Gravity-induced flows: buoyancy-driven flows and interfacial thin-film flows

Abstract

Gravity is a ubiquitous force that induces a series of flows.In this Dissertation, I will discuss two aspects of gravity-induced flows using theory and experiments: the buoyancy-driven flows in miscible liquids and the gravitational draining liquid thin-film flows in air. I will first show a pattern formation system induced by the buoyancy-driven flow: the layering in a latte.Distinct patterns form after pouring hot espresso into a glass of warm milk. By experimentally identifying critical conditions to produce the layering, the mechanics of the layering is related to double-diffusive convection, which is commonly discussed in oceanography. The mixing dynamics during the pouring are further modeled and studied. I will then show how to control the layered structure by pouring and then employing this single-step process to produce soft, layered materials. I will then focus on the gravitational draining film on a vertical plate.I will first show the Marangoni rising flow on a draining film when the draining film contacts a liquid bath with surfactant. The thickness profile of the draining film determines the dynamics of the rising flow. Next, I will show a self-similar film structure, inspired by the observation of a draining film near a vertical edge. The nonlinear partial differential equation (PDE), which describes the film profile with three independent variables, can be converted to an ordinary differential equation (ODE). Finally, together with the structure of the draining film, I will show the gravitational spreading of a liquid on a funnel and a bowl. The geometries on where the liquid converges cause different spreading dynamics and induce new thresholds for fingering instabilities.