Modeling Droplets and Emulsions with Insoluble Surfactant Flowing Through Complex Environments

Multiphase flows are so common in everyday life as to go unnoticed, yet they have eluded rigorous characterization, especially in confined settings and under the influence of surfactant. The objective of the present work is two-fold: (1) to develop high-accuracy and extensible computational tools to study confined and contaminated emulsions, and (2) to elucidate new physics that remain difficult or impossible to probe using other experimental or numerical techniques. Mathematical formulations and numerical algorithms are developed in the context of the boundary-integral method, and applied to a wide range of systems and fluid properties, including droplets interacting with fibrous and non-axisymmetric particles, and high-density contaminated emulsions flowing through a porous medium.

A boundary-integral formulation is introduced that enables droplets to interact with arbitrary smooth surfaces in tight-squeezing conditions. The behavior of droplets flowing between and around cylindrical particles is simulated, with respect to capillary number, viscosity ratio, drop size and solid-particle aspect ratio. Flow rectification is demonstrated for constrictions that are nonsymmetric with respect to flow reversal. The internal circulation within droplets is analyzed as a dynamical system and visualized by introducing an algorithm for the 3D advection of a `material surface' with an arbitrary boundary. While regular flow is predicted within drops trapped between two cylindrical particles, chaotic advection within drops trapped in a three-sphere constriction suggests superior mixing properties.

The interfacial behavior of surfactant-laden drops squeezing through a three-sphere constriction is considered. Sharp surfactant-concentration gradients form during various stages of the squeezing process. Even a low degree of contamination significantly decreases the critical capillary number for droplet trapping. Increasing the degree of contamination affects surface mobility and further decreases the critical capillary number as well as drop squeezing times, up to a threshold above which the addition of surfactant negligibly affects squeezing dynamics. Finally, a high-density emulsion squeezing through a periodic array of spheres is considered. Away from critical squeezing conditions, the presence of surfactant increases squeezing times, while the inverse correlation is observed near the critical capillary number.

Full pdf - https://www.colorado.edu/mse/node/521/attachment