Numerical methods and analysis for interfacial fluid flow with soluble surfactant

New Jersey Institute Of Technology, Newark NJ

Investigators

Abstract

This project investigates fundamental problems that are motivated by applications to surfactant-mediated flow. The theoretical approach has the potential to be adapted to a wider variety of practical situations that are similar from a mathematical point of view. Using this approach, the project investigators have recently begun the development of a fast and accurate hybrid numerical method to study the effects of solubility of surfactant on the two-phase flow of immiscible fluids in the practically important but theoretically challenging limit of large Peclet number or slow diffusion. Surfactants influence the dynamics of fluid mixtures by altering the surface tension at interfaces between immiscible fluids and are energetically favored to remain on an interface. However, in many examples the slow diffusional mobility of a surfactant that is soluble in the bulk flow near to but not on an interface can exert an important influence on the interface dynamics. The large bulk Peclet number limit of this investigation introduces a separation of spatial scales that presents a substantial challenge for traditional numerical methods. The conceptual underpinning of the approach taken here combines analytical, singular perturbation techniques in the small diffusion limit with fast and accurate numerical methods for two-phase interfacial flow. An important benefit of this approach is that highly accurate surface-based methods, such as the boundary integral or boundary element method, can be adapted to the study of surfactant solubility. Without the treatment that is under development by the investigators these methods do not apply. The project is expected to develop innovative theoretical models and numerical methods for the analysis and simulation of surfactant-mediated drop breakup and tip-streaming with soluble surfactant. It will develop new, fast, efficient and accurate numerical methods that are expected to be useful to scientists and engineers studying emulsion formation and stability as well as emerging microfluidic applications that range from chemical processing techniques to advanced medical applications. An additional and important impact of the project is the education and training of graduate students and postdoctoral fellows. The interdisciplinary training they receive on this project will be valuable preparation for a range of careers in mathematics and science.