Northwestern University

Mon 23 Feb 2015, 4:00pm
Department Colloquium
LSK 200

Math Department Colloquium/Fluids Seminar: Sessile drop dynamics

LSK 200
Mon 23 Feb 2015, 4:00pm5:00pm
Abstract
Oscillations of the sessile drop are of fundamental interest in a number of industrial applications, such as inkjet printing and drop atomization. We generalize the stability analysis for the free inviscid drop (Rayleigh, 1879), focusing on the wetting properties of the solid substrate and mobility of the threephase contactline. We report oscillation frequencies and modal structures for the `symmetrybroken’ Rayleigh drop that display spectral splitting/reordering and compare with experiments. To organize and explain the hierarchy of frequencies, we construct a corresponding `periodic table of mode shapes’ from the spectral data. In addition to the oscillatory spectrum, we report a new hydrodynamic instability that has fundamental implications for fluid transport.
Profile: Dr Joshua Bostwick received bachelors degrees in Physics and Civil Engineering from University of WisconsinMilwaukee in 2005, and his PhD from Cornell University in 2011. He worked as a postdoctoral researcher at North Carolina State University and is currently Golovin Assistant Professor in the Department of Engineering Science and Applied Mathematics at Northwestern University. His research interests span surface tension, hydrodynamic instability, wetting and spreading, elastocapillarity, dynamical systems, constrained variational principles, symmetry methods.
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Caltech

Fri 27 Feb 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)

PIMSUBC distinguished colloquium: Blowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations.

ESB 2012 (PIMS)
Fri 27 Feb 2015, 3:00pm4:00pm
Abstract
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D NavierStokes Equations. We first review some recent theoretical and computational studies of the 3D Euler equations. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. We then present strong numerical evidence that the 3D Euler equations develop finite time singularities. To resolve the nearly singular solution, we develop specially designed adaptive (moving) meshes with a maximum effective resolution of order 10^{^12} in each direction. A careful local analysis also suggests that the solution develops a highly anisotropic selfsimilar profile which is not of Leray type. A 1D model is proposed to study the mechanism of the finite time singularity. Very recently we prove rigorously that the 1D model develops finite time singularity.
This is a joint work of Prof. Guo Luo.
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Seminar Information Pages

Note for Attendees
Refreshments will be served at 3:40pm in the Math Lounge area, MATH 125 before the colloquium.