Executive Summary : | Active matter, a field of study involving biological microorganisms, has gained significant attention in recent years due to its sophisticated dynamics. This field encompasses various systems such as bacteria, algae, E. Coli, cell colonies, synthetic colloidal motors, and flocks of birds. The study of active matter has led to the development of self-propulsion of catalytic particles in viscous flows, which can be used to model active matter. These self-propelled artificial swimmers are used for drug delivery to areas of inflammation in the human body. The project aims to study chemically active droplets in viscous flows, considering their potential biomedical applications. It is known that solid phoretic swimmers can self-propel under shear or gravitaxis when exposed to an externally imposed flow. The project will explore the perpendicular direction where the same isotropic swimmer is exposed to an externally imposed flow using the Advection-Diffusion equation and Stokes equations governing the flow. The main focus of this project is to determine the magnitude of the particle stresslet, which corresponds to the Einstein viscosity for a dilute suspension. The non-Newtonian properties of an active emulsion and their consequences will also be explored. The project aims to address a challenging, contemporary physical problem using mathematics as the language to demonstrate these results. |