Milling of Crystals in an Inline Silverson L4R Rotor-Stator Mixer

UM - HSMRP Milling of Crystals in an Inline Silverson L4R Rotor-Stator Mixer Kanan Ghaderzadeh and Richard V. Calabrese* Dept. of Chemical & Biomolecular Engineering University of Maryland College Park, MD 074- USA HSMRP - DOMINO Project Meetings 3 May 08

Wet Milling of Active Pharmaceutical Ingredients Crystallization Reactor Filtration & Drying Dry Jet Mill (Heat & Fines) 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

Approach Perform definitive wet milling experiments to investigate effect of operating conditions, particle mechanical properties and mixer geometry on size reduction and ultimate crystal size. Develop & validate a class of mechanistic models that consider the influence of elastic/plastic deformation and fracture toughness, as well as conditions of agitation. Exploit the mechanistic model framework to predict ultimate crystal size, fracture kinetics and 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 in holding vessel recirculation loop Standard batch unit Experiments: Mill sucrose, glycine & ascorbic acid in an anti-solvent: isopropyl alcohol (IPA) Set uniform initial size distribution for all experiments via sieving Measure crystal size distribution via laser diffraction (Horiba Partica LA-950) Estimate local energy dissipation rate via CFD and power draw measurements 3

Inline Mill Setup and Parametric Experiments Vessel Working Volume = liters Uniform particle suspension verified via FBRM probe. Parametric experiments: Weight fraction of solids in suspension = 0% Anti-solvent is Isopropyl Alcohol (IPA) = 786 kg/m 3 Grab samples from vessel to Horiba laser diffraction unit Temperature held constant at 5 C Square Hole Stator Rotor Speed (energy inputs) Flow Rates (residence time) Crystals (mechanical properties) Shear Gap (Rotor Size) Crystal mass fraction 5000 RPM 6500 RPM 8000 RPM. LPM 3.0 LPM 4. LPM Sucrose = 590 kg/m 3 Glycine = 60 kg/m 3 Ascorbic Acid = 650 kg/m 3 0. mm.7 mm % and 5 % 0% 5% 4

Mechanical Properties Measurement Technique Nano-Indentation: A micro-tip is pressed into a single crystal. Young s modulus E: estimated from the initial slope of stress-strain response curve Nano-indentation (Hysitron TriboIndenter) Hardness H: H = F/(a ) F = load on tip Fracture toughness K c : K c = ξ (F c 3/ ) ξ = calibration factor; c = radial crack length Load F Load Resolution nn Displacement Resolution Data Acquisition Rate 0.0 nm 30 khz a c 5

Flow rate = 4. LPM Fixed flow rates Flow rate =. LPM Results From Laser Diffraction Measurements Sucrose in IPA Standard Shear Gap = 0. mm Effect of Rotor Speed D90 vs Tank Turnover Different Rotor speeds D90 = 90% cumulative volume Number of tank turnovers = Tank Turnover = 5 Mill Head Passes Q V V t t = milling time, V = volume of slurry in vessel, Q V = volumetric flow rate to mill head. 6

8000 RPM Fixed rotor speeds 5000 RPM Results From Laser Diffraction Measurements Effect of Flow Rate D90 vs Tank Turnover Different Flow Rates =., 3.0, 4. LPM D90 = 90% cumulative volume Sucrose in IPA Standard Shear Gap = 0. mm Tank Turnover = 5 Mill Head Passes 7

Standard Shear Gap = 0. mm Relationship between D90 and Other Measures of Particle Size D90 correlates well to D95 and D80 and is used as a measure of largest particle size. Mean diameters such as D 3 and D 43 are not useful measures of the large size tail. Comparison to cumulative volume diameters: D95, D80, D50, D0 PVM Images Sucrose in IPA Results From Laser Diffraction Measurements D95 D90 and D80 D90 8

Physical Properties and Brittleness Index of Different Crystals Three crystalline materials with different physical properties are used in the wet milling experiments to investigate the effect of physical properties. A Brittleness Index for Different Crystals is calculated based on the Lawn & Marshal (979) approach (discussed subsequently). Higher Brittleness Index = Easier to Break = Smaller D90 = Larger D0 Glycine Sucrose *Ascorbic acid exhibits anisotropic behavior which leads to high scatter in indentation results. 9

Rotor Speed = 6500 RPM Flow Rate = 3.0 LPM Rotor Speed = 8000 RPM Flow Rate = 4. LPM Effect of Particle Physical Properties D90 vs Number of Tank Turnovers Crystals: Sucrose, Glycine, Ascorbic Acid Ascorbic Acid Log Glycine Sucrose Log 0

Effect of Particle Physical Properties Size of Atritted Chips in Milling of Different Crystals Sucrose Prior to milling Log Log PVM images Sucrose

Effect of Solids Concentration ( Sucrose milled in IPA at 6500 RPM 3.0 LPM) The ultimate D90 is independent of slurry concentration The rate of breakage increases with particle concentration The dependence of slurry viscosity on solids concentration cannot explain this.* μ m = μ L +.5 ϕ + 0.05 ϕ + 0.0073 e 6.6 ϕ, ϕ = volume fraction Solid Concentration (by weight) 0% % 5% 0% 5% Viscosity of the Mixture (Slurry).04 cp.09 cp.0 cp.35 cp.66 cp *Thomas, David G. 965. Transport Characteristics of Suspension: VIII. A Note on the Viscosity of Newtonian Suspensions of Uniform Spherical Particles. Journal of Colloid Science 0(3): 67 77.

Classical Theories of Milling (Grinding Laws) von Rittinger s model (867): the energy required for size reduction is related to change in surface area. Kick s model (885): the energy required for size reduction is proportional to the ratio of the initial size to the final size: Bond s model (95): the energy required for size reduction depends upon both volume and surface and falls in-between von Rittinger s and Kick s law: de sp = c R dx x de sp = c K dx x de sp = c B dx x 3/ Common Practice: Kick s law is applicable for large particle size (coarse crushing and crushing) von Rittinger s law is applicable to small particle size (ultra-fine grinding) Bond s law is suitable for intermediate particle size (the most common range for many milling processes) von Rittinger s Law 0 Micron 0 mm Bond s Law Kick s Law Griffith (9): reasoned that the fracture strength and its size-dependence is due to the presence of microscopic flaws or cracks in the bulk material. σ f π a f = K c Stress at fracture Crack size Fracture toughness σ f a f 3

Mechanistic Models for Particle Attrition GAHN AND MERSMAN (997) Based on Elastic Mechanism Mechanistic model for attrition loss in crystallizers. Cone shape particle collides with the mixer blade at velocity u. Elastic deformation dominates the process. Model can be rearranged to: V V ~ ρ 4/3 p u 8/3 x H /3 K c GHADIRI AND ZHANG (00) Based on Plastic Mechanism Mechanistic model for single particle impact at velocity u on a hard surface. Cubic particle undergoes edge fracture Plastic deformation dominates the process. Lateral cracks result in breakage. V V ~ ρ pu x H K c CURRENT STUDY Based on Elastic-Plastic Mechanism Mechanistic model for attrition loss by edge collision. Corner of cubic particle collides at velocity u with hard surface. Part of impact energy dissipates due to plastic deformation. The remaining energy causes fracture due to elastic deformation. V V ~ ρ p u H x E K c V = fractured crystal volume x = initial crystal size V = initial crystal volume H = hardness ρ p = crystal density K c = fracture toughness u = impact velocity ϯ C. Gahn and a Mersmann, Theoretical Prediction and Experimental Determination of Attrition Rates, Chem. Eng. Res. Des., vol. 75, no., pp. 5 3, 997. M. Ghadiri and Z. Zhang, Impact attrition of particulate solids. Part : A theoretical model of chipping, Chem. Eng. Sci., vol. 57, no. 7, pp. 3659 3669, 00. 4

Current Mechanistic Model Based on Elastic-Plastic Deformation Cubic particle collides with a hard surface at its corner (edge fracture) The impact energy dissipates causing both plastic deformation and elastic deformation: W impact = W plastic + W elastic V ~ x 3 V ~ l i 3 m = ρ p V Impact Energy W impact Substituting the above terms gives upon rearrangement: a 3 = mu H+ H E W elastic = H E mu H+ H E The elastic energy imparted to the particle is the driving force for fracture. The plastic energy is dissipated locally by deforming the 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 Griffin s Law (9): Fracture happens when σ f π a f = K c σ f is the stress at fracture a f is the flaw length scale K c = Fracture toughness Plastic Energy W plastic mu = ρ p x 3 u H a 3 Elastic Energy W elastic H E a3 H = Hardness E = Elastic Modulus (Young s modulus) Flaw length scale: a f = f(x) Assume linear relationship: a f x Combining these equations yields: Generally H H reduces to: V V ~ ρ p u H x E K c H + H E V V E and the final model ~ ρ p u H x E K c 5

Mechanistic Models vs Classical Laws Current study s (elastic-plastic mechanism) model is equivalent to Bond s law (95) Starting from current study s model: V V ~ ρ p u x / H E K c Setting the specific energy as E sp = u, and rearranging the model gives: E sp ~ E K c V ρ p H x / V Setting particle volume as V ~ x 3 and differentiating ( ΔV ~ dx 3 ~ x dx ): de sp ~ E K c x dx ρ p H x / x 3 = E K c dx ρ p H x 3/ which is similar to Bond s law with n=3/: de sp = c B dx x 3/, and c B ~ EK c ρ p H Mechanistic Models Classical laws Similarity Lawn and Marshal (brittleness index, 979) Gahn & Mersmann (elastic mechanism, 997) Ghadiri & Zhang (plastic mechanism, 00) Kick s law (885) Defines the brittleness index as H K c. de sp = c dx c K x K ~ empirical In-between Rittinger s law and Bond s law Rittinger s law (867) de sp = c dx x 7 4, c ~ K c 3/ ρ p H / de sp = c R dx x, c R ~ K c ρ p H Current study (elastic-plastic mechanism) Bond s law (95) de sp = c B dx x 3, c B ~ EK c ρ p H 6

Cohesive Stress Resisting Fracture Two opposing forces act on the particle: a cohesive force or resistance to fracture due to crystal mechanical properties and a disruptive force due to agitation or particle impact. Assumption: ΔV Disruptive Stress = V Cohesive Stress Then, the cohesive stress can be extracted from the mechanistic models as: Model based on plastic deformation mechanism (Ghadiri & Zhang von Rittinger s law): V V ~ ρ p u K cohesive stress = τ c ~ K c c /Hx H x Model based on elastic deformation mechanism (Gahn & Mersmann in between Bond s & Rittinger s law): ( V V )3/4 ~ ρ p u Disruptive Stress = ρ p u Particle size = x 3/ K 3/ c /H / x cohesive stress = τ c~ K c 3/4 H / x 3/4 Model based on elastic-plastic deformation mechanism (Current study Bond s law): V V ~ ρ p u EK c /H x / cohesive stress = τ c~ EK c H x / 7

Mechanistic Model for Maximum Stable Particle Size, x Breakage occurs when the crystal is exposed to a disruptive stress that exceeds the cohesive stress. In general, the disruptive stress is given by τ D ~ ρ p u where u is the particle collision or impact velocity. The maximum stable particle size, x, occurs when the disruptive stress balances the cohesive stress (τ C τ D ). 3 different cohesive stresses are proposed so 3 different mechanistic models result: Cohesive Model Maximum Stable Particle Size Plastic Mechanism (G&Z) (von Rittinger, 867) x D ~ k c ρ P HD u Elastic Mechanism (G&M) (in-between Bond s & von Rittinger s law) Elastic-Plastic Mechanism (Bond, 95) x D ~ ( x D ~ ( 3 K c ρ P H D 3 4 ) 4/3 EK c ρ P HD ) u 4 u 8/3 8

Disruptive Stress Promoting Fracture In a rotor-stator mixer the disruptive stress τ D ~ ρ p u is due to turbulence causing particle-particle collisions or particle impact with surfaces. Several definitions of characteristic velocity u can be proposed. Model Mechanism DISRUPTIVE STRESS (τ D ) Macroscale Turbulence x ~ l Collision Velocity ~ Rotor Tip Speed τ D ~ ρ p u tip Inertial Subrange Turbulence η x l Collision Velocity ~ Eddy Velocity τ D ~ ρ P u(x) ~ ρ P (ɛx) /3 ~ ρ p u tip ( x D )/3 Energy Dissipation rate = ɛ = Power Mass = Power ρ V DZ V DZ = Volume of Dispersion Zone ɛ N 3 D u tip 3 l is macroscale of Turbulence ~ Rotor Diameter, D η = ( 3 / ) /4 = Kolmogorov Length Scale ~ to 0 m D D = rotor diameter N = rotor speed 9

Mechanistic Model for Maximum Stable Particle Size, x Breakage occurs when the crystal is exposed to a disruptive stress that exceeds the cohesive stress. The maximum stable particle size, x, occurs when the disruptive stress balances the cohesive stress (τ C τ D ). As has been noted, different disruptive stresses and 3 different cohesive stresses are proposed. As a result 3 = 6 different mechanistic models can be developed: Based on u tip COHESIVE MODEL DISRUPTIVE MODEL BREAKAGE MODEL Plastic Mechanism (G&Z) (von Rittinger, 867) Elastic Mechanism (G&M) (in-between Bond s & von Rittinger s law) Elastic-Plastic Mechanism (Bond, 95) Macroscale Model Inertial Subrange Model Macroscale Model Inertial Subrange Model Macroscale Model Inertial Subrange Model x D ~ k c ρ P HD x D ~ ( k c ρ P HD )3/5 x D ~ ( x D ~ ( 3 K c ρ P H D 3 4 3 K c ρ P H D 3 4 x D ~ ( x D ~ ( EK c ρ P HD EK c ρ P HD u tip u tip 6/5 ) 4/3 u 8/3 tip ) /7 u 4/7 tip ) u tip 4 ) 6/7 u /7 tip 6 5 < 4 7 < 7 < 0

Inertial Subrange Models for Predicting Maximum Stable Particle Size x is the size of largest particle (D00) that can survive under the disruptive force imposed by the rotor speed. D95, D90, or D80 can be used instead of the largest particle size. Here, x = D90 is used to compare the mechanistic correlations. Equilibrium data for sucrose, glycine, and ascorbic acid at different rotor speeds are well fit by a line with slope =.6. This 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 4 7 =. 4 and elastic-plastic mechanism which predicts slope of 7 =. 7. 8000 rpm 6500 rpm 6000 rpm 5000 rpm Inline mixer with standard shear gap

Geometric Similarity vs. Local Conditions (Inertial Subrange Models) Analogous to Weber number for drop breakup, a dimensionless number for solid fracture can be defined. It is the ratio of inertial or disruptive force to the cohesive force, and is referred to as a Comminution number (Co): Inertial force Co = Cohesive force The inertial subrange models can also be written in terms of local energy dissipation rate rather than tip speed u tip = N D. Choose x = D90 MODEL BASED ON COMMINUTION NUMBER BREAKAGE MODEL (COMMINUTION NUMBER) BREAKAGE MODEL (DISSIPATION ZONE ɛ) Plastic Mechanism Elastic Mechanism Elastic-Plastic Mechanism Co P = ρ P u tip K c H D Co E = ρ P u tip K c 3 H D 3 4 Co EP = ρ P u tip E K c HD x D ~ (Co P) 3/5 x D ~ (Co E) /7 x ~ ( x D ~ (Co EP) 6/7 x ~ ( k c ρ P H )3/5 K c 3 ρ P H x ~ ( EK c ρ P H )6/7 ɛ /5 ) /7 ɛ 8/7 ɛ 4/7 Geometric Similarity Local Conditions

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 ability 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. D90 D =.6 0 5 Co EP 6/7 3

Inline Unit - Effect of Shear Gap Width Standard Rotor D= 3. mm Standard Shear Gap = 0. mm Sucrose in IPA Small Rotor D= 8. mm Enlarged Shear Gap =.7 mm For the standard inline unit, the initial crystal size is greater than the shear gap width (clearance between rotor and stator). Additional experiments were performed with an enlarged shear gap (smaller rotor) unit. Enlarged Shear Gap Enlarged Shear Gap Enlarged Shear Gap Enlarged Shear Gap Enlarged Shear Gap Standard Shear Gap Standard Shear Gap Standard Shear Gap 4

CFD Simulations & Power Draw Predictions Meshing Strategy: ANSYS Workbench is used for meshing Mesh with 7.8 million cells (6 hexahedral cells across the standard shear gap and 0 cells across the enlarged shear gap). Solution Methodology: ANSYS Fluent - RANS model Sliding mesh simulation Realizable k- model Enhanced wall functions Equal pressure inlet and outlet Five different shear gaps are built and meshed. Simulations are conducted for 5 revolutions and the torque on the shaft is obtained for each simulation. D = 3. mm Standard shear gap D = 8. mm Enlarged shear gap Contours of normalized turbulent energy dissipation rate for Silverson L4R inline mixer with standard and enlarged shear gap at 8000 rpm (normalized by N 3 D of standard shear gap) rotor rotor 5

Inline Unit - Mean velocity field (m/s): Standard shear gap vs enlarged shear gap Standard Shear Gap D = 3. mm Water, N = 8000 rpm, Free Pumping Flowrate = 6 LPM Enlarged Shear Gap D = 8. mm Water, N = 8000 rpm, Free Pumping Flowrate = 7 LPM 6

Silverson L4R Mixer Cooling Unit (TC) Wet Milling of Sucrose in IPA in Standard Batch Mixer Temp Probe RPM/AMP 6000 Sampling Stirre r FBRM Power Draw Data of Padron (00) Rotor Speed Power W N P Square Hole Stator Geometry Number of Holes 9 Dimension of Holes Inner Diameter.6.4.6 mm 8.5 mm 5000 RPM 3.0.3 6500 RPM 50.5.3 8000 RPM 94..3 N P = Power ρ f N 3 D 5 Log 7

Mechanistic Correlation Based on Local ɛ V DZ = Stator Holes Volume + Shear Gap Volume Local ɛ = Power ρ f V DZ Stator Hole Volume Shear Gap Volume Dispersion Zone Volume V DZ Inline Mixer, Standard Shear Gap. ml 0.4 ml.6 ml Inline Mixer, Enlarged Shear Gap. ml.8 ml 4.0 ml Standard Batch Mixer 0.9 ml 0. ml. ml Sucrose All Data Similar to Davies Plot * for liquid-liquid dispersion *Davies, J.T. 987. A Physical Interpretation of Drop Sizes in Homogenizers and Agitated Tanks, Including the Dispersion of Viscous Oils. Chemical Engineering Science 4(7): 67 76. 8

D90 (μm) D90 (μm) D90 (μm) Inertial Subrange Models for Maximum Stable Particle Size Based on local energy dissipation rate, ɛ Plastic Mechanism Elastic Mechanism D90 ~ ( k c ρ P H )3/5 ɛ /5 K c 3 D90 ~ ( ρ P H ) /7 ɛ 8/7 Elastic-Plastic Mechanism D90 = 3.6 ( EK c ρ P H )6/7 ɛ 4/7 D90 ~ ( EK c ρ P H )6/7 ɛ 4/7 9

Breakage Rate Kernel Exponential Breakage Kernel: First order - analogy with reaction rate r A = k 0 e E a RT C A C B k 0 is collision frequency, e E a RT is fraction of collisions with more energy than the activation energy (successful collisions). Based on Coulaloglou and Tavlarides (97)*. Successful collisions have kinetic (disruptive) energy greater than particle cohesive energy: Fraction of Particles Breaking = e τ c τ D Mechanism Plastic Elastic Elastic-Plastic Exponential Kernel g d = Probability of Breakage Breakage Time Breakage Time ~ d /3 ɛ /3 Probability of Breakage ~ e τ c τ D g d = c d /3 ɛ /3 e c K c ρ p H ɛ /3 d 5/3 3/ g d = c d /3 ɛ /3 e c K c ρ p H / ɛ /3 d 7/ g d = c d /3 ɛ /3 e c E K c ρ p H ɛ /3 d 7/6 The time available for breakage is proportional to the lifetime of eddies of order of the particle size. For inertial subrange eddies : t b ~ d /3 ɛ /3 Power law breakage kernels were not as successful at fitting the data. * Coulaloglou, C. A., and L. L. Tavlarides. 977. Description of Interaction Processes in Agitated Liquid-Liquid Dispersions. Chemical Engineering Science 3(): 89 97. 30

Fracture Kinetics (Inline Units) Elastic-Plastic Mechanism of Current Study Log Population balance for milling process : f(d, t) t = f D, t g D β D, D dd D Production g D f(d, t) 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: Loss D90(t) t = g D90 D90(t) Breakage kernel based on elastic-plastic deformation mechanism: g d = c d /3 ɛ /3 e c E Kc ρp H ɛ /3 d 7/6 An optimization algorithm is used to identify c & c D90 t = c ɛ /3 e c E K c ρ p H ɛ /3 D90 7/6 D90 /3 3

Log Log Elastic Mechanism Fracture Kinetics (Inline units) Plastic Mechanism 3

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 have been developed from a balance between disruptive and cohesive forces allowing the functional form of the cohesive forces to be extracted for each model. An inertial subrange model for crystals undergoing elastic-plastic deformation (current study s model) well describes the crystal breakage behavior in rotorstator mixers. 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 rate in the dispersion zone. CFD simulations of the Silverson L4R inline mixer were performed to estimate local power consumption for different shear gap widths and rotor speeds. To model fracture kinetics, a breakage rate kernel has been developed. The mechanistic framework shows promise for application to a broad class of milling devices. 33