Article pubs.acs.org/crystal
Mechanisms Influencing Crystal Breakage Experiments in Stirred Vessels Sheena M. Reeves†,‡ and Priscilla J. Hill*,† †
Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi State, Mississippi 39762, United States Chemical Engineering Department, Prairie View A & M University, Prairie View, Texas 77446, United States
‡
ABSTRACT: Crystal breakage experiments in saturated solutions and nonsolvents often fail to accurately represent breakage in a suspension crystallizer because the saturated solution experiments have other mechanisms occurring, and the nonsolvent experiments have different particle dynamics and hydrodynamics. This research investigates NaCl crystal breakage in an aqueous saturated solution and in the nonsolvent acetonitrile at different magma densities and agitation rates to determine the significance of these effects. It is concluded that due to significant agglomeration in a saturated solution a nonsolvent should be used. The approach of performing experiments with both suspension fluids at the same magma density, and using the Zwietering correlation to adjust the agitation rate of the nonsolvent experiment for comparison with the saturated solution is shown to decrease the differences between the resulting crystal size distributions compared to operating both systems at the same agitation rate.
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significant effect on flowability because it produces more rounded particles that improve flowability, but it also produces fine particles that reduce flowability.6 Despite its importance, breakage in crystallizers is not as well studied as crystal growth and nucleation. One difficulty with studying breakage is isolating the mechanism so that growth, dissolution, nucleation, or agglomeration does not occur simultaneously. There are two approaches to isolating this mechanism. One approach is to suspend the crystals in nonsolvents so that there will not be any subsaturation or supersaturation, and therefore no driving force for other mechanisms to occur. The second approach is to use a saturated solution. The theory is that if the solution is at saturation then there is not a driving force for the other mechanisms. However, it is well-known that aging can occur in near saturated solutions. The difficulty with using nonsolvents is that they rarely have the same viscosity and density as the desired saturated solution, and therefore, they are not hydrodynamically similar to the saturated solution system. Previous research on particle breakage in a stirred vessel investigated the effect of particle concentration on the particle size distribution (PSD) at high solids concentrations13,14 and in dilute suspensions.15 Mazzarotta16 suggested a technique for estimating the product size distribution in agitated crystal suspensions, but she did not look at product shape. Later research on sugar crystal attrition showed that parent crystals became more rounded as residence time was increased.8
INTRODUCTION Particle breakage is important in the process industries because it alters the particle size and shape distributions. Both product quality and process operability strongly depend on particle size and shape. For example, paint opacity1 and gloss1,2 are largely influenced by the pigment particle size, and the properties of the kaolin used in coating paper are strongly affected by the size and shape distributions.3 A review of particle size effects on pharmaceuticals4 indicates that both size and shape distributions influence the dissolution rates and release rates of the drugs, as well as the grittiness of chewable tablets. Particle size and morphology strongly affect the flowability of particulates whether these are food particles,5 pharmaceuticals,4 or crystals in general.6 Since fragmentation and attrition change the size and shape of solid particles, they can have a significant effect of manufacturing processes. Attrition refers to the case where small fragments are chipped off parent crystals, resulting in a bimodal size distribution of larger particles that are approximately the same size as the parent particles and a large number of fines. Fragmentation refers to the case where many of the child particles produced are approximately the same order of magnitude in size as the parent particles. A key unit operation that is often present in solids processing is crystallization. This operation includes several mechanisms that affect the crystal size and shape distributions: nucleation, growth, dissolution, agglomeration, and breakage. While breakage is often assumed to be negligible, it can be significant. Attrition influences crystallizer operations because it produces fine particles that function as secondary nuclei and change the entire crystal size and shape distribution.7−11 An additional influence on the size/shape distribution is the growth rate dispersion of the attrition child crystals.12 Attrition has a © 2012 American Chemical Society
Received: July 14, 2011 Revised: April 19, 2012 Published: April 23, 2012 2748
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Table 1. Operating Conditions for Selected Crystal Breakage Experiments in Saturated Solutions (SS) and Nonsolvents (NS) crystal (crystal system) 13
22
nickel ammonium sulfate (monoclinic ) sodium chloride17 (cubic22) potassium sulfate7 (orthorhombic22) potassium sulfate16 (orthorhombic22) potassium sulfate19 (orthorhombic22) sucrose8 (monoclinic22) citric acid18 (monoclinic) pentaerythritol18 (tetragonal) potassium chloride18 (cubic) potassium sulfate18 (orthorhombic) sodium chloride18 (cubic) sodium perborate18 (dendritic) sodium sulfate18 (monoclinic) sucrose18 (monoclinic) a
size range, μm
fluid
agitation rate, rpm
magma density, kg/m3
time
1200−1800 300−400 600−1000 500−600, 1000−1180 1000−1180 1180−1400 500−600 500−600 250−300 355−425 355−425 425−500 710−850 355−425
SS, NS NS, SS NS SS SS NS NS NS NS NS NS NS NS
500−900 0−1600 0−2000 950, 1100 650 1100 700a 600a 800a 1000a 900a 800a 700a 700a
88.5−265.5 0−510 363 13.33−30.00 5−60 100 100 100 100 100 100 100 100 100
0−24 h 5s 0−60 min 0.5−10 h 2h 0−8 h 1h 1h 1h 1h 1h 1h 1h 1h
Agitation rates in this study are adjusted for off bottom clearance for each crystalline material.
that breakage experiments in saturated solutions could show the combined effects of Ostwald ripening and breakage. Previous work with benzoic acid formed by reaction crystallization investigated aging effects on the crystals.26 In this study it was observed that as the crystals aged for 145 min, the number density of 3 μm particles decreased by approximately 2 orders of magnitude, while the number density of 10 μm particles increase by over an order of magnitude. This is consistent with Ostwald ripening. However, a simple Ostwald ripening model did not fully explain the experimental results. During aging, the crystals changed shape from irregular to more regularly shaped platelets. It was concluded that the change in shape contributed to the model error. Other aging effects can occur in near saturated solutions. Specifically, in the case of temperature cycling, small crystals will dissolve when the temperature increases. Then when the temperature is lowered, the remaining crystals will grow. Over time, temperature cycling results in more of the larger crystals and fewer of the smaller crystals.27 One concern with using different solutions to suspend the particles is that the solutions frequently have different densities and viscosities, which can significantly alter the flow patterns in the vessel, and hence the impact velocities and attrition rates. Therefore, different methods may be used to adjust the operating conditions to achieve hydrodynamic similarity. The aim is to aid in determining how breakage experiments should be conducted to obtain breakage data under crystallizer operating conditions. In these initial studies, the first part is determining if other mechanisms have a significant effect on the breakage results when NaCl crystals are suspended in aqueous saturated solutions. If so, then breakage experiments should be conducted in nonsolvents. The second part is determining if simple correlations such as the Reynolds number and the Zwietering correlation can be used to adjust the agitation rate so that the breakage results from a nonsolvent match the results from a saturated solution. If this can be done, then an experimenter can isolate breakage effects in a nonsolvent and then apply the results to saturated solutions.
Many investigators used nonsolvents for isolating the breakage mechanism,7,8,13−15,17,18 while others used saturated solutions16,19−21 to minimize other mechanisms, such as growth and dissolution. A variety of crystal types with different initial crystal sizes were studied. A comparison of the various operating conditions given in Table 1 indicates that most existing studies are not sufficient to compare the effects of nonsolvents to those of saturated solutions because experiments were not performed in both fluids. In other cases, the operating parameters for the two cases are not the same. For example, the size ranges of potassium sulfate particles studied in the nonsolvent (600−1000 μm, 355−425 μm) are different from the size ranges studied in the saturated solutions; and the nonsolvent magma densities of 100 and 363 kg/m3 are larger than those used in the saturated solutions. Therefore, direct comparisons between saturated solutions and nonsolvents cannot be made. The only known study where the results were compared between a saturated solution and a nonsolvent concluded that the results between the two systems were significantly different due to the number fraction of nuclei formed.17 However, this study did not adjust any operating parameters to make the systems hydrodynamically similar. It has been noted that attrition in a nonsolvent and a saturated solution will produce different results and that the effect of supersaturation must be taken into account.23 One primary reason for this is that in a saturated solution edges and corners that are removed by attrition can regrow and be broken again, whereas crystal edges and corners do not grow back in nonsolvents. One mechanism that can affect particle size in nearly saturated solutions is Ostwald ripening. Ostwald ripening occurs in many systems including aqueous ionic systems24 and systems with biological macromolecules.25 During Ostwald ripening the mass of solid particles remains constant, but the small particles tend to dissolve while the larger particles grow larger.22,24 On the basis of the Gibbs−Thomson relationship between particle size and solubility, particles become more soluble as their size decreases. In most aqueous systems, the increase in solubility only becomes significant when the particles are less than 1 μm in size.22 The ripening rate is strongly influenced by the solubility and temperature. Materials that are moderately soluble in a solvent ripen much more quickly than materials that are sparingly soluble. The concern is
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THEORY Various methods are used to compare results from breakage in two different suspensions. Three of the more common methods are using identical tip speeds, using identical mixing Reynolds 2749
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where two systems have particles with the same size distribution and where the same equipment is used, some of the factors cancel when determining the ratio of just suspended agitation rates. Specifically, the tank and impeller diameters are the same, the particle size used is the same, and gravity is a constant. Therefore, the term K1(DT/DI)K2g0.45L0.20/DI0.85 is the same for both cases. The resulting ratio of agitation rates is given by
numbers, matching the degree of particle suspension using the Zwietering correlation, and using CFD simulations. Most of the highest impact velocities are due to collisions between the impeller and crystals.10 Previous research has shown that the tip speed in a vessel influences the impact velocity of the impeller on a crystal.9,28 Therefore, one simple approach to achieving similarity is to compare both suspension fluids at the same impeller tip speed and magma density. One dimensionless number often used for determining hydrodynamic similarity during mixing in a stirred tank is the Reynolds number for mixing, NRe. NRe =
Njs,1 Njs,2
NIDI2ρL μ
(1)
This ratio is constant for given fluid properties at a fixed temperature and does not include any particle properties. Therefore, it does not address how well the particles are suspended. One of the initial approaches for predicting the minimum agitation rate required to keep particles suspended is based on empirical correlations using dimensionless numbers.29 This minimum impeller speed, Njs, is the speed at which particles will be just suspended in the slurry and none of the particles will remain in the same location at the bottom of the vessel. Zwietering’s correlation is as follows 0.45 (DT /DI)K 2 ⎛ ρs − ρL ⎞ 0.45 0.10 0.20 0.13 ⎜ ⎟ ⎜ ⎟ g ν L Ms DI0.85 ⎝ ρL ⎠
⎛ ρs − ρL,2 ⎞0.45 0.10 0.13 ⎜ ⎟ ν2 Ms,2 ⎝ ρL,2 ⎠
(4)
where the subscripts 1 and 2 denote the two systems used. This expression explicitly includes particle properties by including the solid density and the solids concentration in the slurry. The Zwietering correlation and CFD models have been compared to each other and to experimental results. One comparison of the Zwietering correlation with CFD simulation yielded good agreement between the two methods, but the simulation predicted a lower value of Njs over a range of tank diameter to impeller diameter ratios.30 It was noted that this was reasonable given that the simulation uses a mean particle diameter for spherical particles and that the real system will have a distribution of particle diameters and nonspherical particles. Later research compared CFD and Zwietering correlation predictions to experimental results at mass concentrations ranging from 1 to 20% w/w; and it concluded that for particles larger than 300 μm both methods underpredicted the just suspended speed, but the CFD model was better for smaller particles.31 Later work with 300 μm glass beads at a mass concentration of 2.5% w/w indicated that the Zwietering correlation overpredicted Njs.32 A more extensive study compared CFD simulations that used various models for the drag coefficient and the Zwietering correlation with experimental results for particles ranging in size from 3 to 10 mm.33 It was shown that the Zwietering correlation underpredicted Njs at low particle concentrations and that the CFD simulations either underpredicted or overpredicted Njs depending on the drag coefficient model used.33 That is, the method used for scaling needs further research. On the basis of the previous research comparing CFD simulations and the Zwietering correlation with experimental data, neither approach provides an exact match to experimental data and neither approach is consistently better at predicting the degree of particle suspension. Therefore, the Zwietering correlation will be used for comparison in this work.
In this expression NI is the impeller rotation rate (rev/s), DI is the impeller diameter (m), ρL is the fluid density (kg/m3), and μ is the fluid viscosity (kg/(m s)). This dimensionless number indicates whether there is laminar flow (NRe < 10) or turbulent flow (NRe > 10,000). Since it includes fluid properties such as density and viscosity, it can be used to account for differences in physical properties in different suspending fluids. However, it does not consider particles or any phenomena caused by particles. To obtain the same mixing Reynolds number for two systems, the impeller speed can be adjusted. Let subscripts 1 and 2 indicate two fluids with different densities and viscosities. For the case where the same equipment is used for both systems so that DI is a constant, the ratio of the impeller speeds given by eq 2 will result in both systems having the same mixing Reynolds number. ρL,2 μ1 NI,1 = NI,2 μ2 ρ L,1 (2)
Njs = K1
=
⎛ ρs − ρL,1 ⎞0.45 0.10 0.13 ⎜ ⎟ ν1 Ms,1 ⎝ ρL,1 ⎠
(3)
2
where g is the gravitational acceleration (m/s ) and the liquid properties are represented by the kinematic viscosity ν (m2/s) and the liquid density ρL (kg/m3). The geometry of the tank is accounted for by using the tank diameter DT (m), the impeller diameter DI (m), and the constants K1 and K2 to account for the impeller type. The particles are included in the correlation by using the particle diameter L (m) and the solid density ρs (kg/m3), and by using MS to represent the solid concentration as 100 times the mass of solid divided by the mass of liquid. This correlation can be used to adjust stirring speeds to account for differences in the density and viscosity of various suspending fluids. Although the properties for two systems may be different, the relative agitation rates needed for just suspended conditions can be determined using the Zwietering correlation. For the case
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EXPERIMENTAL METHODS
Ostwald ripening should not have a large effect on the experimental results unless breakage produces a significant mass fraction of particles smaller than 1 μm. Theoretically, the dissolving particles are smaller than 1 μm.22 The sample particles being studied range in size up to several hundred micrometers. Although there may be a large number of particles less than 1 μm in size, the total mass of the dissolving particles should be a small fraction of the total particle mass. Since ripening occurs more rapidly in systems with higher solubility, the ripening effect was tested experimentally with a given solute in at least two suspension fluidsone in which it was moderately soluble and one in which it was only sparingly soluble. The solubilities of sodium chloride at 20 °C are 35.9 g NaCl/100 g water and 0.0003 g NaCl/100 g acetonitrile. 2750
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Table 2. Properties of Suspension Fluids at 20 °C liquids aq NaCl sat. soln acetonitrile
ρ, g/cm3 35
1.1972 0.785735
ρ, kg/m3
μ, cP 35
1197 785.7
1.990 0.37534
Materials. Deionized water for the experiments was supplied from a Barnstead Nanopure Diamond Water Purifier. Acetonitrile obtained from Fisher Scientific was the 0.2 μm filtered HPLC grade with a purity >99.7%. The sodium chloride was certified as containing greater than 99.0% NaCl. Sodium chloride crystals were chosen because of their highly regular cubic shape, which makes it easier to determine if a crystal has been chipped, and because NaCl has almost constant solubility in water in the range from 10 to 30 °C. The solubilities of NaCl in water at 10, 20, and 30 °C are 35.8, 35.9, and 36.1 g NaCl/100 g H2O, respectively.34 Since temperature fluctuations are less than 1 °C during the experiment, this almost constant solubility minimizes the effect of temperature fluctuations. In these experiments, acetonitrile is used as a nonsolvent and water is used to form the saturated solution, where both are operated at 20 °C. Selected physical properties are shown in Table 2, where the kinematic viscosity is calculated using the following equation.
⎛ m2 ⎞ ⎛ kg ⎞ ⎛ kg ⎞ ν ⎜ ⎟ = μ ⎜ ⎟ ρ ⎜ 3⎟ ⎝ ms ⎠ ⎝m ⎠ ⎝ s ⎠
μ, kg/(m·s)
ν, m2/s
0.00199 0.000375
1.662 × 10−6 4.773 × 10−7
water based on solubility data. The solution was then heated above the saturation temperature to 50 °C to ensure the complete dissolution of the NaCl crystals in the water. The density and the conductivity of the saturated solution were measured before and after experiments to check for changes in the solution concentration. Deionized water was used to minimize the presence of impurities that could alter crystal morphology and solubility. To verify that a solution was at saturation, conductivity testing was conducted with a Fisher Scientific accumet Excel XL 50 Dual Channel pH/ion/conductivity meter. Conductivity and TDS (2 cell type, cell K = 1.00/cm, factor = 0.60) measurements of the saturated solution were recorded before the experiment and after vacuum filtration. Values were recorded for select experiments for comparison. Density measurements were taken of selected experiments using an Anton Paar DMA 4500 density meter (Anton Paar, Ashland, VA; repeatability, st dev density, 0.00001 g/cm3, temp 0.01 °C). Approximately 1 mL of sample is inserted into the measuring cell of the meter. All density readings were recorded at 20 °C. Each breakage experiment was conducted with parent particles of given size range at a fixed magma density (g crystal/100 mL suspension fluid) and a fixed agitation rate. For a magma density of 5 g crystals/100 mL suspension fluid, 25 g of NaCl would be added to 500 mL of suspension fluid. The suspension fluid was specified as either the aqueous saturated solution or the nonsolvent acetonitrile. Initially, the suspension fluid was placed in a 1 L beaker on a hot plate where the temperature was monitored using an attached thermocouple that was plugged directly into the hot plate. Since the room temperature was below 20 °C, a hot plate was needed to heat the solution. The hot plate controlled the solution temperature directly by using the thermocouple placed in the beaker (Figure 1). The solution temperature was set to a constant temperature of 20 °C, and the crystals were not added to the vessel until the solution was heated. The solution temperature was held at 20 ± 0.3 °C. Given the almost constant solubility of NaCl in that temperature range, the change in solubility was negligible. The stirrer speed was selected on the basis of the agitation rate needed for the experiment (±5 rpm). Stirring at high agitation rates did not elevate the slurry temperature more than 0.3 °C. Once the operating conditions were satisfied, the predetermined quantity of unbroken NaCl was added to the beaker and a timer started. Once the total allotted residence time was reached, the stirrer was immediately stopped and the slurry was filtered. Slurry samples with saturated solutions were rapidly filtered to prevent changes in the crystal size. Once the sample is removed from the vessel, it can change temperature, which causes the solution to become either subsaturated or supersaturated. This causes the crystals to dissolve, nucleate, or grow. To minimize these effects, the samples were rapidly filtered using vacuum filtration and washed with the nonsolvent acetone. Vacuum filtration was performed using a Büchner funnel mounted on a vacuum flask. Whatman #50 filter paper (particle retention = 2.7 μm) was used, and the vacuum was supplied by an oilfree Welch Dryfast Vacuum Pump designed for chemical duty. The entire sample was filtered, and the particles were placed in a desiccator for at least 10 min to remove any excess moisture before analysis. The mass balances of the crystals were analyzed for each experiment. Specifically, the mass of solids added to the crystallizer and the mass of dried solids removed from the crystallizer were weighed. To achieve an accurate representation of a sample, segregation of particles due to particle size must be taken into account. Therefore, the broken particles were sieved using the initial parent particle sieve size, a predetermined medium particle size tray, and the bottom recovery pan for fines. For each experiment, the mass of particles in each size range was measured and the mass fractions were calculated. The resulting three particle size samples were then used for the image analysis procedure where the mass fractions of particles analyzed in
(5)
There are significant differences in the physical properties of the two suspension fluids. The kinematic viscosity of the saturated solution is greater than three times the kinematic viscosity of acetonitrile. Apparatus. All breakage experiments were conducted in a 1 L, flat bottomed glass vessel with a thermocouple and a four blade propeller
Figure 1. Schematic of apparatus used in breakage experiments. stirrer as shown in Figure 1. Temperature control was performed using a Fisher Scientific hot plate that included a thermocouple for monitoring the temperature. Agitation was performed using a 2 in. diameter impeller driven by a Fisher Scientific digital stirrer. For all experiments, the top of the vessel was covered with Parafilm M laboratory film (Pechiney Plastic Packing, Chicago, IL) which was placed as close to the impeller shaft as possible to reduce evaporation and to prevent the solution from splashing out of the beaker over time. Procedures. The commercial NaCl crystals were sieved using Mesh 30 (600−850 μm), Mesh 40 (425−600 μm), and Mesh 60 (250−425 μm) sieve trays during a five min shaking period. The Mesh 30, Mesh 40, and Mesh 60 crystals were placed in separate, sealed plastic containers until needed for experimentation. Only Mesh 40 crystals were used for the research presented in this paper. Saturated solutions (SS) for breakage experiments were prepared using literature data for the solubility of NaCl in water at 20 °C (35.8 g NaCl/100 g H2O). A saturated solution was made by mixing a known mass of NaCl crystals into a predetermined quantity of deionized 2751
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Figure 2. Comparison of crystal size distributions of NaCl crystals in acetonitrile (ACTL) and aqueous saturated solutions (SS) at (a) 1000 rpm for 30 min, (b) 1000 rpm for 60 min, (c) 1500 rpm for 30 min, (d) 1500 rpm for 60 min, (e) 2000 rpm for 30 min, and (f) 2000 rpm for 60 min. each of the three size ranges matched the mass fractions in the original sample. This sampling method produced a more accurate PSD measurement than choosing particles at random or choosing a constant number of particles from each bin. The mass of the particles analyzed was chosen for all experiments so that more than 600 particles were represented, which was reported to provide an acceptable sample size.36 If the sample size is too small, the size distribution obtained does not accurately represent the actual size distribution. The sample size should be large enough so that measuring additional particles does not significantly change the size distribution. This was tested by comparing distributions from different particle counts for a sample of NaCl crystals. For size ranges with number fractions greater than 0.05, each number fraction changed by less than 5% for sample sizes greater than 600 particles. For example, the number fraction in a size interval could change from 0.148 to 0.142 by counting 700 particles rather than counting 600 particles. Therefore, at least 600 particles were measured for each size distribution. Before beginning breakage experiments, a set of runs was conducted to test the reproducibility of results. For each run, 25 g of NaCl was
suspended in 500 mL of acetonitrile or aqueous saturated solution (MD5) at an agitation rate of 1500 rpm. The agitation time used for this experiment was 30 min. With respect to each suspension fluid, no significant difference existed in the mass fractions of each run. Furthermore, the average standard deviation for each number fraction at a given major axis range is ∼0.01. This shows good reproducibility.
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RESULTS AND DISCUSSION The size distributions are shown as number fractions, Ni/N, over a range of size intervals. The number of particles in size interval i is Ni, and the total number of particles is N. In cases where there is a wide range of particle sizes, the use of logarithmic size intervals is recommended to prevent too much noise in the data.36 Therefore, the size is shown on a log scale so that changes in number fractions of particles smaller than 100 μm can be seen and so that excess noise is reduced. The size intervals are set so that the ratio of largest length in two consecutive intervals is 21/3. In all cases, the size is the major 2752
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min of agitation has a larger number fraction at 2000 rpm than at 1500 rpm. This is consistent with a higher rate of breakage at a higher agitation rate. The secondary peak at 2000 rpm at 60 min is located at 125 μm. For both 1500 and 2000 rpm, the secondary peak indicates that some fragments are formed. One difference at 2000 rpm is that there is a third peak in the smallest size interval after 60 min in acetonitrile, which indicates that attrition is occurring. If Ostwald ripening or aging were significant in the saturated solution, then the number fraction of particles larger than 25 μm would increase with time, and the number fraction of particles
