Effects of bead packing limit concentration on microhydrodynamics-based prediction of breakage kinetics in wet stirred media milling

Development of a Semi-Mechanistic Modeling Framework for Wet Bead Milling of Pharmaceutical Nanosuspensions

“…, as per results from a study completed at NJIT comparing milling rates of crosslinked polystyrene (CPS) beads to YSZ beads [29,48,49]. CPS beads in this study were noted to have a density of 1040 kg/m 3 .…”

“…Equation (3) shows that the apparent breakage rate constant k j equals the pre-factor in front of t; one may consider A * j a as the true breakage rate constant because V m (1 − c)t/V tb appears to be the effective milling time in recirculation milling, also known as mean residence time of the circuit (mill and holding tank). According to the microhydrodynamic theory [28,29,59], the average frequency of drug particle compressions between the beads a is calculated by multiplying the probability of a single drug particle to be caught by the beads p and the average oscillation frequency of a single bead ν, and is a function of bead material density ρ b , Poisson's ratio PR b , Young's modulus YM b , and diameter D b , as well as the granular temperature θ, which is dependent on both operation-design variables and drug suspension properties such as apparent shear viscosity (refer to Appendix B for the principal equations of the microhydrodynamic theory). Inserting a (refer to Equation (A13) in Appendix B) into Equation (3), we obtain Equation ( 4), or Model A, which is the most general microhydrodynamics-based model for the prediction of the particle size evolution during wet bead milling.…”

“…The value of 1.39 found for DP1 could be due to a tendency to aggregate at certain mill scales, which takes longer than expected to break down. Bead loading BL has been shown to be the most impactful parameter for particle breakage in the literature [29,47,48]. An increase in BL increases the number concentration of the beads and the value of the radial distribution function at contact, decreases the inter-bead distance, and dramatically increases the number of bead-bead collisions, which ultimately increases the frequency of drug particle compressions and the apparent breakage rate constant [20,29].…”

“…Density is an important property of the bead materials as it directly affects the energy input to the process, and therefore collision frequency and stress [29,48]. A detailed microhydrodynamic analysis suggests that because these have higher density, Yttriumstabilized zirconia (YSZ) beads induce more frequent and forceful collisions than crosslinked polystyrene (CPS) beads, which favors drug particle breakage as signified by If the process stays within 56-90% bead loading, then the simple cubic term on bead loading is appropriate (i.e., N 2 = 3), but in excess of 90% bead loading, a more complex term instead of BL N2 is needed, as shown in Equation (11).…”

“…where θ is the granular temperature defined as one third of the bead-milled suspension relative mean-square velocity, R diss is the effective drag coefficient, e is the restitution coefficient for the bead-bead collisions, and g 0 is the radial distribution function at contact. In a more comprehensive microhydrodynamic model developed by Guner et al [29], the following Lun model [77] was used for g 0 :…”