James Sprittles (Mathematics Institute, University of Warwick, UK). Modelling & Computation of Capillary Microflows.

Understanding the formation of liquid drops, their interaction with solid surfaces and their collisions with surrounding drops is the key to optimising a whole host of processes ranging from 3D printing to cloud formation. Accurate experimental observation of these phenomena is complex due to the small spatio-temporal scales or interest and, consequently, mathematical modelling and computational simulation become key tools with which to probe such flows.

Drop formation, dynamic wetting and coalescence are all so-called 'singular' capillary flows, in which classical modelling approaches lead to infinite values of flow variables and computation becomes increasingly complex.  In this talk, I will describe the mathematical models proposed for this class of flows and the techniques which have been used to obtain both analytic and computational results. Simulations will then reveal the applicability of similarity solutions and new unexpected flow behaviours.

Finally, I will describe the development of models to describe gas microfilms that appear in both drop collisions and in dynamic wetting.  These microfilms cannot be described by the Navier-Stokes equations and instead require the development of a model based on the kinetic theory of gases.  Simulation results obtained using this model will be discussed and compared to experimental data that highlight the influence of the surrounding gas.