Faxén-like relations for a nonuniform suspension



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The Physics of Fluids


The first part of the paper shows how ensemble averages that correspond to a prescribed statistically nonuniform spatial distribution of particles can be evaluated starting from a statistically uniform ensemble. The method consists of attributing to each realization of the uniform ensemble a suitable weight which is explicitly constructed. As an application of this general procedure, in the second part of the paper, the behavior of particles subjected to force or torque in a statistically nonuniform suspension and the behavior of a suspension subjected to a uniform shear are studied. In particular, it is shown how the average translational and angular velocities of the particles with respect to the mixture satisfy Faxén-like relations. Furthermore, it is pointed out that several quantities which vanish in an identical way in the case of a uniform suspension are nonzero in the presence of spatial nonuniformities.



Particle-laden flows, instability of shear flows


Copyright 2004 Physics of Fluids. Recommended citation: Ichiki, Kengo, and Andrea Prosperetti. "Faxen-like relations for a nonuniform suspension." Physics of fluids 16, no. 7 (2004): 2483-2496. DOI: 10.1063/1.1734951 URL: https://aip.scitation.org/doi/abs/10.1063/1.1734951 Reproduced in accordance with the original publisher’s licensing terms and with permission from the author(s).