GALCIT Colloquium

Continuum analysis of many fluid problems are marred by the development of discontinuous flow fields or introduction of singular behavior. Examples include shocks, contact surfaces, vortex sheets, wall-fluid or fluid-fluid interfaces, and moving contact lines. In this talk I will provide a systematic formulation and introduction of surfaces and lines of discontinuities in an otherwise regular flow. I show that in many cases a less general representation of such surfaces or lines have been adapted for analyzing such problems, resulting in inconsistent or contradictory conclusions. Addressing these implicit assumptions, could result in a better continuum representation of the physical world. As representative examples, I consider the problem of moving contact line, slip boundary condition, and vortex sheet representation of the wake of a body. In the moving contact line problem, I show that the nature of the flow at the moving contact line is a vorticity dipole which results in an integrable stress term which produce a finite force. As a result, a dynamic Young equation will be introduced. On a fluid boundary with another fluid or a solid, I will present a unified slip boundary condition which produces the adequate level of slip or no-slip at the interface. Finally, I introduce the vortex-entrainment sheet as an inviscid model of wake of an immersed body and revisit the problem of flow around a corner and Kutta condition.