DROP BREAKUP IN THE FLOW-THROUGH FIXED-BEDS VIA STOCHASTIC SIMULATIONIN MODEL GAUSSIAN FIELDS

Shaqfeh and Koch have shown that the how through a dilute disordered f ixed bed of fibers produces lame polymer conformation change beyond a certain critical flow rate [J. Fluid Mech. 244, 17 (1992)]. We now exa mine the effect of this flow on the shape and breakup of viscous drops . Because the flow through a dilute fixed bed is equivalent to a certa in anisotropic Gaussian flow field, we follow our previous paper and r eproduce a model of the flow through a spectral expansion where the wa ve number vectors are chosen from statistical distributions which ensu re that the desired velocity field will be realized [Phys. Fluids 9, 1 222 (1997)]. We examine the dynamics of model drop shapes, averaged ov er the Gaussian statistics of the flow field, by synthesizing a large number of flow realizations. The drop surface is modeled using the fir st, second, and third order small deformation theories which can accur ately predict critical conditions in classical strong flows. While the first order model yields a bounded average drop shape for all flow co nditions, the second and third order models demonstrate that the flow through fixed beds is indeed ''strong'' since beyond a certain value o f the pore-size capillary number, Ca similar to 0.15, large average dr op deformation occurs and the average drop shape becomes unbounded ('' drop breakup''). This critical condition is determined for various vis cosity ratios and fixed bed particle volume fractions. Similar to a si mple shear flow, we find that there is a critical viscosity ratio, chi similar to 2.5, beyond which breakup is not observed in the fixed bed for any Ca. In addition, the critical condition is shown to depend he avily on the transient nature of the flow in the bed since approximate ly half of the flow fields in which drop breakup occurs would not brea k an initially spherical drop ar any Ca if they were steady. For super critical capillary numbers, we define conditions under which the unbou nded drop shapes fragment into smaller droplets and we examine the dro p breakup rates as a percentage of the drop population. (C) 1997 Ameri can Institute of Physics.