Fry, H.M.; (2011) A study of droplet deformation. Doctoral thesis , UCL (University College London).

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Abstract

In both engineering and medical applications it is often useful to use the knowledge of the conditions under which adhering liquid droplets appear, deform and interact with surrounding fluids, in order to either remove or create them. Examples include the de-wetting of aircraft surfaces and the process of injecting glue into the bloodstream in the treatment of aneurysms. The particular types of models discussed here theoretically are based on droplets with a large density compared to that of the surrounding fluid. Using this ratio as a small parameter, the Navier-Stokes equations may be simplified, and in view of the nature of the interfacial bound- ary conditions the droplet may be considered as solid to leading order at any given time step for a certain time scale. In the first part of the thesis, we study an example of an initially semicircular droplet adhering to a wall for low-to-medium Reynolds numbers (along with simpler test problems). We numerically determine unsteady solutions in both the surrounding fluid and the droplet, coupling them together to obtain a model of the droplet deformation. Analysis within the droplet leads to the identification of two temporal stages, and the effect on large-time velocities is discussed. The second part of the thesis sees a similar approach applied to a surface mounted droplet completely contained within the boundary layer of an external fluid for high Reynolds numbers. The two-fluid interface for such a regime is analysed using a lubrication approximation within the viscous sublayer of a triple-deck structure. Finally, the lubrication is abandoned and we present a fully non-linear solution in air over any obstacle shape, as well as a two-way interacting model of droplet deformation, capable of simulating the free surface of the droplet as it becomes severely distorted.

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