For more information about this meeting, contact Xiantao Li.
| Title: | Conformal approaches to interfacial instabilities in fluids |
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| Seminar: | CCMA Luncheon Seminar |
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| Speaker: | Andong He, Department of Mathematics, Penn State |
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| Abstract: |
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| 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 |
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| Date: | 04 / 08 / 2011 |
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| Time: | 12:15pm - 01:30pm |
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