Secondary Nucleation Studies on Lactose: A Mechanistic Understanding 1

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Shailesh G Agrawal , Jeremy Mcleod , A.H.J.(Tony) Paterson , Jim R. Jones

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School of Engineering and Advanced Technology, Massey University, Private Bag 11 222, Palmerston North, New Zealand [email protected] 2 Hilmar Cheese Company, Hilmar, California, USA

Abstract Secondary nucleation is a general term describing generation of new nuclei due to the presence of solute crystals and is the dominant mechanism of nucleation in many commercial crystallizers. Most of the studies on this phenomenon have produced empirical relationships unique to the system investigated. This study takes a mechanistic approach to try to elucidate the fundamental processes behind secondary nucleation. Secondary nucleation of lactose was studied under stirred conditions. The variables investigated were: stirrer speed (400 and 550 rpm), seed loading (2, 5 and 10% w/w), absolute alpha-lactose supersaturation (6.7, 8.4 and 10.7 gm of α-lactose/100 gm of water) and seed size (106-212, 212-300, 300-425 and 425-600 micron). All experiments were conducted at 30oC. A Malvern Mastersizer was used to quantify the nucleation rate. Blank runs were conducted to quantify the contribution of primary nucleation (absence of seed crystals) and attrition (absence of supersaturation). The results showed that for the conditions studied, the impeller-crystal contacts were the dominant contributor to secondary nucleation. It was found that, at a given constant supersaturation, the nucleation rate normalized by contact frequency is only a function of the kinetic energy of collision. These findings provide a mechanistic understanding of secondary nucleation that can be used to scale-up from bench to industrial scale processes and optimise crystalliser performance. Introduction Industrial crystallizers are often operated with high crystal slurry concentrations at low supersaturations, which create an environment conducive to secondary nucleation. Despite these conditions promoting secondary nucleation and therefore playing an important role in the crystallization process, the reasons why are unclear. Intuitively, slurries of crystals will require agitation to keep them suspended, which will generate crystal-crystal and crystal-impeller contacts. These contacts are most likely to influence the extent of secondary nucleation. Secondary nucleation is most commonly expressed as an empirical function of agitation level, suspension density and supersaturation as (Myerson and Ginde, 2001): Where, Ni is the impeller speed [rps or rpm], MT is the suspension density [kg of crystal per kg of suspension or kg of crystal per m3 of suspension], is the supersaturation. j, k, and b are empirical constants. These models are very system specific and difficult to transfer beyond the unique environment in which they were developed. This study examines nucleation operating parameters on a fundamental level meaning the results are independent of the scale and design of the process.

Theory Secondary nucleation occurs by various mechanisms like crystal fracture, attrition, shear and contact nucleation. Fracture is likely to happen in high crystal density systems that produce brittle crystals and involve violent mixing/pumping. Secondary nucleation by shear generally requires high levels of supersaturation and shear levels that normally do not exist in industrial crystallizers. The production of nuclei from the displacement of the ordered solute cluster layer present at the solution-crystal interface by contact, termed as contact nucleation is the most important source of nuclei in mixed suspension (Randolph and Larson, 1988). The present study focuses on such contact secondary nucleation. It is possible that some degree of micro-attrition takes place from the crystal surface during the contacts but such a phenomenon will be very difficult to distinguish from pure contact nucleation and hence is considered as a part of contact nucleation in the present study. Contact nucleation involves contact of the crystal with solid surfaces such as baffles, impeller blades and walls as well as other crystals. (Ottens and de Jong, 1973) took a mechanistic approach to quantify secondary nucleation in stirred systems. The expression for contact nucleation (modified to the units used in this work) put forward by them is as follow: [2] Where is the nucleation rate [#min-1kg-1] is the empirical nucleation constant [J-1 (g of solute 100 g-1 of the solvent)-b] , the kinetic energy of contact [J] is the contact frequency per unit mass of slurry [#min-1kg-1] is the absolute supersaturation [g of solute 100 g-1 of the solvent] and b is an empirical constant The two dominant forms of contact occurring in suspended slurries are either crystalcrystal or crystal-impeller impacts. Hence, in order to evaluate ; and must be known for each of these two forms of contact. Crystal-Impeller Contacts The kinetic energy for crystal-impeller contact is defined by equation 3, where m is the crystal mass and is impact velocity. The impact velocity can be substituted by the impeller tip speed given by equation 4 (Cherry and Papoutsakis, 1986; Ottens and de Jong, 1973).

where, is the impeller speed [min-1], Di is the impeller diameter [m]. The mass, m of a single crystal is defined as:

where, dc is the geometric mean crystal diameter [m] and [kgm-3].

is the crystal density

The frequency of crystal-impeller contacts per unit mass of slurry can be calculated by:

Where is the crystal number concentration per kg of slurry [# kg-1], is the volumetric pumping rate of the impeller [m3s-1], K is the discharge coefficient of the impeller, is the crystallizer volume [m3], is the collision probability [per pass through the swept volume of the impeller]. The first term in equation (6) represents the circulation time [min-1] and physically signifies the number of passes a fluid element makes through the impeller zone. The second term gives the number of particles that are present in the fluid element. However, not all the particles entering the impeller zone will collide with the impeller. The third term measures the collision probability of the crystals with the impeller and is a function of Stokes number. The collision probability can be estimated as follows (Gahn and Mersmann, 1999):

where, ψ is the Stokes number defined by:

T is the target length [m] and is taken as the width of the edge of impeller blade for the present study, µ s is the slurry viscosity [kgm-1s-1], ( ρ c − ρ s ) is the density difference between the crystal and the slurry [kgm-3] and vrel is the relative velocity between the crystal and the impeller [ms-1] and is taken as the impeller tip speed, as the tip speed (the tangential component) is expected to be much larger than the fluid axial velocity for two bladed impeller. The collision probabilities were calculated for the mean values of the experimental conditions used in this study and are given in table 1. Combining the equations (3), (4), (5), (6) and substituting in equation 2 gives the contact secondary nucleation due to impeller-crystal contact as:

Crystal-Crystal Contacts For crystal-crystal contact, the impact velocity in equation (3) is the root mean square velocity between the contacting particles (vc-c ). Cherry and Papoutsakis, (1986) suggested that when the size of smallest eddy is comparable or smaller than either the particle size or the average inter- particle distance, the root mean square velocity is of the same order of eddy velocity. From Kolmogrov theory, the velocity (ve) and size of smallest eddy (Le) is given by:

Where, ε is the energy dissipation rate per unit mass of slurry [m2s-3] is the kinematic viscosity of the slurry [m2s-1]. The energy dissipation rate is estimated by:

is the power number and is a function Reynolds number. Reynolds number for an agitated system is given by:

The value of power number was estimated from Nagata, (1975) cited in Cherry and Papoutsakis, (1986) for a two bladed impeller. The crystal-crystal collision frequency per unit mass is of the order (Cherry and Papoutsakis, 1986) :

Where,

is the volume of crystals per unit is mass of slurry [m-3kg-1] given by:

Substituting the expression for

in equation 4 gives:

Combining equations (2), (3), (4), (5), (10) and (16) contact secondary nucleation due to crystal-crystal contacts is given by:

Experimental Apparatus: Secondary nucleation runs were carried out in 1 litre glass vessels (11.5 cm diameter) baffled (width 8% of the beaker diameter) at 180o and covered with lids to reduce evaporation and to prevent dust particles from entering. The crystal slurries were stirred using a two bladed (45o blade angle), 5 cm diameter and 1 mm thick impeller. A Phipps and Bird Model 7790-402 four shaft stirrer (Phipps and Bird, Richmond, Virginia, USA) enabled four simultaneous runs to be made. The vessels were submerged in a 30oC water bath. Parameters studied: Four parameters were studied: Seed crystal size (106-212, 212300, 300-425 and 425-600 microns), impeller speed (400 and 550 rpm), absolute supersaturation (6.7, 8.4 and 10.7 g of alpha lactose monohydrate (α-LMH) per 100 g of water), and seed loading (2, 5 and 10 % w/w). The combination of four particle sizes and two impeller speeds provided eight levels of kinetic energy, and four particles sizes and three seed loadings (by mass) gave twelve levels of seed loading (by number), as is shown in Table 1. Procedure: The seed crystals were pre-treated to prevent initial breeding caused by the fines adhering to their surface. The crystals were washed with cold RO water for 5-10 seconds with manual shaking to ensure all seeds were in suspension and had been exposed to the wash water. The water was immediately drained off and the seeds rinsed with the same supersaturated lactose solution which was used for the experimental runs. The rinsing continued till the rinsed solution was devoid of any fines. It typically took 4-5 rinsing steps to achieve this. Figure 1 depicts the importance of seed pre-treatment. The treated crystals were added to the beakers containing supersaturated lactose solution held at 30oC in a water bath. The mass of solution and seed crystals were measured to give the desired seed loading and to obtain a total slurry mass of 300 grams. The beakers were then moved to the constant temperature water bath with the multiple impellers and stirring started. Stirring speed was set fast enough to fully suspend the seed crystals.

Table 1: Values of different parameters for impeller-crystal contact induced secondary nucleation Average seed crystal size: log mean of the sieve sizes (microns)

Number concentration of seed crystals for various seed loading weight percents (# per kg of slurry)

2%

5%

10%

150

7.31E+06

1.83E+07

3.65E+07

252

1.54E+06

3.85E+06

7.70E+06

357

5.42E+05

1.35E+06

2.71E+06

505

1.91E+05

4.79E+05

9.57E+05

Kinetic energy of contact (J) & Particle size/ impeller speed combination number (#)

400 rpm

550 rpm

1.50E-09 (#1) 7.11E-09 (#3) 2.02E-08 (#5) 5.72E-08 (#7)

2.84E-09 (#2) 1.34E-08 (#4) 3.82E-08 (#6) 1.08E-07 (#8)

Collision probability

0.5 0.66 0.8 0.9

Figure 1: Importance of seed pretreatment for fines. The beaker on the left contained untreated settled seed crystals and would have led to an over-estimation of secondary nucleation, while that on the right is the washed seeds. A handheld digital refractometer was used to measure the dissolved lactose concentration before and after the runs. Due to the nucleation and growth of the crystals the dissolved lactose concentration dropped over the course of each experiment. The drop in absolute supersaturation was low (6-13% of the initial value) and hence the runs were considered to be carried out at almost constant supersaturation. The limitation of trying to operate with constant supersaturation meant that runs with higher seed loading needed to be carried out for shorter times. The time of each run is shown in Table 2. Laser diffraction (Malvern Mastersizer Hydro 2000S) was used to quantify the nucleation rate (Kauter, 2003; Tait et al., 2009). As the Malvern measures the volumeweighted size distribution it was critical to eliminate the larger seed crystals to correctly enumerate the nuclei formed. To do this, at the end of each run the slurry was filtered through a 36 micron sieve to remove the seeds and allow the nuclei to pass through. A known volume of filtrate, containing only the secondary nuclei, was introduced in the Malvern cell containing a known volume of dispersing liquid. Slightly supersaturated lactose solution (1.2g α-LMH per 100 g of water) at the Malvern cell temperature of 2526o C was used as the dispersing liquid. The total number of nuclei per ml was calculated from the particle size distribution (PSD) and the volume concentration (% v/v) readings reported by the Malvern. Four replicates of each condition were performed and the average values along with the standard deviation are reported.

To quantify the contribution of primary nucleation, runs in the absence of any crystals were conducted at all supersaturations. Runs were also performed with seed crystals in slightly supersaturated solutions (0.21 gm α-LMH per 100 gm of water) to assess the contribution of pure macro-attrition to the overall secondary nucleation. Table 2: Run time (t) for different trials conducted for each experiment with two impeller speeds of 400 and 550 rpm, and four particle sizes of 106-212, 212-300, 300-425 and 425-600 microns Supersaturation Seed loading(% w/w) (g α-LMH/100 g water) 2 5 10 6.7 60 min 8.4 60 min 45 min 30 min 10.7 60 min Results and Discussions The blank runs conducted to quantify macro-attrition and primary nucleation did not show any measurable crystals thus ruling out any independent contribution from these sources to secondary nucleation. Table 3 gives the hydrodynamic parameters of the stirred system. The density and viscosity of lactose solution at the average concentration of the experimental conditions was determined from the data by Buma, (1980) and that of slurry at various seed loading levels by correlations from Abulnaga, (2002). The smallest eddy size is smaller than the mean particle seed crystal size at both the impeller speeds. Hence the impact velocities of the particles can be replaced by the eddy velocity. The kinetic energy values for crystal-impeller contacts, as in Table 1, are roughly four orders of magnitude higher than that for crystal-crystal contacts shown in Table 3. Table 3: Values of different parameters for crystal-crystal contact Parameter Re Np ε [m2s-3] Le[µm] [ms-1] EKE [J]

Seed size [µm] 150 252 357 505

400 rpm 550 rpm 1.34E+04 1.84E+04 0.4

0.4

0.14 61 0.020

0.36 48 0.026

5.72E-13 2.71E-12 7.71E-12 2.18E-11

9.22E-13 4.37E-12 1.24E-11 3.52E-11

A linear relationship between the crystal number concentration and the nucleation rate for a combination of two impeller speeds and four particle sizes when supersaturation is held constant at 8.4g α-LMH/100 g water is obtained, as shown in Figure 2. Best fit lines are used to guide the eye. A linear fit with the particle number concentration as per equation (9) and orders of magnitude higher impact energy, shows that impeller-crystal contacts dominate the contact secondary nucleation in the present study. Crystal-crystal contacts, even though occurring higher in number (increases with particle number concentration squared, equation (17)) do not seem to possess sufficient kinetic energy to dislodge the solute clusters from the crystal solution interface to generate secondary

nuclei. Therefore, kinetic energy seems to be the single most important parameter governing contact secondary nucleation.

Figure 2: Effect of seed loading on secondary nucleation rate at constant supersaturation (8.4g α-LMH/100 g water). Standard deviation error bars for 4 replicates are shown The other salient features of Figure 2 are: i) high scatter in experimental data which is typical of nucleation studies. ii) Nucleation rate increases with an increase in particle size. iii) Nucleation rate is greater at 550 rpm stirrer speed than at 400 rpm. iv) Points (ii) and (iii) can be combined to restate that the nucleation rate increases with an increase in the kinetic energy (a combination of impeller speed and the crystal size, equations (3),(4) & (5)). At constant kinetic energy, nucleation rate increases with an increase in the number concentration of seed crystals. v) The slope of the fitted lines depends on the kinetic energy, contact frequency and the collision probability as per equation (9). As discussed in previously, kinetic energy is the most important parameter controlling secondary nucleation Hence, the slope of the lines is largely determined by the kinetic energy. It can be stated that the slope of the lines decreases with decrease in kinetic energy. vi) The y intercept value of the lines (when the number concentration of seed crystals is zero) can be regarded as the contribution of primary nucleation to secondary nucleation. The primary nucleation rate values [#kg-1min-1] vary in the narrow range of 1.4×107 to 6.1×107 for 400 rpm and 4.15×107 to 1.6×108 for 550 rpm.

vii) The lowest kinetic energy run (150 micron/400 rpm) had the least slope and the lowest nucleation rates in spite having the highest crystal number concentration. Any further reduction in kinetic energy will lead to a horizontal line with y = primary nucleation rate, with no affect of the presence of seed crystals. The kinetic energy at 150 micron/400 rpm, 1.50E-09 J can be regarded as the threshold energy below which no contact secondary nucleation is expected to occur at the studied supersaturation. In order to better understand the secondary nucleation mechanism the nucleation rate was normalized by the contact frequency per unit mass and plotted against the kinetic energy of contacts as shown in Figure 3. K, Di and Vc were considered constants for the system studied and thus the contact frequency per unit mass was be approximated by:

Figure 3: Effect of seed loading on secondary nucleation from kinetic energy and contact frequency perspective at constant supersaturation (8.4 g α-LMH/100 g water) When this approach is taken all the lines presented in Figure 2 collapse into a single curve. In Figure 2 it is difficult to quantify the effect of each parameter on secondary nucleation. Figure 3 presents a single curve for the empirical parameters of suspension density, impeller speed and particle size and shows that secondary nucleation depends on the fundamental parameters of kinetic energy and collision frequency. A curve fitted through the combined data gives a power law exponent 1.19 (± 0.03 at 95% confidence interval (C.I.)) for kinetic energy. This is close to the value of 1 reported by Kubota and Kubota, (1982) and Clontz and McCabe, (1971). The slope of the lines in Figure 2 at constant supersaturation of 8.4 g/100 g of water is given by

. By taking the ratio of the slopes between lines

in Figure 2, the known and unknown constant parameters like K, k, Vc, Di are removed. At constant supersaturation, the ratio of the slopes is given by:

The ratio of the experimental slopes matched, within ±33%, with that of the model prediction for all but one of the ratio combinations as shown in Table 4. Table 4: Comparison of ratio of experimental and theoretically predicted slopes for secondary nucleation Particle size /impeller speed combination ratio #8/#4 #7/#3 #6/#2 #8/#7 #7/#6 #8/#2 #3/#2 #8/#5 #5/#4 #7/#5 #4/#3

Experimental ratio of the slopes (Figure 3)

Ratio of the slopes of the model equation

10.9 20.9 38 2.8 1.5 155.7 2.7 8 1.4 2.92 5.3

16.3 16.3 32 2.9 1.3 136.6 2.2 11.3 1.4 3.92 2.9

% difference

33.1 -28.2 -19 3.5 -15.3 -15.4 -22.7 29.2 0 25.5 -82.7

A similar process of normalization of secondary nucleation rate and plotting against kinetic energy was repeated for data at supersaturations of 10.7 as shown in Figure 4. The exponential dependence of kinetic energy was 1.14 (±0.056 95% C.I.) which is again close to the literature value of 1. Further investigation at more supersaturations is needed to comment conclusively on the dependence of the kinetic energy exponent on supersaturation.

Figure 4: Secondary nucleation at constant seed loading of 2% (w/w) at 10.7 from a kinetic energy and frequency of contacts perspective. Standard deviation error bars based on 4 replicates are shown. The 8 kinetic energies of correspond to the same combinations of impeller speed and crystal size as shown in Figure 2

Conclusion This study presents secondary nucleation studies on lactose carried out under stirred conditions. The variables investigated were seed loading, seed size, supersaturation and stirrer speed. Secondary nucleation was shown to be dominated by the crystal-impeller contact nucleation. It was found that for the studied supersaturation there exists a minimum kinetic energy below which secondary nucleation is not expected to occur. This has important ramifications in determining which size crystals, at the given impact energies and supersaturation, will participate in secondary nucleation. When the nucleation rate was normalized by the contact frequency per unit mass and plotted against the kinetic energy of the contacts, a single curve for the given supersaturation was obtained for all seed loadings, impeller speeds and seed size. The relationship between the kinetic energy and normalized nucleation rate is independent of the mechanism of contacts or scale of operation. This gives a better tool for predicting and controlling secondary nucleation phenomenon in industrial crystallizers. References 1)Abulnaga, B. E., 2002, Slurry Systems Handbook. (McGraw-Hill). 2)Buma, T. J., 1980, Viscosity and density of concentrated lactose solutions and of concentrated cheese whey. Netherland Milk and Dairy Journal, 34, 65-68. 3)Cherry, R. S. & Papoutsakis, E. T., 1986, Hydrodynamic effects on cells in agitated tissue culture reactors. Bioprocess Biosystems Eng, 1, 29-41. 4)Clontz, N. A. & Mccabe, W. L., 1971, Contact Nucleation Of Magnesium Sulphate Heptahydrate. Chemical Engineering Symposium Series No 110, 67, 6-17. 5)Gahn, C. & Mersmann, A., 1999, Brittle fracture in crystallization processes Part B. Growth of fragments and scale-up of suspension crystallizers. Chem Eng Sci, 54, 12831292. 6)Kauter, M. D., 2003, The Effect of Impurities on Lactose Crystallization. (University of Queensland, St. Lucia). 7)Kubota, N. & Kubota, K., 1982, Contact nucleation of MgSO4 · 7 H2O at low impact energy levels. J Cryst Growth, 57, 211-215. 8)Myerson, A. S. & Ginde, R., 2001, Crystals, Crystal Growth, and Nucleation, in: Myerson, A. S. (Ed.) Handbook of Industrial Crystallization. Second ed. (ButterworthHeinemann), p. 47. 9)Nagata, S., 1975, Mixing - pinciples and applications, New York, (Halsted Press, New York). 10)Ottens, E. P. K. & De Jong, E. J., 1973, A Model for Secondary Nucleation in a Stirred Vessel Cooling Crystallizer. Industrial & Engineering Chemistry Fundamentals, 12, 179-184. 11)Randolph, A. D. & Larson, M. A., 1988, Theory of Particulate Processes. Second ed. (Academic Press, San Diego), p. 123. 12)Tait, S., White, E. T. & Litster, J. D., 2009, A Study on Nucleation for Protein Crystallization in Mixed Vessels. Crystal Growth & Design, 9, 2198-2206.