An arbitrary Lagrangian-Eulerian method for interfacial flows with insoluble surfactants

Interfacial flows, fluid flows involving two or more fluids that do not mix, are common in many natural and industrial processes such as rain drop formation, crude oil recovery, polymer blending, fuel spray formation, and so on. Surfactants (surface active substances) play an important role in such processes because they significantly change the interfacial dynamics.; In this thesis, an arbitrary Lagrangian-Eulerian (ALE) method has been developed to numerically simulate interfacial flows with insoluble surfactants. The interface is captured using a coupled level set and volume of fluid method. To evolve the surfactant concentration, the method directly tracks the surfactant mass and the interfacial area. The surfactant concentration, which determines the local surface tension through an equation of state, is then computed as surfactant mass per interfacial area. By directly tracking the surfactant mass, the method conserves the surfactant mass exactly. To accurately approximate the interfacial area, the fluid interface is reconstructed using piecewise parabolas. The evolution of the level set function, volume fraction, interfacial area, and the surfactant mass is performed using an ALE approach. The fluid flow is governed by Stokes equations, which are solved using a finite element method. The surface forces are included in the momentum equation using a continuum surface stress formulation. To efficiently resolve the complex interfacial dynamics, interfacial regions of high surface curvature, and near contact regions between two interacting interfaces, the grid near the interface is adaptively refined.; The method is extendible to axisymmetric and 3D spaces, and can be coupled with other flow solvers, such as Navier-Stokes and viscoelastic flow solvers, as well. The method has been applied to study the effect of surfactants on drop deformation and breakup in an extensional flow. Drop deformation results are compared with available experimental and theoretical results in the literature. The dynamics that guide the effect of surfactants on drop deformation are revealed by examining the variable surface tension, the Marangoni force, and the surfactant concentration profiles. This study will contribute to improved understanding and control of processes such as polymer blending, fuel spray formation, crude oil recovery, and so on.