Overview
My interests are in applied mathematics and in particular fluid dynamics problems involving moving interfaces. I use modelling, analysis and computations to study problems coming from a variety of applications centering on multifluid flows in microfluidic geometries. Diverse physical effects are included in the models and we have several projects studying the presence of Marangoni forces due to surface tension gradients resulting from the presence of soluble or insoluble surfactants, as well as electrostatic and electrokinetic effects that can be very important in micro- or nano-fluidic applications. Mathematically, the models are reduced systems of the full equations of motion (the Navier-Stokes equations) and typically lead to one- or two-dimensional nonlinear PDEs which are of the "active-dissipative" type due to the presence of long wave instabilities and short wave damping. In many situations low dimensional "interfacial chaos" results and our aim is to understand such qualitative aspects of the solutions via analysis and construct solutions quantitatively via accurate and efficient simulations. A parallel aspect of the work is the evaluations of reduced asymptotic models by comparison with direct numerical simulations of the Stokes and Navier-Stokes equations.