Computer simulation of multiphase flows has grown dramatically in the last
decade. Problems as diverse as the Brownian motion of small colloidal parti
cles or single DNA molecules, the theology of dense suspensions and emulsio
ns, and the dynamics of bubbly liquids have been addressed by dynamic simul
ation. This paper traces the development of the methodologies used to simul
ate multiphase, particulate systems. A central feature in these problems is
to properly account for the hydrodynamic interactions among particles, whi
ch has been accomplished rigorously and successfully in the case of small p
article Reynolds numbers and in the limit of inviscid flow at high Reynolds
numbers. Examples showing how hydrodynamic forces influence suspension str
ucture and determine macroscopic behavior for viscous suspensions are given
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