Deformation of Fluid and Solid Interfaces in Viscous Flow

Abstract

This dissertation covers a variety of problems in viscous fluid mechanics, with a uniting theme of deformable interfaces. The work is divided into three separate sections exploring three distinct geometries: a liquid film on a rough surface, a liquid bridge between two flexible solids, and a flexible fiber in a confined viscous flow.

In the first section, we explore the dynamic of a liquid film on a rough or patterned surface. A liquid-infused surface like this displays many of the same useful properties as conventional gas-cushioned superhydrophobic surfaces. However, liquid-infused surfaces may drain due to an external shear flow, causing the surface to lose its advantageous properties. Using experiments and analytical theory we examine shear-driven drainage of these surfaces, with the goal of understanding and thereby mitigating this failure mode. On patterned surfaces exposed to a known shear stress, we find that a finite length of the surface remains wetted indefinitely, despite the fact that no physical barriers prevent drainage. We then consider the effects of physical barriers, and explore how they modify the drainage of the film. We conclude this section with a study of how drainage can be prevented through the use of chemical patterning, and a brief extension where we propose a new technique for measuring the velocity profile of a thin film flow.

In the next section, we consider how a wetting droplet trapped in the thin gap between two elastic bodies will deflect the bodies towards one another. The deformation increases the total capillary adhesion force between the bodies by increasing the contact radius and narrowing the gap height. We present experiments, scalings, and closed-form solutions that describe the deformation.

In the final section, we present a mathematical model and corresponding series of microfluidic experiments examining the flow of a viscous fluid past an elastic fibre in a three-dimensional channel. Experiments show that there is a linear relationship between deflection and flow rate for highly confined fibers at low flow rates, which inspires an asymptotic treatment of the problem in this regime. The analysis yields insight into the competing effects of flexion and leakage.