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Fluid Dynamics Colloquium

Monday, December 12, 2005, 4:00 pm
Cullimore Lecture Hall, Room 611
New Jersey Institute of Technology

Symmetries and Global Structure in a Sedimenting Suspension

Jonathan Luke

Professor

Department of Mathematical Sciences, NJIT

Abstract

A sedimenting suspension is a fundamental mechanical system with an enormous number of applications. In this talk, the low Reynolds number limit with negligible particle inertia is considered. In this regime, a well-stirred suspension has velocity fluctuations proportional to the container diameter. The condition of being well-stirred is obviously at most an initial condition and velocity fluctuations will evolve as a consequence of changes in the particle distribution. A model is introduced that describes the evolution of density and velocity fluctuations in a large container for short times. This model is a quadratic evolution equation with a linear manifold of stationary solutions, a cone of stable stationary solutions, a monotonically decreasing functional, and an infinite collection of constants of the motion. Moreover, the model makes predictions for the decay of velocity fluctuations and the resulting density stratification.