This one-month program will focus on modeling and simulation of the dynamics of interfaces, in particular, with moving contact lines, in fluid and solid systems. The objective of this program is to bring together applied and computational mathematicians, physicists, as well as researchers in applied sciences to present the latest development of mathematical models and numerical methods, and to discuss applications related to the interfacial phenomena in fluids and solids.
Many fluid/solid systems involve interesting and important dynamics of interfaces between different phases. The different phases can be both liquids, such as water and oil, or a liquid phase and a gas (vapor) phase, or a solid phase above the melting temperature and a gas phase. Very often, a boundary, usually a solid substrate, is present and a contact line forms at the place where the three phases meet, such as in the spreading of a droplet on a solid substrate. Modeling and simulation of such systems is a rather challenging task, as it requires the coupling of interface dynamics with the dynamics of the fluid or solid in the bulk. The problem becomes even more challenging in the presence of moving contact lines. For fluid systems, the difficulty stems partly from the fact that classical hydrodynamic equations, the Navier-Stokes equations, coupled with the conventional no-slip boundary condition predict a singularity for the stress that results in a nonphysical divergence for the energy dissipation rate. The same issues exist in the solid wetting/de-wetting problem. The modeling of interfacial dynamics with moving contact lines and the development of efficient numerical methods are the focus of this one-month program. Besides these theoretical issues, we will also have materials scientists involved in the program to discuss industrial applications.