Revisiting Some Flows with Surfaces and Lines of Discontinuities
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.
Contact: Wesley Yu at (915) 309-7972 firstname.lastname@example.org