Mathematical modelling of electrohydrodynamic flows

Student thesis: Doctoral Thesis


This thesis concerns the analytical and numerical investigation of a bilayer of liquid and gas contained between two electrodes. The work contained in this thesis uses the Taylor-Melcher leaky dielectric model to describe electrostatic effects, which are coupled with the hydrodynamic effects through the normal and tangential stresses. The long-wave approximation is used to obtain a model that consists of two coupled, nonlinear partial differential equations for the interfacial height and the charge density. Several limiting cases of this long-wave model are considered. The first limiting case is when the liquid is perfectly conducting, the second limiting case is when the liquid and gas have high conductivities, and the third limiting case is when the liquid and gas are both perfect dielectrics. The first two limiting cases and the full long-wave model are investigated in detail. This analysis shows that a variety of different behaviours can occur, i.e. levelling, upper contact, thinning, and touchdown behaviour, which are explored, both analytically and numerically. In particular, levelling behaviour is described by linear stability theory, similarity solutions are found for the interface during the upper contact and thinning behaviours, and an extensive numerical investigation of touchdown behaviour is performed. A systematic numerical investigation of parameter space for the long-wave model and the limiting cases is performed. In particular, the regions of parameter space in which each behaviour occurs, and the transitions between these regions, are investigated. Coupled with an investigation of the interfacial dynamics of the different behaviours, this work allows for a more complete understanding of the behaviour of electrohydrodynamic flows.
Date of Award24 Sep 2021
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorStephen Wilson (Supervisor) & Alexander Wray (Supervisor)

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