University of Reading
Department of Mathematics
Dr. Alex Lukyanov

Research Interests

In any multiscale problem sooner or later one has to deal with the dilemma of separation between the bulk and the boundary to formulate a mathematical problem suitable for modelling, that is to deal with formulation of boundary conditions. The conditions at the boundary play a crucial role in the selection of appropriate solutions. One particular form, though very common in every day life experience, of boundary conditions in hydrodynamics is related to the effects of surface tension or capillarity. The interfaces and effects of capillarity, in general, occur due to long-range, electromagnetic by nature, interactions between molecules constituting the phases. As a result, a thin interfacial layer of liquid molecules (about 1 - 3 nm), with different from the bulk matter macroscopic properties, appears. Despite its tiny, molecular dimension, this interfacial layer manifests macroscopically in a form of the strong surface force, the effect which is known as the surface tension. In applications, surface tension effects are central to almost any modern technology, especially in microfluidics and nanofluidics, where the surface to volume ratio increases. There are many unresolved fundamental issues associated with the formation and structure of interfacial layers, such as their life-time, for example, which are vitally important in applications. The systems that I examine vary from the moving contact line problem to curtain coating and thin film flows over structured substrates. Some research topics, I am interested in, are summarized here.

Dynamic wetting in microfluidics;   Hydrodynamic assist and curtain coating;   Thin film flows over structured substrates;   The moving contact lines;   Formation and structure of interfacial layers ;   Molecular dynamics simulations of interfacial layers;   Slip and no-slip behaviour;   Transport in disordered, porous systems; Mathematical aspects of the superfast non-linear diffusion regime.