Çözünür yüzey aktif madde içeren çok fazlı akışların arayüz izleme metodu ile modellenmesi

Surfactants are chemical substances that can accumulate on interfaces and lower theinterfacial tension. The accumulation of surfactant at the interface between two fluids maysignificantly alter the dynamics of a multiphase flow. Nonuniform distribution of surfac-tant can cause large variations on the mechanical response of the system and leads to thenonuniform distribution of capillary (normal) and Marangoni (tangential) stresses which cansignificantly affect the deformation of drops and even may result in breakup. In this thesis,a finite-difference/front tracking method is developed for computations of interfacial flowswith soluble surfactants to understand the effects of surfactants on a strongly deforminginterface. Surfactant transport equations of the bulk and interface surfactant concentrationsare solved together with the incompressible Navier-Stokes equations. A nonlinear equationof state is used to relate the interfacial tension to surfactant concentration at the interface.In order to validate the numerical algorithm, several simple test cases are considered andthe numerical results are found to be in a good agreement with the analytical solutions.The method is then applied to the cleavage of a droplet by surfactant - a problem proposedby Greenspan (1977,1978) as a model for cytokinesis of biological cells.Keywords: Soluble surfactant, front-tracking method, droplet cleavage.iv