrich and M.J. Jones). The faster is not always the better. Rapid growth has a negative effect on the crystal structure; the crystals usually form spherical like shapes and not the preferred faced structure. 2.1.4 Characterization of Crystal Size Distribution 2.1.4.1 Particle Size Distribution Crystalline population coming out from a crystallizer is characterized by its size distribution, which can be expressed in different ways. The crystal size distribution (CSD) may refer to the number of crystals, the volume or the mass of crystals with reference to a specific size range, or the cumulative values of number, volume or mass of crystals up to a fixed crystal size. (Kramer H.J.M. et al 2010) .The first approach refers to a density distribution, whereas the second one to a cumulative size distribution. ( Mersmann, A. 2001) The cumulative variable, F(L), expresses number, volume, or mass of crystals per unit slurry volume between zero size and the size L, whereas the density distribution function, f (L), refers to number, mass, or volume of crystals per unit slurry volume in a size range, whose average size is L. (Cashman, K. and Ferry, J. 1988) The relationship between the cumulative size variable and the density distribution size one is as follows: L
F (L ) = ∫ f (L )dL 0
In Table 1.1 the expression of cumulative and density function variables referred to the number, volume, or mass of crystals is reported. Table 1: Cumulative and density variables.
The most used density distribution variable is the crystal population density, n(L). It can be used to estimate the total number, N T , the total surface AT , and total mass, M T , of crystals by means of the following expressions:
9
Ultrasonic irradiation and its mixing and nucleation consequences
∞
N T = ∫ n (L )dL 0 L
AT = ∫ k s (L )L2 n (L )dL 0 L
M T = ρ ∫ k v (L )L3n (L )dL 0
where ρ is the crystal mass density and k s (L ) and k v (L ) are the surface shape factor and the volume shape factor of the crystals of size L, respectively . (Marsh, B. 1988) 2.1.4.2 Mean particle size To characterize a CSD an average particle size is necessary, for which several parameters are available. Such as; •
d NL =
Mean number diameter, D[1,0]
∑N d ∑N i
i
i
•
dvs =
Mean area diameter, D[3,2]
∑s d ∑s i
=
i
i
•
dvM
∑N ∑N
i
d i3
i
d i2
Mean volume diameter, D[4,3]
∑v d = ∑v i
i
i
∑N d = ∑N d i
i
4 i 3 i
The most popular mean value is the mean volume diameter, which gives the average diameter based on the volume of a size fraction (v i ) and is weighted towards large particles. The mean volume diameter can be converted to the mean mass diameter by multiplying it with the density.
10
Ultrasonic irradiation and its mixing and nucleation consequences
2.1.4.3 The number of crystals The total volume of the crystals produced can be calculated dividing the yield by the crystal density
V crys =
M crys
ρcrys
The volume distribution, found with laser diffraction, gives the percentage of crystals (V frac ) in the fraction with size (d ). The width of the fractions does not remain constant, therefore this needs to be normalized with the integral of the distribution all fractions to give the absolute fraction, which can then be multiplied with V crys to find the volume of that fraction
V (d ) V (d ) =V crys . ∞ frac ∫V frac (d )dd 0
From which the number of crystals (n ) in that fraction can be calculated
n (d ) =
V (d ) k v .d 3
Where k v is the shape factor of the crystals, for which a value of 0.43 was used. The total number of crystals is then found by integrating n with respect to d and multiplying with the solution volume. ∞
N crys =V sol .∫ n (d )dd 0
The actual calculation of the number of crystals was done with a Matlab m-file which is reproduced in MATLAB function and files at the end of the report under name of number of crystals.
2.2 Lactose Lactose ( C 12 H 22O11 ) is the most important carbohydrate of the milk of most species. (DFE Pharma) Its biosynthesis takes place in the mammary gland. Concentrations in milk differs when assessed in different species. Lactose is the first and only carbohydrate every newborn mammal (including human) consumes in significant amounts. Bovine milk contains 45 – 50 grams lactose per liter. Industrially lactose is produced from bovine milk exclusively, or rather from milk derivatives like cheese whey or ultra filtration permeate. Lactose is also known as milk sugar. Lactose is carbohydrate, and as such a disaccharide. One molecule of lactose is built from one molecule each of two other carbohydrates, galactose and glucose.The galactose and glucose moieties are linked together through a so called beta-(1,4) glucosidic linkage. The molecular structure of lactose is shown in figure 2. 11
Ultrasonic irradiation and its mixing and nucleation consequences
Figur2: Molecular structure of lactose
The official chemical name of lactose, which is frequently encountered in regulatory documents is 4O-β-D- galactopyranosyl, D-glucopyranose. 2.2.1 Isomeric forms and solubility of lactose In milk, lactose exists in two isomeric forms, called α- and β- lactose respectively. (Thomas NR ,et al.2009) The molecular structures of α- and β -lactose differ in the orientation of a hydrogen- and a hydroxyl group on carbon atom no.1 in the glucose moiety, as is shown in figure 2.. Both forms change into one another continuously. This phenomenon is called mutarotation. The velocity of mutarotation is determined by factors like temperature, concentration and pH (acidity) of the solution. Lactose solutions strive after a state of equilibrium between the α and β form. It was found that the
β / α ratio decreases from about 1.64 at 0⁰C to about 1.36 at 100⁰C. (Roetman et al. 1974) They used three methods to find the β / α ratio , the results of those methods agreed reasonably well . figure 3a below shows the β / α ratios in equilibrium lactose solution at various temperature obtained by Roetman’s methods. At room temperature the equilibrium results in a ratio of about 40% α-lactose and 60% β-lactose. The time necessary to achieve equilibrium from a solution which contains only a single anomer depends on the rate constant of the mutarotation reaction. Above 50⁰C the equilibrium is achieved in less than an hour. The fact that two forms of lactose exist which differ in molecular structure, has profound effects on various properties of lactose such as crystallization behavior, crystal morphology, solid state properties and solubility.
12
Ultrasonic irradiation and its mixing and nucleation consequences
Figure 3a:
β / α ratios in equilibrium lactose solution at various temperatures obtained by Roetman’s methods.
The solubility characteristics of the α- and β- isomers are distinctly different. When α-lactose is added in excess to water at 20⁰C for instance , about 7 g per 100 g water dissolved immediately. Some αlactose mutarotates to the β anomer to establish the equilibrium ratio 62.7 β: 37.3α; therefore the solution becomes unsaturated with respect to α and more α-lactose dissolves. these two processes (mutarotation and solubilization of α-lactose) continue until two criteria are met: 7 g α-lactose in solution and a β / α ratio of 1.6. The final solubility is 7 g + (1.6*7) g = 18.2 g per 100 g water. (Fox et al. 1998) The solubility of lactose as function of temperature is shown in figure 3b. The solubility of α-lactose is more temperature dependent than of β-lactose . A solution at 60⁰C which is the temperature uses in the experiments for this research , contains approximately 59 g lactose per 100 g water.
13
Ultrasonic irradiation and its mixing and nucleation consequences
Figure 3b: Solubility curves of the lactose anomers and the total solubility at equilibrium
2.2.2 Lactose in the solid state Lactose in solid form can either be in a crystalline state or in an amorphous state. (Platteau, et al. 2004) Crystalline lactose can exist in a number of distinct forms. Most well known are α-lactose monohydrate and β-lactose. Also, two crystalline anhydrous α-lactose types are known, a stable and an unstable (hygroscopic) form. Furthermore, a so-called mixed crystalline form is reported, containing both α- and β- lactose in a special crystal lattice. Crystallinity is the result of a highly ordered arrangement of the lactose molecules. Amorphous lactose lacks crystallinity and the arrangement of the lactose molecules is more or less random. The most frequently encountered forms of solid lactose are described in the following sections. 2.2.2.1 α-Lactose monohydrate The most common way to obtain lactose in solid form is crystallizing from solution. When crystallization is performed at temperatures below 93.5°C, exclusively α-lactose monohydrate is obtained. α-Lactose has the peculiarity that in the crystalline state each lactose molecule is associated with 1 molecule of water. In other words, α-lactose crystallizes as monohydrate. The water is incorporated in the crystal lattice and forms an integral part of it. It is not removed by normal drying processes. Due to this water of crystallization the normal water content of α-lactose monohydrate is around 5%. Only at temperatures as high as 140°C, the crystal water will be removed completely. Crystals of α-lactose monohydrate possess a characteristic tomahawk-like shape, as shown in figure 4. These crystals are very hard and 14
Ultrasonic irradiation and its mixing and nucleation consequences
brittle. On an industrial scale, α-lactose monohydrate is obtained by crystallizing highly concentrated lactose solutions at low temperatures, separating the crystals from the mother liquor by centrifugation and subsequently drying off the adhering moisture from the crystal mass.
Figure 4: Lactose monohydrate crystals
2.2.2.2 Β-Lactose Crystals of β-lactose are exclusively formed when a highly concentrated solution of lactose is crystallized at temperatures above 93.5°C. Crystals of pure β-lactose have a characteristic kite-like form as shown in figure 5. Particles with crystalline β-lactose are more brittle than α–lactose monohydrate crystals. Moreover, it does not contain crystal water. Β-Lactose is often referred to as anhydrous lactose.
Figure 5: Microscopic picture of a typical β-lactose crystal
15
Ultrasonic irradiation and its mixing and nucleation consequences
2.3 Ammonium sulphate Ammonium sulfate (( NH 4 )2 SO4 ) is a salt that is produced by the reaction of ammonia with sulfuric acid. It is most commonly used as a soil fertilizer and is a popular model compound for crystallization research. The temperature dependence of its solubility curve is small and linear, as shown in Figure 6. The metastable zone of ammonium sulfate is also relatively small and limits the degree of supersaturation that can be achieved before primary nucleation occurs. Ammonium sulfate crystals have distinct octagonal shapes as observed in Figure 7. (Jeroen van der Graaf, 2011)
Figure 6 : The solubility curve for ammonium sulfate in g/100 g solution. The grey line is the relation found by (Daudey 1987) while the red line represents a more recent equation from (Westhoff 2002)
Figure 7: Scanning electron microscopy (SEM) images of ammonium sulfate crystals, showing the octagonal shape
16
Ultrasonic irradiation and its mixing and nucleation consequences
2.4 Ultrasound Ultrasound is acoustic (sound) energy in the form of waves having a frequency above the human hearing range. The highest frequency that the human ear can detect is approximately 20 thousand cycles per second (20,000 Hz). This is where the sonic range ends, and where the ultrasonic range begins. These are the effects of ultrasound: 2.4.1 Ultrasonic cavitation When sonicating liquids at high intensities, the sound waves that propagate into the liquid media result in alternating high-pressure (compression) and low-pressure (rarefaction) cycles as illustrated in Figure 1, with rates depending on the frequency. During the low-pressure cycle, high-intensity ultrasonic waves create small vacuum bubbles or voids in the liquid. When the bubbles attain a volume at which they can no longer absorb energy, they collapse violently during a high-pressure cycle. This phenomenon is termed cavitation. Available at: (http://www.hielscher.com/ultrasonics, accessed 16th June) The propagation of acoustic waves induces a pressure field described by
P (t ) = Pa cos(2π ft ) where Pa is the acoustic pressure which is related to the acoustic power, and f is the frequency of the acoustic wave. When the local pressure, given by the sum of P (t ) and the system pressure P0 , becomes below the threshold value, which equals the vapor pressure Pv of the liquid, bubbles can be formed and expand for a period ∆t b ,exp during which the pressure remains below the threshold value. The expansion interval ∆t b ,exp depends on the frequency. Bubbles exceeding the so-called Blake threshold ( Blake et al. 1949) increase strongly in size and eventually collapse when the local pressure increases again. (Virone et al. 2006)
A number of models derived from the Rayleigh–Plesset (RP) equation (Hilgenfeldt et al. 1998, Matula et al. 1999) describe the growth and collapse of formed bubbles as a result of the local pressure field changes. With the RP equation the evolution of the radius of the bubble R can be described by (Virone et al. 2006)
3 2
ρ1RRɺɺ + ρ1Rɺ 2 = Pgas (R , t ) − P (t ) − P0 4η1
Rɺ 2γ − R R
where P0 is the ambient pressure, Pgas the gas pressure inside the bubble, ρ1 the liquid density, γ the surface free energy and η1 the liquid viscosity. From this equation it can be shown that (Matula et al. 1999, Virone et al. 2006) 17
Ultrasonic irradiation and its mixing and nucleation consequences
2γ R 03 − h 3 Pgas (R , t ) = P0 + R 0 R (t )3 − h 3
j
where R 0 is the ambient bubble radius, and h the van der Waals hard-core radius ( h = R 0 / 8.54 for air bubbles). It is assumed that the growth occurs isothermally ( j = 1 ) while the collapse is adiabatic ( j = 1.4 ).(Hilgenfeldt et al. 1998, Neppiras et al. 1980) From the RP equation the maximum pressure of the collapsing spherical bubble was determined. (Virone et al. 2006)
3j
PMax
R = Pgas (R Max ) Max , h
with the maximum bubble value R Max : ( Brennen, 2002)
R Max =
2(Pv − P0 − P (t ) min )∆t b2,exp 3ρ1
At the spot of the collapsing bubble a high-pressure shockwave is created. The shock wave also causes high turbulence. Due to adiabatic compression the temperature at the collapse spot increases to 4000 K, with a temperature spread due to thermal diffusion that is much slower than the shock wave propagation . (Virone et al. 2006) Pressure increase will give higher driving forces, so shock waves of high pressure will induce very high local temporary SS and this in return can induce nucleation . On the other hand, the temperature rise will lead to a decrease in SS because the solubility is increasing. These two effects occur and can influence the nucleation rate . Virone has reported that the SS as well as the pressure both contribute to the chemical potential differences related to nucleation. 2.4.2 macro streaming The maximum pressure field increase depends on the intensity of the ultrasound. When the pressure difference is large enough, a bulk flow is produced due to momentum transfer from the sound waves to the solution. This is known as acoustic or macro streaming. (Leighton 1994) Acoustic streaming induces mixing, but is significantly less effective than conventional stirring at the same power output. (Kumar, et al. 2006). The acoustic streaming was studied quantitatively by many researchers, but few reports have described the streaming velocity in a low frequency ultrasound reactor. Dahlem et al. (1999) have reported acoustic streaming in low frequency batch ultrasound reactors (20 kHz). The authors used PIV technique to measure the velocity field associated with the acoustic streaming in the 18
Ultrasonic irradiation and its mixing and nucleation consequences
reactor. The average velocity of the fluid associated with the acoustic streaming in the radial horn was measured around 0.05 m/s using a Telsonic horn ( radial horn) with an electrical power density of 285 kW / m 3 and a solution volume of 3.5 liter. Kumar et al. (2006 ) have observed average streaming velocity in the range of 0.05 – 0.15 m/s. An ultrasonic horn of 20 kHz in 2 liter solution for three different power density 15, 25 and 35 kW / m 3 was used. Trujillo et al. (2011) have developed a computational fluid dynamics (CFD) to predict the acoustic streaming induced by an ultrasonic horn reactor at 20kHz. The authors used 2 liter of solution for power density of 15, 25 and 35 kW / m 3 . The average velocity was in the range of 0.03 – 0.2 m/s. Kojima et al. (2010) have investigated the pattern of liquid flow of a rectangular sonochemical reactor at 490 kHz as a function of the input power from 10 to 50 W. This corresponds to a power density from 2.5 to 12.5 kW / m 3 using 4 liter solution for each experiment. The observed average flow velocity was in the range of 0.008 and 0.014 m/s. Xu et al. (2012) have numerically simulated the liquid velocity distribution of ultrasonically induced flow in the sonochemical reactor containing 3 liter of solution with a transducer at a frequency of 490 kHz. The authors used three different input power densities of 3, 10 and 16 kW / m 3 . They observed an average streaming velocity in the range of 0.004 – 0.01 m/s. 2.4.3 Local temperature rise The temperature rise will lead to a decrease in SS because of the solubility increasing. This increase is significant because it will be measured to calculate the power input. Due to the temperature rise the solution gets high local heating but this increase of temperature is also distributed due to the macro streaming. The local temperature is partly induced by cavitation, but also induced by the macro streaming.
2.5 Sonocrystallization The ultrasound energy creates sequential compression then expansion. Over several cycles a bubble forms, grows and then collapses. The collapse of the bubble provides energy to encourage the nucleation process at the earliest possible point in time (figure 1) . Ultrasonic irradiation has been shown to have several effects on crystallization for different solutes: a decrease of induction time and metastable zone width (Lyczko, et al. 2002), an increase in nucleation rate (Nishida 2004), an increase in reproducibility (Luque de Castro and Priego-Capote 2007) and a decrease in crystal growth rate and particle size (Nishida 2004) (Kim, Wei and Kiang 2003).
19
Ultrasonic irradiation and its mixing and nucleation consequences
Figure 1: Cycle of a bubble
2.6 Particle image velocimetry (PIV) Particle Image Velocimetry appeared approximately 30 years ago. Since then has become an essential measurement technique in fluid mechanics laboratories in both research institutes and industry. Particle image velocimetry (PIV) is an optical method of flow visualization. The technique relies on a planar beam of light - a light sheet - usually from a laser or from a white light source. The light sheet illuminates particles entrained in a flow. In most applications, such particles are not naturally present in the flow. So the fluid has to be seeded with tracer particles. The fluid is seeded with tracer particles which, for sufficiently small particles, are assumed to faithfully follow the flow dynamics. The fluid with entrained particles is illuminated so that particles are visible. The motion of the seeding particles is used to calculate speed and direction (the velocity field) of the flow being studied. Pairs of photographic images are captured using a high-speed digital camera (Mikrotron, EoSens, MC3011) which were used to track the liquid crystals particle added in the solution (Nematic LC Slurry, NSL40/R25C10W, LCR Hallcrest LTD). PIV software computes how far the particles moved between the two images and a velocity map is generated based upon the definition of velocity, i.e. the first derivative of position with respect to time, the technique consists in measuring the displacement of fluid (∆x) over a given time interval (∆t).
The timeresolved digital particle image velocimetry tool for MATLAB (PIVlab) is used to process the images and to calculate the velocities profiles. PIVlab is an open-source particle image velocimetry (PIV) software that does not only calculate the velocity distribution within image pairs, but can also be used to derive, display and export multiple parameters of the flow pattern. Thielicke et al (2005)
20
Ultrasonic irradiation and its mixing and nucleation consequences
In all experiments in this paper the light used was linear polarized light provided by a LED fiber optic illuminator (REVOX, SLG-50s). The main advantage of using white light source is – beside costs – that applications are not hampered by laser safety rules. Due to the finite extension of a white light source and since white light cannot be collimated as well as monochromatic light, white sources have clearly some disadvantages. Raffel et al. (1998)
2.7 Particle Image Thermometry (PIT) Particle Image Thermometry (PIT) is a technique by which temperature fields can be obtained noninvasively using thermochromic liquid crystals (TLCs) through image processing of experimental true-colour images taken by a high-speed digital camera (Mikrotron, EoSens, MC3011). This is done using a calibration curve (hue versus temperature). With the calibration data, every pixel of the colour photograph is transformed to a temperature value, and thus accurate experimental temperature maps are obtained. (T.P. Bednarz et al. 2007)
TLCs are frequently used in science and engineering to map temperature distributions in fluids or on rigid surfaces. They usually exist in the smectic, the nematic or the cholersteric (also chiral nematic) phases . (T.P. Bednarz et al. 2007) When a white light source shines on the chiral nematic TLC, light of only one particular wavelength corresponding to the temperature is reflected. The temperature visualization is based on the property of some cholesteric and chiral-nematic liquid crystal materials to refract light of selected wavelength as a function of the temperature and viewing angle. Hence, at specific temperature range they appear as small color spots following the flow. (Park, H.G) The visible colour of TLCs turns from colourless (black against a black background) to red at a given temperature. As the temperature is increased, the TLCs’ colour passes through other colours of the visible spectrum in sequence (before turning colourless again at a higher temperature). Their color change ranges from clear at low temperature, through red as temperature increases and then to yellow, greens, blue, and finally clear again at the highest temperature.
TLCs are normally clear or slightly milky in appearance and change their colour over a narrow range of temperatures. The color-temperature play interval depends on the TLCs composition. It can be selected for bands of about 0.5⁰C to 20⁰C, and working temperature of -30⁰C to above 100⁰C. (Stasiek, J.A et al.2002) It has been reported that these color changes are repeatable and reversible as long as the liquid crystals are not physically or chemically damaged. The response time of TLCs equals about 3ms. It is short enough for typical thermal problems in fluids. The most critical part of the TLCs based thermography is to obtain the hue-versus-temperature relationship. The observed colours depend on the observation angle, the scattering properties of the
21
Ultrasonic irradiation and its mixing and nucleation consequences
tracers, colour and refractive index of the immersing liquid. Therefore it is very important to carry out the experiments carefully and always in the same light conditions, with the same fluid and if possible with exactly the same experimental setup as those for the calibration. (Bednarz TP et al 2007)
Simple formulation introduced by Hiller et al (1993) is used to evaluate hue. The 8-bit representation of the hue value assures resolution better than 1%. However, the color – temperature relationship is strongly non-linear. Hence, the accuracy of the measured temperature depends on the color (hue) value, and varies from 3% to 10% of the full color play range. (Kowalewski 2011). For the liquid crystals typically used it results in the absolute accuracy of 0.15⁰C for lower temperatures (red-green color range) and 0.5⁰C for higher temperatures (blue color range). The most sensitive region is the color transition from red to green and takes place for a temperature variation less than one Celsius degree.
Lastly, the size of the TLC particles also needs to be taken into account. Large particles (0.1mm and more) produce strong, clear colors. As the size decreases, their color quickly faints due to the increasing effects of light scattering. Also the camera resolution starts to play an important role in color degradation, when particle images decreases to pixel dimensions of the sensor. Therefore, compromise is necessary for optimal selection of the particle size. (Kowalewski 2011). In a previous report, the mean diameter of the unencapsulated TLC tracers was approximately 50 µ m (Kowalewski 2011). Authors reported that particles of such size guarantee bright, well visible colors of the refracted light and are still small enough to follow the flow. Smaller particles (10 µ m and less) were used for microscopic observations of the temperature field in the vicinity of a vapor bubble.
2.8 Combined Particle Image Thermography (PIT) and Velocimetry Simultaneous measurements of instantaneous velocity and temperature fields provide a promising tool to study the dynamics of thermal plumes and their influence on the local and global heat transfer in thermal and mixed convection. A technique to conduct these measurements in liquids is the combination of PIT and PIV with TLC’s as tracer particles (Schmeling et al 2010).
Possibility to
combine PIV and PIT was first demonstrated by Hiller et al. (1993),who for the first time used the same suspension of TLC particles for digital evaluation of both temperature and velocity fields. Park et al. (2001) documented in details PIV & T method applied to investigate turbulent flow. An extension of PIV technique by using thermochromic liquid crystals as seeding opens new possibility in studying thermally driven flows. Image processed data makes available quantitative, full-field information about the temperature and velocity fields.
22
Ultrasonic irradiation and its mixing and nucleation consequences
3. Experiments and Methods For the experiments conducted in this research project, several materials were used as described in section 3.1. In section 3.2 the experimental set-up is presented.
3.1 Materials •
Ultrasonic processor
The UIP500hd can be operated at 500W continuously. The UIP500hd is amplitude controlled. This means, that the magnitude of the mechanical ultrasonic vibrations (= amplitude) at the front surface of the sonotrode/horn will be constant under all load conditions. You can change the amplitude electronically from 50 to 100% at the front panel of the generator figure 8. You can also change the amplitude mechanically by the use of various booster horns. Once set, the amplitude will be constant, in air, as in water, oil, polymer, dispersions or emulsions - at any pressure. This feature does also give you full control over the most important sonication parameter: The amplitude. The power load of the device, will vary with material to be sonicated (viscosity, temperature, etc.) and with the intensity of sonication (e.g. amplitude and pressure). The maximum power load is 500 watts.
Figur8 : The UIP 500hd sonotrode horns and generators
23
Ultrasonic irradiation and its mixing and nucleation consequences
•
PT-104 convertor (picoLog recorder):
The PT-104 is a four–channel temperature measuring data logger. It offers the ultimate in resolution (0.001 °C) and accuracy (0.01 °C). The PT-104 measures temperature using platinum resistance thermometers (PRTs). Both common industry standards (PT100 and PT1000) are supported. The unit is compatible with two, three and four wire sensors (four wire PT100 sensors are recommended for accurate measurements). A wide range of PT100 sensors are available for use with the PT-104, see figure 9b. •
High speed resolution camera
The CMOS high speed camera EoSens 3CL is a high resolution camera with 1696x1710 pixel. Benefits of CMOS technology are high speed, random access to pixels with free programmability and low power. The camera uses industry-standard C-Mount or F-Mount lenses. The sensor diagonal is 19.27mm with square pixels measuring 8 µm. Free programmability means that the user is free to define the region of interest by size and position and the speed of data output. The frame rate can be selected between 1 fps and several thousand fps depending on resolution and video data width. With a resolution of 1696 x 1710 pixel, 285 fps can be output via the “Full CameraLink®” Interface, created for easy connectivity between the PC and the camera, Camera Link provides simple, flexible cabling for high-speed, high-resolution digital cameras see figure 9a.
Figure 9a: EoSens High speed resolution camera
Figure9b: PT-104 convertor (picoLog recorder)
•
Vessels
-
Vessel A: to maintain a saturated solution of Lactose a cylindrical jacketed glass vessel with a capacity of 2 liter was used. The vessel was connected to a thermostatic bath (Lauda Eco Re 1050) with an external pt-100 sensor which maintained a saturated solution at constant temperature.
-
Vessel B To maintain a saturated solution of ammonium sulfate a cylindrical jacketed glass vessel with a capacity of 4 liter was used. The vessel was connected to a thermostatic bath (Huber CC231) with an external pt-100 sensor which maintained a saturated solution at constant temperature.
24
Ultrasonic irradiation and its mixing and nucleation consequences
•
Thermostatic baths
To control the temperatures during preparing saturation solutions, insonation and growth of the crystals, the following two thermostatic baths were used:
-
Lauda Eco Re 1050 as shown in figure 10a.
-
Huber CC231 as shown in figure 10b.
Figure 10a: Lauda Eco Re 1050 Thermostatic bath
Figure 10b: Huber CC231 Thermostatic bath
3.2 Experimental set-up and method The experimental set-up used to determine the macro steaming and heat input, consisted of a cylindrical jacketed glass vessel (crystallizer) with an inner diameter of 125 mm. The vessel was connected with a thermostatic bath (Lauda Eco Re 1050 ) with external PT100 sensors to regulate the temperature of the solution inside the crystallizer. Temperatures of the input, output of the jacket and solution are all continuously measured and recorded via the Pico log recorder. From the PT-104 convertor, all temperature values are sent to the computer. Data can be viewed both during and after data collection in a spreadsheet or graphical format. The ultrasound transducer is fixed above the crystallizer, 2.5 cm from the sonotrode is immersed inside the solution at the centre of the vessel. A plane of light is created from a light source. The camera is then placed perpendicular to that plane. A schematic drawing and a picture of the setup are shown in figure 11a and 11b. Figure 12 shows some components of the experimental set-up.
25
Ultrasonic irradiation and its mixing and nucleation consequences
Figure 11a: schematic drawing of the experimental set-up for PIV and PIT
Figure 11b: Picture of the experimental set-up for PIV and PIT
26
Ultrasonic irradiation and its mixing and nucleation consequences
Figure12: Components of experimental set-up
A high speed digital camera (Mikrotron, EoSens, MC3011) was used to capture the photographic images which were used to track the liquid crystals particles added in the solution (Nematic LC Slurry, NSL40/R25C10W, LCR Hallcrest LTD). The light used was linear polarized light provided by a LED fiber optic illuminator (REVOX, SLG-50s). The time lapse between two frames was 3.5 ms. The timeresolved digital particle image velocimetry tool for MATLAB (PIVlab) was used to process the images and to calculate the velocities profiles. Temperature fields were obtained using the particle image thermometry (PIT) technique, through image processing of experimental true-colour images taken by a high-speed digital camera (Mikrotron, EoSens, MC3011). To combine PIV and PIT the same thermochromic liquid crystals (TLCs) were used. Temperature fields were obtained using a calibration curve (hue versus temperature). With the calibration data, every pixel of the colour photograph is transformed to a temperature value, and thus accurate experimental temperature maps were obtained.
27
Ultrasonic irradiation and its mixing and nucleation consequences
4 Experimental procedures The following sections describe the ammonium sulfate crystallization procedures , lactose crystallization procedures, PIV analysis and PIT analysis.
4.1. Ammonium sulfate crystallization For the ammonium sulfate crystallization several experiments were done with different saturation temperature at 21, 22, 23 and 24 ⁰C.
1- An excess amount of ammonium sulfate (Technical pure, DSM) was added to demineralized water in the buffer vessel B at least 12 hours prior to any experiment. This was done to ensure a saturated solution. 2- At the start of the experiment 1.2 liter saturated solution was pumped from the buffer vessel into the setup vessel, its jacket being already preheated to prevent immediate nucleation. The solution was then heated to 8 ⁰C above saturation temperature and kept at that temperature for 15 minutes to dissolve any crystals that might have formed during transfer. The solution was then cooled to 1 ⁰C below saturation temperature. In order to minimize temperature overshoot a cooling program with progressively decreasing ramps was used with a cooling rate of 0.5 ⁰C/min 3- The solution was then insonated for the desired period of time.
4- To allow the crystals formed during insonation time to grow, the slurry was maintained at 1⁰C below the initial saturation temperature for 1 hour.
4.2. Lactose crystallization 1- The supersaturated solutions were prepared in vessel B by dissolving 552 grams of pharmaceutical grade alpha-lactose monohydrate per 847.5 grams demineralized water with a supersaturation ratio of 3, at 70 ⁰C and then cooling to the desired temperature. 2- When the desired temperature was reached, 1,2 liter of the solution was pumped to vessel A, in which the sonotrode horn had been placed. Depending on the amount of solution prepared in step 1, the solution remaining in vessel A was used as a blank measurement or discharged. 3- The solution was then insonated for the desired period of time, after which the sonotrode horn was removed and a stirrer was inserted. 4- To allow the crystals time to grow, the solution was maintained at the previous supersaturation temperature for 3 hours. 5- The slurry was filtered with a filter paper of 11 micron by using a vacuum vessel.
28
Ultrasonic irradiation and its mixing and nucleation consequences
4.3. PIV analysis First 1.2 liter of saturated solution at 30°C with a concentration of 25g/100g water was pumped into the vessel in the experimental set-up. Afterwards, the temperature was cooled down with a rate of 0.5°C per minute, to 23°C. Then TLCs was added to the solution to visualize the flow in the vessel. For each different power input (from 50-100% in steps of 10), the ultrasound processor was used to insonate the solution during 150 seconds. After 60 seconds, a movie was taken with the high speed resolution EoSens camera (285 fps and resolution of 1680x1710 pixels). Processing was performed for each power input, to compare macro streaming. For this purpose, we use the PIVlab software process for the right half of the crystallizer as shown in figure 15a . Before this step, the movie is converted to sequence images using virtual dub software.
4.4. PIT analysis First, the calibration curve was determined (hue versus temperature). With the calibration data, every pixel of colour photograph is transferred to a temperature value and thus accurate experimental temperature maps are obtained. For the calibration, images were taken at [23.5 23.75 23.9 24.5 24.9 25.4 26.0°C]. At each temperature, solution should be homogenous. The colour was converted to hue value versus temperature and fitted using MATLAB, the fitted data has a goodness of R-square value equal to (0.9698). R-square measures how successful the fit is in explaining the variation of the data. A value of 0.9698 means that the fit explains 96.98% of the total variation in the data about the average which quite nice. The calibration curve shown in figure 17. The AVI-movie is taken at 100 fps.
26
Temperature
25.5
25
24.5
24
23.5 0.25
0.3
0.35
0.4 0.45 Hue value
0.5
0.55
0.6
Figure 17: A calibration curve obtained from a solution of lactose at supersaturation equal to 1,22
29
Ultrasonic irradiation and its mixing and nucleation consequences
The temperature fields at each time can be obtained using thermochromic liquid crystals (TLCs) through image processing of experimental true-colour photographs. This is done using the calibration curve (hue versus temperature). The equation of the fitted curve is:
T cal = 36,86* hue 4,097 + 23,35 The supersaturation ratio (SS) is changing as the temperature change, so the temperature fields are associated with a supersaturation ratio field. This was also determined and shown in the results below. To calculate the SS, a formula of the solubility curve of lactose was used depending on the data shown in the table below.
Table4: Data of the solubility of lactose
Temperature
(°C)
Equilibrium Coccentration g/100gram water
(°C)
Equilibrium concentration g/100gram water
0,34 2,12 5,75 9,14 14,21 18,78 24,53 30,79 36,72 44,42 49,15 49,91 53,47
10,49 11,26 13,05 14,08 15,61 17,92 21,24 25,6 30,20 37,63 43,26 45,05 49,15
56,94 61,01 65,23 69,03 73,35 77,41 80,96 83,93 86,55 89,09 89,68 89,68
53,76 60,92 68,60 76,03 85,76 96,51 105,98 116,73 124,67 134,14 136,19 136,70
Temperature
Then a formula of the trend line was found using EXEL software. The goodness of this fitted data has R-square value equal to (0.998) which gives an accurate results for the saturated concentration at each temperature.
30
Ultrasonic irradiation and its mixing and nucleation consequences
Concentration Solubility [g/100gram water]
160
y = 10,655e0,0285x
140 120 100
Concentration
80 60
Exponentieel (Concentration)
40 20 0 0
20
40
60
80
100
Temperature (°C)
Figure18: The solubility data of Lactose and its formula of the fitting curve .
From this formula the saturated concentration at each temperature was found,
C * = 10, 655e 0,0285T The actual solute concentration ( C ) at 30 °C , was equal to 25,05 gram/100 gram water. It was assumed that ( C ) remained constant during the cooling process to 23°C. So there isn’t any loss of solvent by evaporation and spontaneous crystallization cannot occur ( cooling occurs in the metastable zone and not in the supersaturated area).
From these relations the SS was found for each temperature.
SS =
C C*
31
Ultrasonic irradiation and its mixing and nucleation consequences
5 Results 5.1 Ammonium sulfate crystallization results For the ammonium sulfate crystallization several experiments were done with different saturation temperature at 21, 22, 23 and 24 ⁰C. In all experiments where ammonium sulfate as solution were used, no crystals were observed. This could be related to the insonating time. If the insonation time becomes too long, the temperature increases to a level so that the supersaturation of the solution decreases or even becomes undersaturated and nuclei dissolve again. Nuclei could also dissolve due to local hot spots caused by the ultrasonic field. Insonating time between 60 and 120 seconds were used.
In this report the experiments did not meet the optimal conditions to create nuclei. In the experiment conducted by Lakerveld 2011 nuclei where successfully created. The investigators used 2 different geometry of the vessels and showed that the number and the shape of the crystals are not the same when two different vessel geometries were tested for insonation with equal volume but different aspect ratio using the same power input and the same insonating. So different vessel geometry affected the number and shape of the crystals. Moreover, in those experiments a different sonotrode probe and reactor was used. These differences could have led to this failed experiment.. Another explanation is the high power input of the UIP500hd used in these experiments. It can be postulated that at high power input the streaming becomes too high, creating a high turbulence, effecting the entire crystallization process. In addition, more heat is transferred to the solution at higher power inputs, which might result in dissolution of nuclei.
5.2 Lactose crystallization results 5.2.1. Initial experiments Experiments were conducted with α-lactose monohydrate. An important limitation of ammonium sulfate is its relatively small metastable zone, so lactose was chosen based on its much wider metastable zone. Due to the wide metastable zone of lactose, very high supersaturation is necessary to induce nucleation within a reasonable period of time. Initial experiments showed that with a concentration of 80 g lactose per 100 g water (0.44 weight percent) crystallization was occurred when a solution was cooling down to 23⁰C (SS = 3,85) even without insonation. With a concentration of 30, 40, and 50 g lactose per 100 g water no crystallization was observed with insonation time 30, 60, 90 and 120 seconds. With a concentration of 60 g lactose per 100 g water (0.375 weight percent) , at 23 ⁰C (SS of 2.9) no crystallization was observed without ultrasound in a period of 3 hours, but when the solution was insonated for 30 seconds it became opaque and crystallization was observed.
32
Ultrasonic irradiation and its mixing and nucleation consequences
A problem with experiments under such high supersaturation is that the theoretical yield is very large (approximately 300 gram for 1,2 liter solution). This is not practical with regards to filtration and makes it difficult to maintain uniform conditions throughout the slurry. Filtration directly after insonation is not possible, because the crystals are very small (<1 µm) and not enough yield can be recovered for measurements. A practical amount of yield was recovered when a growth period of 3 hours was used between insonation and filtration. 5.2.2. Results A set of experiments was done for a concentration of 60 gram lactose per 100 gram water at 23 °C with a supersaturation ratio of 2.9 in which the insonation times varied between 30 and 120 seconds. The crystallization time after the experiment was adjusted so the total time between the start of insonation and filtration remained 3 hours. Blank experiments were done concurrently, but no crystallization was observed in any of them. The following results were found for different power input:
Table2a,b: Insonation times and results for lactose sonocrystallization experiments with respectively 50% and 75% power output, 1200 ml solution and a lactose weight fraction of 0.375 at 22 °C.
Insonation time [sec]
Yield [gram]
Volume based mean diameter [µm]
Number of crystals [ 10 4 /ml]
0 30 30 30 60 90 120 120
1,6 52,66 0 6,02 10,56 26,92 126,01 72,63
118,6 103,3 0,0 89,1 93,88 101,6 99,5 98,70
0,1625 7,51 0 1,258 2,72 3,925 24,4 14,08
Table 2a: 50% power input
Insonation time [sec]
30 60 90 90
Yield [gram]
11,27 25.48 32,05 12,86
Volume based mean diameter [µm]
Number of crystals [ 10 4 /ml]
94,03 112,1 106,6 93,14
1,79 2.73 3,78 2,51
Table 2b: 75% power input
Significant variation between duplicate experiments were found, which makes it difficult to draw conclusions from the results. Figures 13a (for 50% power input) and 13b (for 75% power input) show an increase of yield with insonation time, with one of the experiments for 50% power input at 33
Ultrasonic irradiation and its mixing and nucleation consequences
30 sec insonation time as an outlier. There was also an exception for 75% power input at 90 seconds. It was expected that increasing the insonation time would increase the yield, as more crystals are formed due to cavitations and supersaturation does not become a limiting factor.
50% power input Crystal production [gram]
140 120 100 80 60
50% power input
40 20 0 0
50
100
150
Insonation time [sec]
Figure 13a: The crystal production for different insonation times at 50% power input
75% power input Crystal production [gram]
35 30 25 20 15
75% power input
10 5 0 0
20
40
60
80
100
insonation time [sec]
Figure 13b: The crystal production for different insonation times at 75% power input
Figures 14a and 14b show the number of crystals increases with insonation time, with one of the experiments at 30 seconds insonation time for 50% power input as an outlier. Also the crystal numbers found for one of the experiments at 90 seconds insonation for 75% power inputs are 34
Ultrasonic irradiation and its mixing and nucleation consequences
lower than those found for 60 seconds insonation. As the temperature increases during insonation the supersaturation of the solution is decreasing, which leads to formation of less crystals.
Nnumber of crystals[10^4/ml]
50% power input 3,00E+01 2,50E+01 2,00E+01 1,50E+01 50% US
1,00E+01 5,00E+00 0,00E+00 0
20
40
60
80
100
120
140
Insonation time [sec]
Figure 14a: The number of crystals for different insonation times at 50% power input
Number of crystals[10^4/ml]
75% power input 4,00E+00 3,50E+00 3,00E+00 2,50E+00 2,00E+00 1,50E+00
75% US
1,00E+00 5,00E-01 0,00E+00 0
20
40
60
80
100
Insonation time[sec]
Figure 14b: The number of crystals for different insonation times at 75% power input
35
Ultrasonic irradiation and its mixing and nucleation consequences
5.3 PIV measurements The macro steaming was investigated for different power input using the PIV technique. Figures 15b,and 15c show the results of the velocity distribution as demonstrated by PIVlab program for 50 and 100% power input. Power input were from 50-100% in steps of 10. The acoustic streaming consists in a pattern of one contra-rotation vortex at 50% power input, and 4 vortices at 100% power input. This gives an understanding of the fluid turbulence.
Figure15a: Visualization of flow Pattern in the crystallizer and area used for PIV processing
Figure15b: PIV for 50% power input
Figure15c: PIV for 100% power input
36
Ultrasonic irradiation and its mixing and nucleation consequences
To get a sense of the velocity profile, Matlab was used to apply a colour field to visually assess different velocity’s (see Figure 16a,b,c,d,e and f).
Figure16a: PIV for 50% power input
Figure16c: PIV for 70% power input
Figure16e: PIV for 90% power input
Figure16b: PIV for 60% power input
Figure16d: PIV for 80% power input
Figure16f: PIV for 100% power input
37
Ultrasonic irradiation and its mixing and nucleation consequences
The average velocity was calculated by integration for the entire volume. First the resultant of the velocity at each point was calculated using the following formula:
V ( z , h ) = v x2 + v y2 , Then the average velocity was calculated: calculated
R ∫0 ∫0V (z , h ).2π r .dr dh V = π .r 2 .H H
Also the vorticity was calculated by taking the curl of the velocity field:
Table 3 shows the results for the average velocity and vorticity. Table 3: Results esults for the average velocity and vorticity
Power [%] 50 60 70 80 90 100
Average velocity [m/s] 0,03 0,038 0,04 0,044 0,05 0,058 0,06 0,067 0,06 0,069 0,07 0,073
average vorticity [1/sec] 6,01 7 7,06 7,13 7,81 9,58
The results of the PIV analysis indicated indicate that the average velocity and vorticity increase with increasing input power. Also It was found that the velocity decrease with axial and radial distance from the horn of the ultrasound but increase near the wall and the bottom of the vessel. vessel Vorticity is calculated to understand the turbulence of the solution. Turbulent flows have non-zero non vorticity and are characterized by a strong three-dimensional three dimensional vortex generation mechanism known as vortex stretching.
38
Ultrasonic irradiation and its mixing and nucleation consequences
5.4 PIT measurements Figure 19 shows the temperature field for 50% power input at 80 and 150 seconds, consequently. The mean temperature was determined at each time, at 80 seconds the mean temperature is equal to 23.6°C and at 150 seconds is equal to 24.25°C.
Figure 19: the temperature field for 50% power input at 80 seconds (left ) and 150 seconds (right)
The SS fields are shown in figure 20 below, for the same power input and at the same time during insonation ( 50% power input at 90 and 150 seconds).
Figure 20: the SS field for 50% power input at 80 seconds (left ) and 150 seconds (right)
The same thing was done for 60, 70, 80, 90 and 100% power input at different time of insonation. In figure 21 and 22 , the results of 100% is shown. The mean temperature was determined at each time, at 100 seconds the mean temperature is equal to 24.72°C and at 150 seconds is equal to 25.74°C.
39
Ultrasonic irradiation and its mixing and nucleation consequences
Figure 21: the temperature field for 100% power input at 100 seconds (left ) and 150 seconds (right)
Figure 22: the SS field for 100% power input at 100 seconds (left ) and 150 seconds (right)
It was found from the results that the temperature increase with increasing the power input and the insonating time at the same power. There was a distribution of the temperature at every time of insonation. The temperature was higher near and below the sonotrode than the temperature near the wall of the vessel. Which gave a higher supersaturation ratio near the wall than near and below the sonotrode. Which means that if crystals would formed ( At higher level of SS) , It would be formed first near the wall because of the higher SS. It was also found that the solution became more homogeneous at higher power input because of the better mixing due to the higher average velocity. Table 5 shows the time, the mean temperature difference and the temperature difference rate for each power input, which is used in section 7.1 to calculate the power output. As it was expected the temperature difference rate ( ∆T / ∆t ) increase with increasing the power input of the ultrasound which is proportional to the power output of the ultrasound.
40
Ultrasonic irradiation and its mixing and nucleation consequences
Table 5: The time and the mean temperature difference for each power input
Time difference
Mean temperature
Temperature difference
( ∆t )
Difference( ∆T )
rate ( ∆T / ∆t )
[sec]
[°C]
[°C/sec]
50
60
0,65
0,0108
60
70
0,90
0,0128
70
80
1.10
0,0138
80
90
1,51
0,0168
90
70
1,31
0,0187
100
50
1.02
0,0210
Power input [%]
5.4.1. Power output of the ultrasound The power output of the ultrasound device was calculated in two different ways. First method, a caloric measurements were performed. In these experiments 1200 ml of solution was insonated for the same time used in PIT analysis for each power input. From the temperature difference, the power dissipated in the liquid was calculated using equation below,
P=
mc p ∆T t
Second method, using the mean temperature difference obtained from the PIT analysis in the same equation to find out the power input and compare it with the first method. The power input used by the ultrasound processers was measured using a voltmeter ( van der Graaf, 2011 ) and used to calculate the efficiency of the processer, which is defined as power output divided by power by power input. Table 6 shows the power and efficiency obtained from both methods mention above. The results obtained by PIT is more accurate and reasonable because it deals with the average temperature over the hole volume of the solution. It was found that the power output of the ultrasound increase with increasing the power input. While there are exceptions in the results obtained by the PicoLog method, using the PT100 sensor to measure the temperature of the solution during insonating. One of the reasons, because the sensor measures the temperature at one point and not the average temperature over the hole volume as in the PIT method. Other reason is that the sensor did not placed under the sonotrode, and it was not fixed very well. Also during insonating, some hotspot could be formed which leads to less accuracy measuring by the sensor.
41
Ultrasonic irradiation and its mixing and nucleation consequences
Table6: results of power output using temperature difference from PicoLog and PIT analysis for each power input. Power input
Temperature increase/time using PicoLog
Temperature increase/time using PIT analysis
Power output using PicoLog
Power output using PIT analysis
Power input
efficiency using PIT analysis
efficiency using PicoLog
%
[⁰C/sec]
[W]
[W]
[W]
[-]
[-]
50
[⁰C/sec] 0,0125
0,0108
68,0
58,9
103
0,57
0,66
60
0,0142
0,0128
77,4
69,9
114
0,61
0,68
70
0,0130
0,0138
70,8
74,7
133
0,56
0,53
80
0,0144
0,0168
78,2
91,2
153
0,59
0,51
90
0,0157
0,0187
85,0
101,5
175
0,58
0,49
100
0,0147
0,0210
79,9
110,8
200
0,55
0,40
Because it is more usual to write the power in term of power intensity in kW / m 3 , table 7 is made which is useful for the dissection part.
Table7: Corresponding power intensity for power input and power output using picoLog and PIT method Power output
Power input intensity
Power output intensity using PicoLog
Power output intensity using PIT analysis
% 50 60 70 80 90 100
[ kW / m 3 ] 85,8 95,0 110,8 127,5 145,8 166,6
[ kW / m 3 ] 56,6 64,5 58,9 65,1 70,8 66,6
[ kW / m 3 ] 49,1 58,2 62,3 75,9 84,5 92,4
42
Ultrasonic irradiation and its mixing and nucleation consequences
Discussion and Conclusions In this report, the objective was to determine the macro streaming, 2D temperature field, 2D supersaturation field, the heat output and crystal nucleation induced by ultrasonic irradiation of a vessel containing solutions of supersaturation, at different power inputs and irradiation times.
Other reports have used different sonotrode types, vessel geometries, volumes and power densities. As stated before, the geometry of the sonotrode and the reactor have large influence on the amount of nuclei which are formed. Therefore, head-to-head comparisons with previous experiments should be interpreted with caution.
Regarding macro steaming the experiments showed that when increasing the power, the velocity and the vorticity increased subsequently. When vorticity increases, a turbulent flow, necessary for mass transfer for the crystallization process, is created. The results of these experiments indicate that the average streaming velocity was observed in the range of 0.0379 – 0.0735 m/s for power densities (P/V) from 49 to 91 kW / m 3 in a 1.2 liter solution using 20kHz ultrasound processor with probe diameter of 40 mm.
Kumar et al. (2006 ) observed average streaming velocity in the range of 0.05 – 0.15 m/s. They used an ultrasonic horn of 20 kHz with diameter of the ultrasound horn equal to 13 mm in 2 liter solution for three different power density 15, 25 and 35 kW / m 3 . Trujillo et al. (2011) have developed a CFD to predict the acoustic streaming induced by an ultrasonic horn reactor at 20kHz. In this research, 2 liter of solution for power density of 15, 25 and 35 kW / m 3 was used. The average velocity was in the range of 0.03 – 0.2 m/s. And these experiments seem to be in the same range with other researches like Kojima et al. (2010). Koijma et al investigated the pattern of liquid flow of a rectangular sonochemical reactor at 490 kHz, as a function of the input power between 10 and 50 W corresponding with a power density of
2.5 to 12.5 kW / m 3 , using 4 liter solution for each
experiment. The observed an average flow velocity in range of 0.008 and 0.014 m/s. The quality of the velocity patterns in the experiment of Koijma et al and the present paper were quite similar. Both patterns give higher velocity near and below the horn. It was also found that the velocity decreases with axial and radial distances from the horn of the ultrasound but increased near the wall and the bottom of the vessel. These is in line with the research conducted by Xu et al. (2012). They numerically simulated the liquid velocity distribution of ultrasonically induced flow in the sonochemical reactor containing 3 liter of solution with a transducer at a frequency of 490 kHz. Three different input power densities of 3, 10 and 16 kW / m 3 were used. The authors observed an average streaming velocity in the range of 0.004 – 0.01 m/s.
43
Ultrasonic irradiation and its mixing and nucleation consequences
The power output in these experiments was calculated by two different means; firstly by using PIT method and secondly by using PicoLog recorder to measure the temperature differences. As expected, the temperature difference rate ( ∆T / ∆t )
increased when increasing the power input of the
ultrasound, proportional to the power output of the ultrasound. The PIT method was used to determine 2D temperature profiles. From the 2D temperature measurement 2D supersaturation profiles were determined. The experiments showed that the temperature increases when increasing the power input and insonating time. There was a distribution of the temperature at every time of insonation. The temperature was higher near and below the sonotrode than the temperature near the wall of the vessel. This gave a higher supersaturation ratio near the wall compared to near and below the sonotrode. In the case that crystals had been formed at higher levels of SS, this would mean that the crystals would form near the wall first. It was also found that the solution became more homogeneous at higher power input because of better mixing due to higher average velocities. The results obtained by PIT is more accurate and reasonable because it deals with the average temperature over the whole volume of the solution. The power output of the ultrasound increased with increasing power input. This was not always the case when the PicoLog method with a PT100 sensor to measure the temperature of the solution during insonating, was used. This could be explained because the sensor measures the temperature at one certain point and not the average temperature over the whole volume as in the PIT method. Another explanatory factor is that the sensor was not placed under the sonotrode nor was it fixed very well. Also during insonating it is possible that hotspots had been formed leading to less accuracy of the sensor.
Crystal nucleation was performed at power inputs of 50% and 75% and insonation times from 30 to 120 seconds. The solution used in these experiments was lactose. In these experiments, the reproducibility of the nucleation production was not high, as reported previously by others (Verzijden, 2008 and van der Graaf, 2011). Moreover, these experiments showed that when power input increases, the amount of lactose crystals formed also increased. With higher power input and increased insonation time, both the number of the crystals as well as the mean diameters increased. However there were some exceptions. Above a certain level of insonation time (120 seconds for 50% power and 90 seconds for 75% power ) the volume based diameter did not correspondently grow. It can be postulated that, longer insonation times cause higher temperature and increase the cooling period needed before the temperature stabilizes at 22 °C. As a result the average temperature during the entire period between the start of insonation and filtration increases. The higher average temperature decreases supersaturation and has a negative effect on crystal growth and average particle size. The volume based diameter however increases slightly with insonation time. This suggests insonation increases the crystal growth constant enough to overcome the effect of the increased temperature. This finding has previously been reported (Jeroen) and should be subjected to further research. 44
Ultrasonic irradiation and its mixing and nucleation consequences
Other recommendations for further research include, the use of ammonium sulphate as a solution. More importantly, we did not assess what the effect is of ultrasound on the types of lactose. It can be postulated that the ratio of α and β lactose has influence on the nucleation. However, these test are timely and large financial investments (or sponsoring) are necessary due to high costs of these test.
45
Ultrasonic irradiation and its mixing and nucleation consequences
References HEAT AND MASS TRANSFER OPERATIONS - CRYSTALLIZATION J. Ulrich and M.J. Jones .TVT, Martin-Luther-Univ. Halle-Wittenberg, Germany Integration of membrane filtration and crystallization of L-phenylalanine S.N. Herreilers,June 2007 Seader J.D. and Henley E.J. “Separation process principles” John Wiley & Sons, USA, 1998, ISBN 0471-58626-9 Lakerveld, R. Development of a Task-Based Design Approach for Solution Crystallization Processes. PhD Thesis, Delft University of Technology, 2010. Lyczko, N., F. Espitalier, O. Louisnard, and J. Schwartzentruber. "Effect of ultrasound on the induction time and the metastable zone widths of potassium sulphate." Chemical Engineering Journal 86 (2002): 233–241. F.G. Blake, Tech. Memon. 12 (1949) 551. S. Hilgenfeldt, M. Brenner, S. Grossmann, D. Lohse, J. Fluid Mech. 365 (1998) 171. [4] T.J. Matula, Phil. Trans. Royal Soc. London, Series A 357 (1999) 225. [5] E.A. Neppiras, Phy. Rep. 61 (1980) 159. [6] C.E. Brennen, J. Fluid Mech. 472 (2002) 153. Bernstein J. “Polymorphism in molecular crystals” Oxford University Press, Oxford, 2002, ISBN: 019-850605-8 Richardson et al. “Coulson and Richardson’s Chemical Engineering Vol. 2. Particle Technology and Separation Processes” Butterworth-Heinemann, Oxford, 2002, ISBN 0-7506-4445-1 Kramer H.J.M. et al. “Basic process design for crystallization processes” TU Delft, SPDO course material, 2007 Mersmann, A. (2001) Crystallization TechnologyHandbook, 2nd edn, Marcel Dekker,New York. The Crystal Size Distribution Technique Dr. Joaqu´ın Cort´es. March 9, 2008 Cashman, K. and Ferry, J. (1988). Crystal size distribution (csd) in rocks and the kinetics and dynamics of crystallization iii.metamorphic crystallization. Contributions to Mineralogy and Petrology, 99(401-405). Marsh, B. (1988). Crystal size distribution (csd) in rocks and the kinetics and dynamics of crystallization i. theory.Contributions to Mineralogy and Petrology, 99, 277–291. Kumar, A., T. Kumaresan, A.B. Pandit, and J.B. Josh. "Characterization of flowphenomena induced by ultrasonic horn." Chemical Engineering Science, no. 61 (2006): 7410 – 7420. Leighton, T.G. The Acoustic Bubble. London: Harcourt Brace & Company Publishers, 1994. Particle Image Velocimetry and Thermometry using Liquid Crystal Tracers. Tomasz A. Kowalewski. 4th International Symposium on Particle Image Velocimetry Göttingen, Germany, September 17-19, 2001
46
Ultrasonic irradiation and its mixing and nucleation consequences
Hiller W; Kowalewski TA. (1987) Simultaneous measurement of the temperature and velocity fields in thermalconvective flows, in Flow Visualization IV, Ed. Claude Veret, Hemisphere, Paris, pp. 617622. Kowalewski, T.A., Application of liquid crystal tracers for full field temperature and velocity measurements, Proceedings of the 2001 International Symposium on Env. Hydraulics, 2001. Park, H.G., Dabiri, D. & Gharib, M., Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder, Experiments in Fluids 30, 2001,327-338. Stasiek, J.A. & Kowalewski, T.A., TLCs applied for heat transfer research, Opto-Electronics Review 10, 2002, 1-10. Lactose ,Some basic properties and characteristics http://www.dfamilk.com/search/node/Lactose
Quantitative X-ray diffraction determination of alpha-lactose monohydrate and beta-lactose in chocolate. Thomas NR, Shumway LS, Hansen LD. Platteau, C., J. Lefebvre, F. Affouard, and P. Derollez. "Ab initio structure determination of the hygroscopic anhydrous form of [alpha]-lactose by powder X-ray diffraction." Acta Crystallographica Section B 60, no. 4 (2004): 453-460. Daudey, P. Crystallization of ammonium sulphate. PhD Thesis, Delft University of Technology, 1987. Westhoff, G.M. Design and analysis of suspension crystallizers: aspects of crystallisation kinetics and product quality. PhD Thesis, Delft University of Technology, 2002. C. Brossard, J.-C. Monnier, P. Barricau, F.-X. Vandernoot, Y. Le Sant, F. Champagnat, G. Le Besnerais. Principles and Applications of Particle Image Velocimetry ,Issue 1 - December 2009 .
R. J. Adrian. Twenty years of particle image velocimetry , October 2004
D. Schmeling , J. Bosbach and C. Wagner .Combined Particle Image Thermography (PIT) and Velocimetry (PIV) in Mixed Convective Air Flows. T.P. Bednarz, C. Lei and J.C. Patterson. Particle Image Thermometry for Natural Convection Flows, December 2007. Hielscher - Ultrasound Technology http://www.hielscher.com/ultrasonics/cavitat.htm
Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry, a practical guide. Springer, Berlin Heidelberg New York.
William Thielicke and Eize J. Stamhuis (2005) PIVlab - TIME-RESOLVED DIGITAL PARTICLE IMAGE VELOCIMETRY TOOL FOR MATLAB
47
Ultrasonic irradiation and its mixing and nucleation consequences
MATLAB function and files: Velocity profile field function hh = quiverc(varargin) % Modified version of Quiver to plots velocity vectors as arrows % with components (u,v) at the points (x,y) using the current colormap set(gca, 'color', 'blue'); % Arrow head parameters alpha = 0.33; % Size of arrow head relative to the length of the vector beta = 0.23; % Width of the base of the arrow head relative to the length autoscale = 1; % Autoscale if ~= 0 then scale by this. plotarrows = 1; % Plot arrows sym = ''; filled = 0; ls = '-'; ms = ''; col = ''; lw=1; nin = nargin; % Parse the string inputs while isstr(varargin{nin}), vv = varargin{nin}; if ~isempty(vv) & strcmp(lower(vv(1)),'f') filled = 1; nin = nin-1; else [l,c,m,msg] = colstyle(vv); if ~isempty(msg), error(sprintf('Unknown option "%s".',vv)); end if ~isempty(l), ls = l; end if ~isempty(c), col = c; end if ~isempty(m), ms = m; plotarrows = 0; end if isequal(m,'.'), ms = ''; end % Don't plot '.' nin = nin-1; end end
error(nargchk(2,5,nin)); % Check numeric input arguments if nin<4, % quiver(u,v) or quiver(u,v,s) [msg,x,y,u,v] = xyzchk(varargin{1:2}); else [msg,x,y,u,v] = xyzchk(varargin{1:4}); end if ~isempty(msg), error(msg); end if nin==3 | nin==5, % quiver(u,v,s) or quiver(x,y,u,v,s) autoscale = varargin{nin}; end % Scalar expand u,v if prod(size(u))==1, u = u(ones(size(x))); end if prod(size(v))==1, v = v(ones(size(u))); end if autoscale, % Base autoscale value on average spacing in the x and y % directions. Estimate number of points in each direction as % either the size of the input arrays or the effective square % spacing if x and y are vectors. if min(size(x))==1, n=sqrt(prod(size(x))); m=n; else [m,n]=size(x); end delx = diff([min(x(:)) max(x(:))])/n; dely = diff([min(y(:)) max(y(:))])/m; len = sqrt((u.^2 + v.^2)/(delx.^2 + dely.^2)); autoscale = autoscale*0.9 / max(len(:)); u = u*autoscale; v = v*autoscale; end % Define colormap vr=sqrt(u.^2+v.^2);
48
Ultrasonic irradiation and its mixing and nucleation consequences
vrn=round(vr/max(vr(:))*64); CC=colormap; ax = newplot; next = lower(get(ax,'NextPlot')); hold_state = ishold; %---------------------------------------------% Make velocity vectors and plot them x = x(:).';y = y(:).'; u = u(:).';v = v(:).'; vrn=vrn(:).'; uu = [x;x+u;repmat(NaN,size(u))]; vv = [y;y+v;repmat(NaN,size(u))]; vrn1= [vrn;repmat(NaN,size(u));repmat(NaN,size(u))]; uui=uu(:); hold on
vvi=vv(:);
vrn1=vrn1(:); imax=size(uui);
for i= 1:3:imax-1 ii=int8(round(vrn1(i))); if ii==0; ii=1; end c1= CC(ii,1); c2= CC(ii,2); c3= CC(ii,3); plot(uui(i:i+1),vvi(i:i+1),'linewidth',lw,'color',[c1 c2 c3]); end %---------------------------------------------% Make arrow heads and plot them if plotarrows, hu = [x+u-alpha*(u+beta*(v+eps));x+u; ... x+u-alpha*(u-beta*(v+eps));repmat(NaN,size(u))]; hv = [y+v-alpha*(v-beta*(u+eps));y+v; ... y+v-alpha*(v+beta*(u+eps));repmat(NaN,size(v))]; vrn2= [vrn;vrn;vrn;vrn]; uui=hu(:);
vvi=hv(:);
vrn2=vrn2(:); imax=size(uui);
for i= 1:imax-1 ii=int8(round(vrn2(i))); if ii==0; ii=1; end c1= CC(ii,1); c2= CC(ii,2); c3= CC(ii,3); plot(uui(i:i+1),vvi(i:i+1),'linewidth',lw,'color',[c1 c2 c3]); end else h2 = []; end %---------------------------------------------if ~isempty(ms), % Plot marker on base hu = x; hv = y; hold on h3 = plot(hu(:),hv(:),[col ms]); if filled, set(h3,'markerfacecolor',get(h1,'color')); end else h3 = []; end if ~hold_state, hold off, view(2); set(ax,'NextPlot',next); end if nargout>0, hh = [h1;h2;h3]; end % set(gca, 'color', [0 0 0],'Xcolor','w','Ycolor','w'); % set(gcf, 'color', [0 0 0]); %set(gcf, 'InvertHardCopy', 'off');
49
Ultrasonic irradiation and its mixing and nucleation consequences
velocity_profile_mean2 clear all clc %close all tic format long e X Y U V
= = = =
xlsread('PIVlab_mean400f','PIVlab_mean400f','A4:A15388'); xlsread('PIVlab_mean400f','PIVlab_mean400f','B4:B15388'); xlsread('PIVlab_mean400f','PIVlab_mean400f','C4:C15388'); xlsread('PIVlab_mean400f','PIVlab_mean400f','D4:D15388');
minU = min(U) maxV = max(V) d=length(X) a= min(X); for i=1:d Y(i)=max(Y)-Y(i); X(i)=X(i)-a; V(i)=-V(i); end i=1;j=1; while i<=d Yy(j)=Y(i); Xx(j)=X(i); Vv(j)=V(i); Uu(j)=U(i); j=j+1; i=i+4; end j=1;i=1; checkX=Xx(1); while i<=length(Xx) if Xx(i)==checkX checkY=Yy(i); j=j+1; Yyy(j)=Yy(i); Xxx(j)=Xx(i); Vvv(j)=Vv(i); Uuu(j)=Uu(i); i=i+1; elseif Yy(i)~=checkY % ~= means not= i=i+1; elseif Yy(i)==checkY && imaxhue)=0; foto2hue(foto2hue
