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

Abstract

Initial mixing of viscous immiscible liquids occurs by stretching and folding of large blobs on a global scale; later stages are controlled by repeated stretching, folding, breakup, and coalescence of individual filaments or drops at local or homogeneous flow scales. There is little hope of accounting for every detail as the mixing process evolves from the initial to final stages. Two models are presented: the first model (Mixing I) is suited for batch systems where decomposition into weak and strong flow regions is appropriate; the second model (Mixing II) is suited for continuous flow systems 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 morphology or drop size distribution due to changes in material and process parameters. Two aspects previously ignored are highlighted: formation of satellite drops upon breakup and distributions of stretching leading to wide distributions 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 average size with time (or distance along the mixer in the case of a continuous mixer). The average drop size decreases with increase in drop viscosity or the dispersed phase viscosity and with decrease in the interfacial tension. These results are in qualitative agreement with experimental data. The effect of reorientations in the continuous mixer is found to accelerate the rate of dispersion, and about five reorientations is found to be optimal. The spatial distribution of average drop sizes obtained for Mixing II shows that larger drops are concentrated in the lower shear rate regions.