Coupling between homogeneous rate processes and fluid deformation rate: Brownian particle coagulation in a rapidly dilating solvent

Abstract

P. Curie's principle applied to an isotropic medium of arbitrary EOS does not preclude coupling between homogeneous (chemical,…) rate processes and local fluid dilation rate. Yet, practical examples of this coupling have largely remained unexplored. Using recently studied supercritical “antisolvent” (SAS) examples for precipitating high-value particles (e.g., pharmaceuticals), we suggest that the characteristic dilation time t_V of the swelling solvent can be small enough to noticeably reduce the operative coagulation rate “constant,” β. Moreover, we expect that this coupling can occur under conditions in which postnucleation Brownian coagulation must be accounted for in predicting the efficacy of such micron-sized powder production methods. Accordingly, a rational approximate theory for this rate constant “correction factor,” β/β(0), is proposed here, emphasizing the applicable limit of continuum Brownian diffusion control. We also present a preliminary assessment of the particle size distribution (PSD) consequences of these “corrections,” implying strategies to reduce both mean particle size and PSD spread. Possible generalizations are indicated. © 2010 American Institute of Chemical Engineers AIChE J, 2011