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Surfactant solubility along with inertia leads to interesting non-monotonic drop dynamics which remains unexplained. The goal of this research is to study the dynamics of drops in the presence of surfactant solubility and inertia in channels of varying cross-sections. We are conducting a combined experimental and numerical study on the buoyancy-driven motion of Newtonian drops in confined geometries such as a Hele-Shaw cell (two-dimensional flow), a circular tube (three-dimensional axisymmetric flow), and a rectangular channel (three-dimensional flow) in the presence of soluble surfactants at finite Reynolds numbers.  This study will increase our understanding of how fluid particles in confined domains respond to stresses in the presence of surfactants which are often added as compatibilizers or emulsifiers in a number of applications, such as enhanced oil recovery, food processing, and polymer blending.

During this year, we made progress in the numerical as well as experimental aspects of the project.  Numerically, a hybrid volume-of-fluid (VOF) technique in conjunction with a front-tracking scheme was implemented to study drops in a tube. Non-linear effects associated with the surfactant physical chemistry were included by using the Langmuir adsorption isotherm and surface equation of state that incorporates the effect of monolayer saturation. This scheme provides a precise description of the interface and allows us to simulate strong deformations at large density and viscosity ratios.  In the absence of surfactants, the drop deformation and mobility show good agreement with experimental data.  Specifically, for small drop sizes, as the drop size increased, the drop terminal velocity increased.  At moderate drop sizes, the drop terminal velocity decreased due to wall effects and reaches a plateau velocity.  For large drops the terminal velocity was independent of drop size with a constant film thickness.  For drops with large inertia, the characteristic negative curvature is observed at the rear of the drop.  In the presence of insoluble surfactants, surfactants accumulate at the rear of the drop generating large Marangoni stresses.  This results in reduced drop mobility for all drop sizes.  If the surfactants are soluble, mass transfer to and from the interface reduces the surfactant concentration gradients along the interface resulting in smaller Marangoni stresses which increase the drop mobility.  Experiments were also conducted with air bubbles rising in square and rectangular channels filled with glycerol-water solutions and silicon oils. Surfactants with different adsorption kinetics such as Triton X-100, sodium dodecyl sulfate (SDS), Tween-80, and Span-80 at various concentrations were used.  It was observed that at low surfactant concentrations, as the surfactant concentration was increased, the terminal velocity of the bubbles reduced and the peak in the velocity-volume curve shifted to higher bubble volumes.  Increasing the surfactant concentration to near CMC values remobilized the bubbles.