PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Xiantao Li.

Title:Conformal approaches to interfacial instabilities in fluids
Seminar:CCMA Luncheon Seminar
Speaker:Andong He, Department of Mathematics, Penn State
Abstract:
Interfacial instabilities are prevalent in the realm of fluid mechanics. We introduce two types of instabilities: Rayleigh-Taylor instability and viscous fingering, and demonstrate that how the conformal mapping method can be generally applied. In the case of viscous fingering, a nonlinear unsteady Darcy’s equation which includes inertial effects for a porous-media or Hele-Shaw flow is derived. For zero surface tension we derive a generalized Polubarinova–Galin equation in a circular geometry. The linear stability analysis can be conveniently performed by perturbing the corresponding conformal map. We show that inertia always has a tendency to stabilize the interface, regardless of which fluid displacing which.

Room Reservation Information

Room Number:MB114
Date:04 / 08 / 2011
Time:12:15pm - 01:30pm