Relation of Microstructure to Constitutive Equations
A set of equations for the averaged motion of a suspension of spheres in an inviscid fluid is derived by applying an ensemble average to the exact equations of motion. Constitutive equations to close the system for dilute, incompressible flow are derived by averaging the solution for the flow around a single sphere. The ensemble average is performed by allowing the center of the sphere to take random locations around an arbitrary spatial point. The corresponding volume average yields different results.
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