Theoretical analysis of the dynamics of coalescence

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Understanding the coalescence (and breakup) of drops and bubbles is a vital ingredient in many multiphase flow problems in industry, developing microfluidic technologies and the environment. Examples include oil/gas extraction, inkjet printing, microfabrication and the atmosphere/ocean exchange of CO2. Coalescence is also mathematically interesting as an example of a class of free-boundary problems where the change in the topology of fluid volumes is accompanied by singular, or nearly singular, behaviour driven by the action of surface tension on the highly curved meniscus. The project will use theoretical, numerical and asymptotic methods to analyse the dynamics of this critical phenomenon and develop new solutions to the governing equations. Possible problems to be addressed include: To analyse the initial deformation of two drops when van der Waals attraction first overcomes surface tension. To develop understanding of the role of the external fluid trapped in the interfacial cusp. To develop a matched asymptotic analysis of the boundary-layer structure and wake around a rapidly expanding contact meniscus. Throughout, our solutions will be motivated by, and compared with, observations from recent laboratory experiments.