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Droplet dynamics on heterogeneous surfaces

Groves, Danny 2019. Droplet dynamics on heterogeneous surfaces. PhD Thesis, Mathematics.
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Abstract

The motion of a liquid drop over solid surfaces is easy to visualise, yet, from a scientific standpoint is inherently challenging to study. This arises from the multi-scale nature of the governing physics, including gravity and capillarity in the macro-scale, and slip close to the contact line. This thesis studies droplets through a combined numerical and analytical approach to extract physical insights in complex scenarios. Using the lubrication approximation, the Stokes equations are combined with the appropriate boundary conditions to derive a non-linear partial differential equation for the fluid thickness. To determine how the droplet evolves in time, we develop solution methods to the full equation using a pseudospectral collocation approach in both two-, and three-dimensional settings. Using the boundary integral formulation we also develop a hybrid method which is combined with the analysis to offer an attractive compromise between the low-order models and full-scale computing. Analytical progress is made in the slow spreading and negligible gravity regime by utilising the method of matched asymptotic expansions which has been successful in related works to derive low-order approximate models that predict the solutions of the full equations. Specifically, we consider droplets spreading over flat and horizontal substrates with mass transfer that may occur at free surface, or by evaporation which is maximised close to the contact line. Extensions are also made by considering topographically varying substrates with sufficiently small amplitudes. The outcomes of the analysis are contrasted to simulations of the governing equation for a number of cases. We present convincing numerical evidence that suggest that the reduced models can replace the full model within their domain of validity, and thus mitigate considerably the associated high computational costs required for such simulations, at the same time, uncover experimentally observed phenomena, such as pinning, stick-slip, and hysteresis-type effects induced through surface features.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
Funders: EPSRC
Date of First Compliant Deposit: 28 October 2019
Last Modified: 06 Mar 2020 12:22
URI: http://orca.cf.ac.uk/id/eprint/126327

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