Manchester Applied Mathematics and Numerical Analysis Seminars

Winter 2000/01

November 15, 2000, 2.30 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)


Zero gravity sloshing

Dr. John Billingham, School of Mathematics and Statistics, University of Birmingham

We study the effect of a time-periodic, lateral acceleration on the two-dimensional flow of a Newtonian fluid with a free surface subject to surface tension. The fluid is confined between two plane, parallel walls under conditions of zero gravity. We assume that the velocity of each contact line is a linear function of the dynamic contact angle between fluid and solid at the wall alone. This problem is relevant to the study of fluids processing in a microgravity environment, but is also of more general interest as a flow in which the dynamics of the moving contact lines completely determines the behaviour of the fluid.

We begin by obtaining analytical solutions for the small-amplitude standing waves that evolve when the fluid is inviscid and the lateral acceleration is sufficiently small. This leads to damping of the motion, unless either the contact angles are constant or the contact lines are fixed. In these cases, we include the effect of the boundary layers on the lateral walls, which are the other major source of damping. From this, we can estimate under what circumstances viscosity is negligible. We then study how weak nonlinearity affects the inviscid solution close to resonance.

Finally, we compute numerical solutions of the nonlinear, inviscid problem. We use a desingularized integral equation technique combined with adaptive time-stepping, and artificially modify the advection of the nodes on the free surface to keep their spacing fairly even. After checking the accuracy of our method using the analytical solutions for linear and weakly nonlinear standing waves, we study solutions for large-amplitude lateral accelerations.

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For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).


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