Effects of Fore-Aft Asymmetry on the Sedimentation and Dispersion of Axisymmetric Brownian Particles

Abstract

When sedimenting under the action of an external force field, noncentrosymmetric Brownian particles experience an orienting torque, whose magnitude relative to the disorienting effect of rotary diffusion is represented by χ, the relevant Langevin parameter. The present contribution analyzes the Taylor dispersion accompanying the sedimentation of such axisymmetric noncentrosymmetric Brownian particles. The dimensionless Taylor dispersivity coefficient is represented by the product of a scalar factor, whose magnitude depends upon the geometry of the particle, and a "universal" χ-dependent dyadic, D̂C, which is appropriately represented by the pair of scalar coefficients D̂CII (χ) and D̂CII (χ) corresponding to dispersion of the particles parallel and perpendicular, respectively, to the direction of the external force. With increasing χ the latter coefficients initially increase from the respective values 2/135 and 1/90 for χ = 0 (corresponding to centrosymmetric particles), attain their respective maxima (D̂CII ≅ 2.02 × 10-2 at χ ≅ 1.66, D̂CII ≅ 1.58 × 10-2 at χ ≅ 2.74), and finally decrease monotonically. The effects of particle geometry are illustrated by the example of an asymmetric dumbbell consisting of a pair of homogeneous spheres of unequal size. The variation of the respective magnitudes of the Langevin parameter and the Taylor dispersivity with the size ratio and dimensionless separation parameter, characterizing the shape of such particles, is explicitly presented.