Mixing of viscous immiscible liquids. Part 1: Computational models for strong-weak and continuous flow systems

Initial mixing of viscous immiscible liquids occurs by stretching and foldi ng of large blobs on a global scale; later stages are controlled by repeate d stretching,, folding, breakup, and coalescence of individual filaments or drops at local or homogeneous flow scales. There is little hope of account ing for every detail as the mixing process evolves from the initial to fina l stages. Two models are presented: the first model (Mixing I) is suited fo r batch systems where decomposition into weak and strong flow regions is ap propriate. the second model (Mixing II) is suited for continuous flow syste ms and is intended to be used in conjunction with a fluid mechanical model of the flow. The models presented here use only the most important physics of the local processes while making a connection between the overall global flow and the local dominated processes. The models calculate changes in mo rphology or drop size distribution due to changes in material and process p arameters. Two aspects previously ignored are highlighted: formation of sat ellite drops upon breakup and distributions of stretching leading to wide d istributions of length scales. Similar trends are obtained for both Mixing I and Mixing II models. Results indicate that there is an exponential decrease in the volume averag e size with time (or distance along the mixer in the case of a continuous m ixer). The average drop size decreases with increase in drop viscosity or t he dispersed phase viscosity and with decrease in the interracial tension, These results are in qualitative agreement with experimental data. The effe ct of reorientations in the continuous mixer is found to accelerate the rat e of dispersion, and about five reorientations is found to be optimal, The spatial distribution of average drop sizes obtained for Mixing II shows tha t larger drops are concentrated in the lower shear rate regions. (C) 2001 E lsevier Science Ltd. All rights reserved.