<div>Advances in modern research have unveiled numerous fundamental and practical benefits of studying the hydrodynamics of microorganisms. Many microorganisms, especially bacteria, actively search for nutrients via a process called chemotaxis. The physical constraints posed by hydrodynamics in the locomotion of microorganisms can combine with their chemotactic ability to significantly affect functions like colonization of nutrient sources. In this thesis, we investigate the interplay between hydrodynamics and chemotaxis toward dictating bacterial distribution around fluid-fluid interfaces, which often act as a source of nutrition. We approach our problem statements using mathematical models and numerical and/or semi-analytical tools. Our studies are particularly relevant in the context of hydrocarbon degradation after oil-spills.</div><div><br></div><div>We begin by showing that the flow generated by rising oil drops delocalizes dissolved nutrient patches in the ocean, and aids chemotactic bacteria in improving their nutrition (over non-chemotactic bacteria) by 45%. We then move from studying colonization of soluble nutrient patches to colonization around nutrient sources, e.g., oil drops, marine snow. Towards this, we first demonstrate the phenomenon of hydrodynamics-mediated 'trapping' of bacteria around oil drops and show that a surfactant-laden drop can retain an approaching bacterium on its surface for approximately 35% longer times than a clean drop. We also analyze hydrodynamic trapping of bacteria around settling marine snow particles and show how bacteria can collide with and colonize the marine snow, even when the latter moves 10 times faster than the former. In all the cases above, we show how the hydrodynamic interactions are complemented by chemotaxis to enable extremely effective bacterial foraging. We next explore how propulsion mechanisms of microorganisms affect their ability to form biofilms on fluid-fluid interfaces and unveil the hydrodynamic origins behind the tendency of flagellated bacteria to swim parallel to plane surfactant-laden interfaces. Finally, we summarize our results, identify further avenues of research and propose problem statements related to them.</div>

Microorganisms and drops are ubiquitous in nature: while drops can be found in sneezes, ink-jet printers, oceans etc, microorganisms are present in our stomach, intestine, soil, oceans etc. In most situations they are present in complex conditions: drop spreading on a rigid or soft substrate, drop covered with impurities that act as surfactants, marine microbe approaching a surfactant laden drop in density stratified oceanic waters in the event of an oil spill etc. In this thesis, we extract the physics underlying the influence of two such complicated effects (surfactant redistribution and density-stratification) on the motion of drops and swimming microorganisms when they are in isolation or in the vicinity of each other. This thesis is relevant in understanding the bioremediation of oil spill by marine microbes.<div><br></div><div>We divide this thesis into two themes. In the first theme, we analyze the motion of motile microorganisms near a surfactant-laden interface in homogeneous fluids. We begin by calculating the translational and angular velocities of a swimming microorganism outside a surfactant-laden drop by assuming the surfactant is insoluble, incompressible, and non-diffusing, as such system is relevant in the context of bioremediation of oil spill. We then study the motion of swimming microorganism lying inside a surfactant-laden drop by assuming the surfactant is insoluble, compressible, and has large surface diffusivity. This system is ideal for exploring the nonlinearities associated with the surfactant transport phenomena and is relevant in the context of targeted drug delivery systems wherein one uses synthetic swimmers to transport the drops containing drug. We then analyze the motion of a swimming organism in a liquid film covered with surfactant without making any assumptions about the surfactant and this system is relevant in the case of free-standing films containing swimming organisms as well as in the initial stages of the biofilm formation. In the second theme, we consider a density-stratified background fluid without any surfactants. In this theme, we examine separately a towed drop and a swimming microorganism, and find the drag acting on the drop, drop deformation, and the drift volume induced by the drop as well as the motility of the swimming microorganism.</div>