Crystal Wet Milling and Particle Attrition in High Shear Mixers

Transcription

1 HSMRP-DOMINO Crystal Wet Milling and Particle Attrition in High Shear Mixers Kanan Ghaderzadeh* and Richard V. Calabrese University of Maryland College Park, MD USA DOMINO-HSMRP Project Meetings 27 September 2017

2 Wet Milling of Active Pharmaceutical Ingredients Crystallization Reactor Filtration & Drying Dry Jet Mill Downstream Processes Fines Crystallization Reactor with Inline Wet Mill Filtration & Drying Downstream Processes Wet Mill Advantages of Wet over Dry Milling for Crystal Size Control: Eliminates need for separate dry milling unit Allows for better control of temperature and morphology

3 Approach Perform definitive wet milling experiments to investigate the effect of: Rotor speed Flow rate Particle mechanical properties Mixer geometry Slurry Concentration on size reduction. Develop & validate a class of mechanistic models for the milling process considering the influence of the following on crystal breakage: Brittleness index Elastic deformation Plastic deformation Exploit the mechanistic models to predict ultimate crystal size, breakage kinetics and wet milling performance at different scales. Equipment: Silverson L4R bench scale unit with square hole stator Standard inline unit placed in holding vessel recirculation loop Enlarged shear gap inline unit placed in holding vessel recirculation loop Standard batch unit Experiments: Mill sucrose, glycine and ascorbic acid in an anti-solvent: isopropyl alcohol (IPA) Set uniform initial size distribution for all experiments via sieving Measure milled crystal size distribution via laser diffraction (Horiba Partica LA-950) Estimate local energy dissipation rate via CFD and power draw measurements 3

4 Particle Size Measurement Techniques Sieving Initial particle size distribution: Particles that pass through a #40 sieve and are trapped above a #60 sieve, microns, are used as feed to wet milling experiments. Laser Diffraction (Partica LA-950, Horiba) Range = 10 nm 3 mm Focused Beam Reflectance Measurement (FBRM) (Mettler Toledo) Range = 0.5 μm 2 mm Particle Vision Measurement (PVM) (Mettler Toledo) Range = 20 μm 1 mm Front Illumination Back Illumination 4

5 Particle Morphology and Physical Property Measurement Techniques JEOL JSM-6490LV Scanning Electron Microscope (SEM) Nano-indentation (Hysitron TriboIndenter) Resolution ϯ Magnification ϯ 0.5 to 300,000 Maximum Specimen Size ϯ Ϯ JEOL SEM A to Z, 2012, Peabody, MA. High Vacuum mode: 3.0 nm(30kv) Low Vacuum mode: 4.0 nm(20kv) 8" coverage, 12" specimen can be loaded Carbon vapor deposition via Balzers Mini Deposition System MED 010 Load resolution* 1 nn Displacement resolution* 0.02 nm Data acquisition rate* 30 khz *Hysitron TriboIndenter Manual, 2006, Minneapolis, MN. 5

6 Mechanical Properties Measurement Technique Nano-Indentation: A hard tip is pressed into a single crystal with unknown mechanical properties. The load F placed on the indenter tip is increased as the tip penetrates further into the specimen and soon reaches a user-defined value. Young s modulus E: is estimated from stress-strain response during the loading and unloading process. Hardness H: is calculated by H = F/(2a 2 ) where F is the applied load and a is the diagonal length of indentation*. Fracture toughness K c : is calculated by K c = ξ (F c 3/2 ) where ξ is a calibration factor and c is the radial crack. a c Load F *Taylor, L. J. et al Mechanical Characterisation of Powders Using Nanoindentation. Powder Technology : Ponton, C. B., and R. D. Rawlings Vickers Indentation Fracture Toughness Test Part 1 Review of Literature and Formulation of Standardised Indentation Toughness Equations. Materials Science and Technology 5(9):

7 Inline Mill Setup and Parametric Experiments Vessel Working Volume = 2 liters Uniform particle suspension verified by sampling vertically in the holding vessel via a FBRM probe. Parametric experiments: Weight fraction of solids in suspension = 10% Anti-solvent is Isopropyl Alcohol (IPA) Grab samples from vessel to Horiba for PSD Temperature held constant at 25 C 3 Rotor Speeds (different energy inputs) 3 Flow Rates to Mill (different mill head residence times) 3 Crystal Materials (different physical properties) Slotted Disintegrating Square Hole Round Hole Shear Gap or Rotor- Stator Clearance (Different Rotor Size) Solids Concentration (Different weight fraction of solid in anti-solvent) 5000 RPM 6500 RPM 8000 RPM 2.1 LPM 3.0 LPM 4.2 LPM Sucrose Glycine Ascorbic Acid 0.2 mm (standard) 1.7 mm (enlarged) 2% and 5 % 10% 15% 7

8 Inline Mixer Standard Shear Gap (8000 RPM 3.0 LPM) Initial Distribution Final Distribution

9 Flow rate = 4.2 LPM Fixed flow rate Flow rate = 2.1 LPM Results from Laser Diffraction Measurements Standard Shear Gap = 0.2 mm Effect of Rotor Speed D90 vs Tank Turnovers Different Rotor speeds D90 = 90% cumulative volume diameter Number of tank turnovers = 1 Tank Turnover = 25 Mill Head Passes Q V V t t is milling time, V is volume of slurry in holding vessel, and Q V is volumetric flow rate to mill head Sucrose in IPA 9

10 8000 RPM Fixed rotor speed 5000 RPM Results from Laser Diffraction Measurements Effect of Flow Rate D90 vs Tank Turnovers Flow Rate = 2.1, 3.0 & 4.2 LPM D90 = 90% cumulative volume diameter Sucrose in IPA Standard Shear Gap = 0.2 mm 1 Tank Turnover = 25 Mill Head Passes 10

11 D 10 = 1 n d i n i=1 D10 = 10% cumulative volume diameter Results From Laser Diffraction Measurements Sucrose in IPA Effect of Rotor Speed D10 and D 10 vs Tank Turnovers Rotor Speed = 5000, 6000 & 8000 RPM Fixed Flow Rate = 4.2 LPM SEM Log Log 1 Tank Turnover = 25 Mill Head Passes 11

12 Relationship between D90 and Other Measures of Particle Size Sucrose in IPA To determine the relationship between D90 and other measures of particle size, D90 for the sucrose experiments was plotted against other relevant size measures. Comparison to cumulative volume diameters: D95, D80, D50, D10 Comparison to mean diameters: D 43, D 32, D 10 D95 D90 and D80 D90 12

13 Physical Properties and Brittleness Index of Crystalline Materials Three crystalline materials with different physical properties are used to investigate the effect of physical properties. A modified Brittleness Index for these crystals is defined by analogy to Lawn & Marshal (1979) for each deformation mechanism. The models are discussed subsequently. Modified (Elastic) (Plastic) (Elastic-Plastic) Higher Brittleness Index = Easier to Break = Smaller D90 & Larger D10 *Ascorbic acid exhibits anisotropic behavior which leads to large scatter in indentation data (Glycine) (Sucrose) 13

14 Rotor Speed = 6500 RPM Flow Rate = 3.0 LPM Rotor Speed = 8000 RPM Flow Rate = 4.2 LPM Effect of Particle Physical Properties D90 vs Number of Tank Turnovers Crystals: Sucrose, Glycine, Ascorbic Acid Log Log 14

15 Effect of Particle Physical Properties Size of Attritted Small Chips for Milling of Different Crystals Ascorbic Acid Log Glycine Sucrose Log Crystal E (GPa) H (MPa) K c (MPa m 1/2 ) H/EK c (1/MPa m 1/2 ) Ascorbic Acid Glycine Sucrose D10 and D 10 of Sucrose and Ascorbic Acid are very similar but D10 and D 10 of Glycine is smaller. Ascorbic acid has anisotropic behavior which leads to high scatter in indentation results. Higher Brittleness Index = Easier to Break - Smaller D90 & Larger D10 15

16 Chord Length D32/D32_0 (%) D 32 Initial D 32 vs Tank Turnover Different Rotor Speed and Flow Rates (FBRM Data) Wet Milling of Sucrose at Different Rotor Speed and Flow Rates Initial D 32 = 180 ± 14 μm FBRM and PVM Probe is in Holding Tank By increasing rotor speed (increasing energy input) and decreasing flow rate (increasing residence time) the milling performance improves 5000 rpm 3.0 lpm 5000 rpm 2.1 lpm 6500 rpm 3.0 lpm 6500 rpm 2.1 lpm 8000 rpm 3.0 lpm 8000 rpm 2.1 lpm Number of Tank Turnovers (D32_0 D32_10 ) / D32_0 = 64 % size reduction at 8000 RPM and 2.1 LPM 16

17 RBI/RBI_0 (%) Wet Milling of Sucrose in IPA at Different Rotor Speed and Flow Rates (PVM Data) RBI = Relative Backscatter Index Wet Milling of Sucrose at Different Rotor Speed and Flow Rates Initial RBI = 4.2 ± 0.3 By increasing rotor speed (increasing energy input) and decreasing flow rate (increasing residence time) the milling performance improves 5000 rpm 3.0 lpm 5000 rpm 2.1 lpm 6500 rpm 3.0 lpm rpm 2.1 lpm 8000 rpm 3.0 lpm rpm 2.1 lpm Number of Tank Turnovers (RBI_0 RBI_4 ) / RBI_0 = 61 % size reduction at 8000 RPM and 2.1 LPM 17

18 Wet Milling of Sucrose in IPA at 6500 rpm and 3.0 lpm (PVM images at successive times) t = 0 t = Micron 100 Micron 100 Micron t = 1 tank turnover 100 Micron t = 3 tank turnovers 18

19 Wet Milling of Sucrose in IPA at 6500 rpm and 3.0 lpm (PVM images at successive times) 100 Micron t = 5 tank turnovers 100 Micron t = 11 tank turnovers 100 Micron t = 15 tank turnovers As the number of small particles increases during milling, the laser input scatters significantly and does not reflect back to the sensor. As a result, the contrast and resolution decreases as the sensor becomes increasingly saturated. 19

20 Sucrose SEM Images Before Milling After Milling 300 Micron 20 Micron 20

21 Effect of Solid Concentration ( Sucrose milled in IPA at 6500 RPM 3.0 LPM) The ultimate D90 appears to be independent of particle concentration As expected, the rate of breakage increases with particle concentration The dependence of slurry viscosity on solids concentration can be estimated from*: μ m = μ L ϕ ϕ e 16.6 ϕ, ϕ = volume fraction Solid Concentration (by weight) 0% 2% 5% 10% 15% Viscosity of the Mixture (Slurry) 2.04 cp 2.09 cp 2.20 cp 2.35 cp 2.66 cp *Thomas, David G Transport Characteristics of Suspension: VIII. A Note on the Viscosity of Newtonian Suspensions of Uniform Spherical Particles. Journal of Colloid Science 20(3):

22 Mechanistic Model Development: Empirical Approach of Lawn & Marshall (1979) Elastic Deformation Mechanism of Ghan & Mersmann (1997) Plastic Deformation Mechanism Ghadiri & Zhang (2002) Elastic-Plastic Deformation Mechanism of Current Study Fracture Toughness: A. A. Griffith (1921): fracture strength predicted from molecular structure yields values that are orders of magnitude larger than measurements Griffith reasoned that the fracture strength and its sizedependence were due to the presence of microscopic flaws or cracks in the bulk material. σ f a f σ f Stress at fracture π a f = K c Crack size Alan Arnold Griffith ( ) was an English engineer. Fracture toughness 22

23 Rittinger s Law Bond s Law Kick s Law Classical Theories of Milling (Grinding Laws) Peter von Rittinger ( ) was an Austrian pioneer of mineral processing Rittinger s model (1867) suggests that the energy required for size reduction is related to change in surface area. And can be written as: de sp = c R dx x 2 Friedrich Kick( ) was an Austrian mechanical engineering professor. Kick s model (1885) suggests that the energy required for size reduction is proportional to the ratio of the initial size to the final size. And can be written as: de sp = c K dx x 1 Fred C. Bond ( ) was an American mining engineer. Bond s model (1952) suggests that the energy required for size reduction depends upon both volume and surface area. That is, it falls inbetween Rittinger s and Kick s law: de sp = c B dx x 3/2 E sp It is common practice to assume that von Rittinger s, Kick s, and Bond s laws apply to different product size ranges. Kick s law is applies to large particle size (coarse crushing and crushing), Von Rittinger s law applies to very small particle size (ultra-fine grinding), Bond s law is suitable for intermediate particle size (the most common range for many industrial milling processes) x 10 Micron 10 mm 23

24 Mechanistic Theories of Attrition LAWN AND MARSHALL * (1979) Based on Indentation Data Lawn and Marshall used indentation measurements to propose a brittleness index in terms of hardness (H) and fracture toughness (K c ) as: Brittleness Index = H K c They measured the minimum crack size and crack load of different materials and concluded that the materials with higher brittleness index are easier to break. GAHN AND MERSMANN (1997) Based on Elastic Mechanism Gahn and Mersmann developed a mechanistic model for attrition loss occurring in suspension crystallizers. They assumed a cone shape particle collides with the mixer blade. They assumed that elastic deformation of the particle during impact is responsible for fracture. Their model can be rearranged to the following relationship: V V ~ ρ 4/3 p u 8/3 x H 2/3 K c 2 GHADIRI AND ZHANG (2002) Based on Plastic Mechanism Ghadiri and Zhang developed a mechanistic model for single particle impact on a hard surface. They assumed that plastic deformation dominates the breakage process which occurs at the location of lateral cracks. They assumed that a cubic particle undergoes edge fracture and derived the following relationship: V V ~ ρ p u 2 x H K c 2 V = fractured volume x = crystal length scale V = initial volume H = hardness ρ p = crystal density K c = fracture toughness u = impact velocity * D. B. Lawn, B. R., Marshall, Hardness, toughness and brittleness, an indentation analysis, J. Am. Ceram. Soc., vol. 62, no. 7, pp , ϯ C. Gahn and a Mersmann, Theoretical Prediction and Experimental Determination of Attrition Rates, Chem. Eng. Res. Des., vol. 75, no. 2, pp , M. Ghadiri and Z. Zhang, Impact attrition of particulate solids. Part 1: A theoretical model of chipping, Chem. Eng. Sci., vol. 57, no. 17, pp ,

25 Current Mechanistic Model Based on Elastic-Plastic Deformation Cubic particle collides with a hard surface at its corner The impact energy is consumed due to both plastic deformation and elastic deformation: W impact = W plastic + W elastic Impact Energy W impact mu 2 = p V u 2 H a 3 Substituting the above terms gives upon rearrangement: a 3 = mu2 H+ H2 E Plastic Energy W plastic W elastic = H2 E mu2 H+ H2 E Griffin s Law (1921): Particle fracture occurs when σ f π a f = K c. σ f = stress at fracture a f = flaw length scale The elastic energy provides the driving force for fracture. The plastic energy is dissipated locally over volume a 3. Therefore, the stress at fracture σ f can be estimated from the available elastic energy per volume: σ f ~ W elastic l i 3 Elastic Energy W elastic H 2 E a3 The flaw length scale is a function of particle size: a f = f(x) A simple linear functionality is assumed : a f x Combining these equations gives: Generally, H H2 V V ~ ρ p u 2 H 2 x E K c H + H2 E E V V V = l i 3 V = x 3 and the model reduces to: ~ ρ p u 2 H x E K c 25

26 Relating Mechanistic Theories to Classical Theories Lawn and Marshall (1979) model is equivalent to Kick s law (1885) Classifying the brittleness index as H K c without taking into account the effect of particle size, is similar to Kick s law. Kick assumes that the energy required for size reduction is proportional to ratio of final size to initial size. de sp = c K dx x 1 E sp = c K log x product x Feed The energy required to reduce size from 100 to 10 is equal to the energy required for size reduction from 10 to 1. That is, particle size dependency is not seen in Kick s law. Ghadiri and Zhang (2002) model is equivalent to von Rittinger s law (1867) Starting from Ghadiri and Zhang model V V ~ ρ p u2 x H K c 2 V ~ x 3 ΔV ~ dx 3 ~ x 2 dx Plastic By setting the specific energy as E sp = u 2 and rearranging the Ghadiri and Zhang model gives: K 2 c V E sp = differentiate de ρ p H x V sp = K c 2 x 2 dx ρ H x = K 2 c dx p x3 ρ H p x 2 Which is the von Rittinger s law, with n = 2 as de sp = c R dx x 2 and c R = K c 2 ρ p H Gahn and Mersmann (1997) model is in-between Rittinger s law and Bond s law Starting from Gahn and Mersmann model V V ~ ρ4/3 u 8/3 x H 2/3 K c 2 Setting the specific energy as E sp = u 2 and rearranging the Gahn and Mersmann model gives: E sp = K c 2 V 4 2 ρ3 H 3/4 differentiate de sp = K 3/2 c ρ H 1/2 3 x V which translates to an energy model in between von Rittinger s and Bond s law with n = 7/4 : de sp = c Elastic dx x 7/4 dx x 7/4 and c = K c 3/2 ρ p H 1/2 Current study s model is equivalent to Bond s law (1952) Starting from curcrent study s model V V ~ ρ p u2 x 1/2 H E K c Setting the specific energy as E sp = u 2 and rearranging the model gives: E sp = E K c V Hx 1/2 V Which is the Bond s law with n=3/2 differentiate de sp = E K c x 2 dx Hx 1/2 x 3 = E K c dx Hx 3/2 de sp = c B dx x 3/2, and c B = EK c Elastic-Plastic ρ p H 26

27 Cohesive Force Resisting Fracture Assumption: ΔV Disruptive Stress = V Cohesive Stress Then the cohesive stress can be extracted from the mechanistic models as: Empirical model - indentation data (Lawn & Marshal Kick s law): V V ~ ρ p u 2 c K cohesive stress = c K c K c H H Model based on plastic deformation mechanism (Ghadiri & Zhang von Rittinger s law): V V ~ ρ p u2 K c 2 /Hx cohesive stress = K c 2 Model based on elastic deformation mechanism (Gahn & Mersmann in between Bond s & Rittinger s law): ( V V )3/4 ~ ρ p u2 H x 3/2 K 3/2 c /H 1/2 x cohesive stress = K c 3/4 H 1/2 x 3/4 Disruptive Stress = ρ p u2 Particle size = x Model based on elastic-plastic deformation mechanism (Current study Bond s law): V V ~ ρ p u2 EK c /H x 1/2 cohesive stress = EK c H x 1/2 27

28 Mechanistic Model for Maximum Stable Particle Size, x Disruptive Stress The forces acting on the particle can be divided into two opposing forces, cohesive forces and disruptive forces. The cohesive stress acts to resist fracture whereas the disruptive stress acts to break the particle. The disruptive force is derived from hydrodynamic considerations: Model Mechanism DISRUPTIVE STRESS (τ D ) Macroscale Turbulence x ~ l Collision Velocity ~ Tip Speed ρ p u tip 2 Inertial Subrange Turbulence η x l Collision Velocity ~ Eddy Velocity ρ P u(x) 2 ~ ρ P (ɛx) 2/3 ~ ρ p u tip 2 ( x D )2/3 (Geometric Similarity) Local Energy Dissipation Rate = ɛ = Power Mass = Power ρ f V DZ V DZ = Volume of Dispersion Zone ɛ N 3 D 2 u tip 3 l is macroscale of Turbulence ~ Rotor Diameter, D η is Kolmogorov Length Scale ~ 1 to 10 m D (Constant Power Number, N p ) 28

29 Mechanistic Model Development for Maximum Stable Particle Size, x Breakage occurs when the crystal is exposed to disruptive stresses that exceed the cohesive stresses. The maximum stable particle size, x, occurs when the disruptive stress balances the cohesive stress (τ C τ D ). As noted, 2 different disruptive stresses and 4 different cohesive stresses are proposed. As a result, 2 4 = 8 different mechanistic models can be developed: Based on u tip COHESIVE MODEL DISRUPTIVE MODEL BREAKAGE MODEL Empirical Model: (Lawn & Marshall, Kick) Plastic Mechanism: (Ghaderi & Zhang, von Rittinger) Elastic Mechanism: (Gahn & Mersmann, bet. Bond & von Rittinger) Elastic-Plastic Mechanism: (Current Study, Bond) Macroscale Model Inertial Subrange Model Macroscale Model Inertial Subrange Model Macroscale Model Inertial Subrange Model Macroscale Model Inertial Subrange Model x D ~ 1 D e x D ~ ( ck c ρ P H )3/2 x D ~ 2 k c ρ P HD 2 x D ~ ( k c ρ P HD )3/5 x D ~ ( x D ~ ( 3 K c 2 ρ P H 1 2 D K c 2 ρ P H 1 2 D 3 4 x D ~ ( x D ~ ( EK c ρ P HD 1 2 EK c ρ P HD 1 2 ρ P H ck c u tip 2 1 u tip 3 1 u tip 2 1 u tip 6/5 1 ) 4/3 u 8/3 tip 1 ) 12/17 u 24/17 tip ) 2 1 u tip 4 1 ) 6/7 u 12/7 tip 6 5 = ~ ~ 1.7 e.g. Log-Log representation: Log x D ~ Log EK c ρ P HD Log 1 u tip 29

30 Inertial Subrange Models for Predicting Maximum Stable Particle Size x is the size of largest particle (D100) that can survive under the disruptive force imposed by the rotor speed. In practice, D95, D90, or D80 are used instead of the largest particle size, because of the large uncertainty in D100 measurements and statistical considerations. Here, x = D90 is used to compare the mechanistic correlations, e.g. (D max ~ D90). Equilibrium data for sucrose, glycine, and ascorbic acid at different rotor speeds are well fit by a line with slope = 1.6. This slope suggests that the inertial subrange models better fit the experimental data than the macroscale models. Furthermore, this slope is in agreement with models based on elastic mechanism which predicts the slope of = 1. 4 and elastic-plastic mechanism which predicts slope of 12 7 =

31 Comminution Number & Local Energy Dissipation Rate for Inertial Subrange Models Analogous to Weber number in drop breakup, a dimensionless number for solid fracture can be defined. It is the ratio of disruptive force to cohesive force, and is referred to as a Comminution number (Co): Inertial force Geometric Similarity (constant N p ): Co i = Solid cohesive force x = D90 The use of Comminution number will allow the models to be specified in simple form. MODEL BASED ON Empirical Approach: (Lawn & Marshall, Kick) Plastic Mechanism: (Ghaderi & Zhang, von Rittinger) Elastic Mechanism: (Ghan & Mersmann, bet. Bond & von Rittinger) Elastic-Plastic Mechanism: (Current Study, Bond) COMMINUTION NUMBER Co I = ρ P u tip 2 c K c H Co P = ρ P u tip 2 K c 2 H D Co E = ρ P u tip 2 K c 3 2 H 1 2 D 3 4 Co EP = ρ P u tip 2 E K c HD 1 2 BREAKAGE MODEL (COMMINUTION NUMBER) x D ~ (Co I) 3/2 x D ~ (Co P) 3/5 x D ~ (Co E) 12/17 x ~ ( x D ~ (Co EP) 6/7 BREAKAGE MODEL (LOCAL DISSIPATION RATE ɛ) x ~ ( ck c ρ P H )3/2 1 ɛ x ~ ( k 2 c ρ P H )3/5 K c 3 2 ρ P H 1 2 x ~ ( EK c ρ P H )6/7 1 ɛ 2/5 1 ) 12/17 ɛ 8/17 1 ɛ 4/7 31

32 Inertial Subrange Models for Predicting Maximum Stable Particle Size Wet milling data for sucrose, glycine, and ascorbic acid are plotted for each breakage model. The degree of success of each model to collapse the equilibrium data is assessed based on goodness of fit. The current study s model is able to collapse the data for different materials onto a single curve. (Lawn & Marshall, Kick) (Ghaderi & Zhang,von Rittinger) (Gahn & Mersmann, bet. Bond & von Rittinger) Geometric Similarity (constant N p ) (Current Study, Bond) D90 D = Co EP 6/7 32

33 Effect of Shear Gap Width (Clearance between Rotor and Stator) For the standard unit, the initial crystal size is greater than the shear gap width Wet Milling of Sucrose in IPA Standard Rotor D= 31.1 mm Standard Shear Gap = 0.2 mm Small Rotor D= 28.2 mm Enlarged Shear Gap = 1.7 mm Silverson L4R Inline Mixer Standard Shear Gap Enlarged Shear Gap Stator Square Hole Stator (104 Square Hole Slots) Size of Stator Slots 2.4 mm 2.4 mm 2.0 mm Thickness of stator 2.0 mm Height of stator ring 18.9 mm Inner Diameter of stator 31.5 mm Rotor Diameter 31.1 mm 28.2 mm Shear Gap Width 0.2 mm 1.7 mm 33

34 Meshing Strategy There are 26 stator holes on the each row of the stationary part Stationary part is sliced to 13 parts in order to have a symmetric part Each part has angle ( = 360 ) Ansys Workbench is used for meshing Hexahedral mesh is used for higher accuracy and adaptability Tmerge is used to rotate and merge the 13 parts to get the complete stationary part Two mesh files are produced one with 1.7 million cells and one with 7.8 million cells (6 hexahedral cells across the shear gap). Coarse mesh is simulated first and is used as initial condition for fine mesh simulation. CFD Simulations Solution Methodology Relizable K-ε model Two equation model Enhanced Wall Function Solution method Second order upwind for momentum, turbulent energy, and dissipation Second order implicit for time Standard method for pressure Sliding mesh Rotator zone is set to rotate at 4000 and 8000 Pressure Inlet, Pressure Outlet Zero gauge pressure

35 Free Pumping Flowrate = 17 LPM Free Pumping Flowrate = 16 LPM Simulation Results, Velocity Vector Field Rotor Speed= 8000 RPM Standard Shear Gap D = 31.1 mm Enlarged Shear Gap D = 28.2 mm 35

36 Simulation Results, Power Draw Prediction Meshing Strategy: Ansys Workbench is used for meshing Two mesh files are produced,one with 1.7 million cells and one with 7.8 million cells (6 hexahedral cells across the shear gap). Coarse mesh simulation is used to initiate the fine mesh simulation. Solution Methodology: Ansys Fluent is used for simulation Realizable k- model Enhanced wall function Sliding mesh Pressure inlet and outlet Second order integration in time and space Standard method for pressure Five different shear gaps are built and meshed. Simulations are conducted for 15 revolutions and the torque on shaft is obtained from each simulation. N = 8000 RPM N P = Power ρ f N 3 D 5 D = 31.1 mm D = 28.2 mm Re = ρ f Rotor Speed Standard Shear Gap, D = 31.1 mm Enlarged Shear Gap, D = 28.2 mm u D μ N (RPM) u tip (m/s) Re Power (W) N P u tip (m/s) Re Power (W) N P , , , , , , , , , ,

37 Inline Mixer Enlarged Shear Gap (8000 RPM 3.0 LPM) Initial Distribution Final Distribution

38 Effect of Shear Gap Width (Clearance between Rotor and Stator) Q V = 3.0 LMP Enlarged Shear Gap Enlarged Shear Gap Enlarged Shear Gap Standard Shear Gap Standard Shear Gap Standard Shear Gap 38

39 Wet Milling Experiments in Standard Batch Mixer Silverson L4R Mixer Cooling Unit (TC) Temp Probe PSD Sample FBRM RPM/AMP 6000 Stirrer Overflow Vent Sampling Port Temp Probe FBRM Probe Inline Square Hole Batch Square Hole Predicted (CFD) 1 Measured 2 Rotor Speed Power N P Power N P 5000 RPM RPM RPM Mixer Head Square Hole Stator Geometry Number of Holes 92 Dimension of Holes Inner Diameter mm 28.5 mm Rotor Geometry (Shear Gap = 0.2 mm) Number of Blades 4 Diameter 28.1 mm 1 Current Study 2 Padron, G.A., 2001, Measurement and Comparison of Power Draw in Rotor-Stator Mixers. M.Sc. Thesis (University of Maryland, College Park, MD, USA). 39

40 Batch Mixer at 8000 RPM Initial Distribution Final Distribution

41 Wet Milling of Sucrose in IPA in Standard Batch Mixer (Effect of Rotor Speed) Log 41

42 Particle Breakage: d max ~ max 4/7 ε max = P ρ V DZ For correlating the data of different scenarios in the same mixer V DZ is same so it is only the power that is important. d max,senario 1 Power of scenario 1 = ( d max,senario 2 Power of scenario 2 Dispersion Zone ) 4/7 For correlating data in different mixers/scales V DZ has a critical rule. d max,mixer 1 = ( Power of mixer 1 V DZ mixer 1 d max,mixer 2 Power of mixer 2 V DZ mixer 2 ) 4/7 Drop Break Up - IKA Labor Pilot: B.N.Murthy s Drop Breakup Data (Single Pass) and P.E Rueger s Power Data concludes: d max ~ max 2/5 max 9 avg V DZ = Volume of Dispersion Zone = Volume of Shear Gap and Stator Holes Volume of Shear Gap and Stator Slots (Dispersion Zone) V DZ 1500 mm 3 Total Volume of the Mixing Head V MH mm 3 ε max = P ρ V DZ V DZ 1 9 V MH

43 Mechanistic Correlation Based on Local ɛ V DZ = Volume of Stator Holes + Shear Gap Volume Local ɛ = Power ρ f V DZ Stator Holes Volume Shear Gap Volume Dispersion Zone Volume V DZ Inline Mixer, Standard Shear Gap 1.2 ml 0.4 ml 1.6 ml Inline Mixer, Enlarged Shear Gap 1.2 ml 2.8 ml 4.0 ml Batch Mixer, Standard Shear Gap 0.9 ml 0.2 ml 1.1 ml Similar to Davies Plot* for liquid-liquid dispersion *Davies, J.T A Physical Interpretation of Drop Sizes in Homogenizers and Agitated Tanks, Including the Dispersion of Viscous Oils. Chemical Engineering Science 42(7):

44 D90 (μm) D90 (μm) D90 (μm) D90 (μm) Inertial Subrange Models for Predicting Maximum Stable Particle Size Based on local energy dissipation rate, ɛ Empirical Model Plastic Mechanism (Lawn & Marshall, Kick) Ghaderi & Zhang, von Rittinger) D90 ~ ( ck c ρ P H )3/2 1 ɛ D90 ~ ( k c 2 ρ P H )3/5 1 ɛ 2/5 Elastic Mechanism Elastic-Plastic Mechanism (Gahn & Mersmann, between Bond & von Rittinger) (Current Study, Bond) K c 3 2 D90 ~ ( ρ P H 1 2 ) 12/17 1 ɛ 8/17 D90 ~ ( EK c ρ P H )6/7 1 ɛ 4/7 D90 = 13.6 ( EK c ρ P H )6/7 1 ɛ 4/7 44

45 Breakage Rate Kernel (Inertial Subrange) There are two common methods of defining the Breakage Kernel: I. Power Law Kernel II. Exponential Kernel Based on reaction rate analogy r A = k 0 e E a RT C A C B Collision theory: k 0 is collision frequency, e E a RT is fraction of collisions with more energy than the activation energy (= successful collisions). After Coulaloglou and Tavlarides (1979)*. Successful collisions are those that have a kinetic (disruptive) energy, greater than particle cohesive energy: Fraction of Particles Breaking = e τ c τ D Mechanism: d = particle size g d = Exponential Kernel 1 Probability of Breakage Breakage Time Breakage Time ~ d 2/3 ɛ 1/3 Probability of Breakage ~ e τ c τ D Empirical: (Lawn & Marshall, Kick) g d = c 1 d 2/3 ɛ 1/3 e Plastic: (Ghaderi & Zhang, von Rittinger) Elastic: (Ghan & Mersmann, Bond & von Rittinger) c 2 c K c ρ p H ɛ 2/3 d 2/3 g d = c 1 d 2/3 ɛ 1/3 e c 2 K c ρ p H ɛ 2/3 d 5/3 3/2 g d = c 1 d 2/3 ɛ 1/3 e c 2 K c ρ p H 1/2 ɛ 2/3 d 17/12 Elastic-Plastic: (Current, Bond) g d = c 1 d 2/3 ɛ 1/3 e c 2 E K c ρ p H ɛ 2/3 d 7/6 Time available for breakage is assumed to be proportional to the lifetime of eddies of size d (Batchelor ϯ ). For inertial subrange eddies : t b ~ d 2/3 ɛ 1/3 * Coulaloglou, C. A., and L. L. Tavlarides Description of Interaction Processes in Agitated Liquid-Liquid Dispersions. Chemical Engineering Science 32(11): ϯ Batchelor G K, Proc Cambridge Phil Soc 1952a

46 Milling Kinetics (Inline Units Only) (Elastic-Plastic Mechanism of Current Study) Population balance equation for a milling process can be written as (D = particle size): f(d, t) t = f D, t g D β D, D dd D (Birth) g D f(d, t) If consider only largest size interval, then production equals zero and we obtain: f(d90, t) = g D90 f(d90, t) t If assume that f D90, t D90(t) then: D90(t) = g D90 D90(t) t The breakage kernel based on the elastic-plastic mechanism is: g d = c 1 d 2/3 ɛ 1/3 e c2 E Kc ρp H ɛ 2/3 D 7/6 An optimization algorithm is used to fit c 1 and c 2 to the data: (Death) D90 t = c 1 ɛ 1/3 e c 2 E K c ρ p H ɛ 2/3 D90 7/6 D90 1/3 46

47 Log Milling Kinetics (Inline Units Only) (Elastic-Plastic Mechanism of Current Study) 47

48 Log Log Milling Kinetics (Inline Units Only) Elastic Mechanism Plastic Mechanism 48

49 Summary and Conclusions: The effect of rotor speed, flow rate, crystal physical properties & concentration and mixer geometry (shear gap width; inline vs. batch) have been investigated A class of mechanistic models for ultimate crystal size are developed and shown to be in agreement with classical attrition models. These are obtained from a balance between disruptive and cohesive forces allowing the functional form of these forces to be extracted for each model. It is shown that an inertial subrange model for crystals undergoing elastic-plastic deformation (current study s model) well describes the crystal breakage behavior in rotor-stator mixer. Ultimate crystal size data for both a standard and an enlarged shear gap inline device, as well as a standard batch mixer, can be correlated based upon local energy dissipation in the dispersion zone. CFD simulations for the Silverson L4R inline mixer were performed to estimate power consumption for different shear gap widths and rotor speeds. To model milling kinetics, a breakage rate kernel has been developed The mechanistic framework shows promise for application to a broad class of milling devices and for extension to dispersion of nanoparticle agglomerates. 49