Summary: Effective Viscosity Properties of Dilute Suspensions of
Arbitrarily Shaped Particles
In this paper we derive high-order asymptotic expansions of the effective viscos-
ity properties of a dilute periodic suspension composed of freely-suspended arbitrarily
shaped particles dispersed in an incompressible Newtonian fluid. High-order terms are
not only function of the viscous moment tensor but also of a distortion tensor that
characterizes the periodic array.
Mathematics subject classifications (MSC2000): 35B30.
Keywords: effective viscosity, dilute suspension, viscous moment tensor, high-order expansions.
Short title: Dilute suspension of arbitrarily shaped particles
In this paper we consider the derivation of macroscale properties of a dilute suspension
composed of identical arbitrarily shaped viscous particles dispersed in an incompressible
Newtonian fluid from knowledge of its microscopic properties. This problem becomes in-
creasingly important in chemical engineering, polymer science, and biophysics. Analytic