Mathematical modelling of fluid flows in textured and autophoretic microchannels
File(s)
Author(s)
Game, Simon
Type
Thesis
Abstract
Further advancement in the field of microfluidics relies on the improved understanding and exploitation of fluid phenomena at the micro-scale. Such phenomena may influence the design of microfluidic devices, to achieve desirable effects in the fluid. This thesis specifically concerns itself with superhydrophobic drag reduction and self-diffusiophoretic (autophoretic) motion. The former can be achieved in practice by texturing microchannel boundaries with grooves parallel to the flow direction. Such grooves contain an inert gas and/or vapor, the low viscosity of which results in apparent slip flow in the liquid phase. With applications of textured microchannels including direct liquid cooling of microelectronics, there is a need for predictive mathematical models that can be used for design and optimization. This thesis is comprised of the motivation, development and discussion of such models, including analysis and numerical computations. In the context of textured channels, we study the effects of gas viscosity (interfacial shear), meniscus protrusion, channel aspect ratio, thermal transport and slowly varying three-dimensional geometry and show how to generate accurate predictions using Chebyshev collocation and domain decomposition numerical methods. In addition, we use the same numerical formulation to study autophoretic (self-diffusiophoretic) channels, in the presence of advection. Such channels rely on a chemical interaction between its boundaries and a solute (e.g. adsorption, repulsion) to generate an effective slip velocity at the solid-liquid interface proportional to the concentration gradient. We study the general case of corrugated boundaries, showing how advection can lead to flow enhancement, or flow reversal. We also study channels with flat boundaries, and demonstrate that advection can lead to the spontaneous emergence of non-trivial flow fields.
Version
Open Access
Date Issued
2018-06
Date Awarded
2019-01
Copyright Statement
Creative Commons Attribution NonCommercial Licence
Advisor
Papageorgiou, Demetrios
Keaveny, Eric
Sponsor
Imperial College London
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)