Colóquio 

18/06/2001, 17:00 — 18:00 — Anfiteatro Qa2, Torre Sul, IST
Giovanni P. Galdi, University of Pittsburgh

Fundamental Problems in the Sedimentation of Particles in Newtonian and Viscoelastic Liquids

Over the last 40 years the study of the motion of small particles in a viscous liquid has become one of the main focuses of engineering research. The presence of the particles affects the flow of the liquid, and this, in turn, affects the motion of the particles, so that the problem of determining the flow characteristics is highly coupled. It is just this latter feature that makes any fundamental mathematical problem related to liquid-particle interaction a particularly challenging one.

Interestingly enough, even though the mathematical theory of the motion of rigid particles in a liquid is one of the oldest and most classical problems in fluid mechanics, owed to the seminal contributions of Stokes, Kirchhoff, Thomson (Lord Kelvin) and Tait, only very recently have mathematicians become interested in a systematic study of the basic problems related to liquid-particle interaction.

This lecture concentrates on the mathematical analysis of one of the several important and still not completely understood aspects of this fascinating subject, that is, the orientation of symmetric particles sedimenting in Newtonian and viscoelastic liquids. As is well known, the general phenomenon of particle orientation plays a crucial role in many engineering problems, like the manufacturing of short-fiber composites, separation of macromolecules by electrophoresis, flow-induced microstructures, and also in blood flow problems.