Executive Summary : | Motion of bubbles and drops arrises in various industrial applications. It is very important to study the effect of various aspects that are associated with motion of drops. In order to study these effects, the governing equations are required. The well known Navier-Stokes equations are used to describe flow of a fluid. The present project is aimed to study the effect of Marangoni stresses and interfacial viscosity on migration of surfactant-laden droplets in transient flow. Studies pertaining to migration of single phase drops have been carried out owing to their importance in diverse fields of science and engineering. Effect of various aspects such as thermocapillary migration, Marangoni effect, effect of electric field, interfacial viscosity etc. Much of the literature available on the aforementioned topics have dealt with the migration and cross-stream migration of an isolated drop and its deformation under the steady state condition. Some of the investigators have reported on the cross-stream migration of drops in Poiseuille flow. In the current project, we would like to address the effect of Marngoni stresses that are caused due to variation in temperature and the presence of surfactant on the drop surface and interfacial rheology on motion of a droplet in transient viscous flow. The equations that will govern the hydrodynamics, heat transfer and transport of surfactant are unsteady Stokes equations, unsteady conduction equation and unsteady surfactant transport equation. A solenoidal decomposition technique will be used to study the hydrodynamic problem. We use the method of regular perturbation for low surface P\'{e}clet numbers $Pe_{s}$, where $Pe_{s}$ is taken as perturbation parameter and solve the problem up to a second-order approximation. The solutions for high surface P\'{e}clet number will also be discussed. Our study will shed lights on the importance of having transient behavior in the governing equations leading to the migration and other aspects of droplet motion. |