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Title: Mathematical problems on fluid flow over structured surfaces
Author: Kirk, Toby Lawrence
ISNI:       0000 0004 7657 6284
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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In this thesis we study a range of mathematical problems on liquid flow over surfaces that are structured, with an emphasis on modern superhydrophobic surfaces exhibiting apparent slip. One challenge in analysing the flow over such surfaces is to understand the relationship between the particular design and properties of a surface on the microscale, and the effects on the liquid flow on the macroscale. The microscale structure is then replaced with a Navier slip condition and apparent slip length characterising the apparent slippage at the surface. Another challenge is to determine the impact of this model on different flows, and how it can be used to influence dynamics. We consider two distinct important scenarios of substrate structuring in this thesis. In part I, we study gravity-driven film flow down an incline with an emphasis on heterogeneous superhydrophobic coatings and their passive influence on the interfacial dynamics and stability. The structuring varies in space, and the apparent slip length is prescribed. A set of long-wave model equations are derived, and the consequences of several stick-slip patternings (some regions of no-slip and some of slip) are analysed. In part II, we consider pressure-driven flow in microchannels where, due to the size of the channels, the superhydrophobic structuring has to be resolved in detail, and the apparent slip length is not prescribed but found from the solution, and it is used to characterise the slippage of a given structuring. Emphasis is placed on the case of a periodic array of parallel ridges and their application to direct liquid cooling. The slip length and convective heat transfer quantities depend greatly on the particular geometry of the channel and the structuring, and we quantify their dependence on several geometrical and thermophysical (such as Marangoni or thermocapillary) effects using asymptotic theory.
Supervisor: Papageorgiou, Demetrios Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral