Density-induced coupling effects on the dispersivity of a flexible chain particle

A model is introduced to investigate the transport properties of an inhomogeneously dense flexible chain particle. The specific model used is a sedimenting non-neutrally buoyant inhomogenously weighted flexible Brownian dumbbell, and it is shown that density inhomogeneity gives rise to a novel coupling effect between the "shape-fluctuation" and "size-fluctuation" dispersion mechanisms. The previously reported shape-fluctuation dispersion term stems from the dumbbell's nonspherical shape and the ensuing anisotropic mobility tensor, while the already investigated size fluctuation term is the result of the dependence of the overall dumbbell translational mobility on the separation distance between the constitutive spheres. Because the density of the constitutive spheres is unequal, the external force simultaneously reorients and deforms the flexible dumbbell, and it is this mutual dependence between dumbbell orientation and size that induces the coupling. Numerical results are presented for the case of a tethered dumbbell composed of two spheres, identical in size but differing in density. The "weak-field" limit is addressed, where the externally applied torque and particle deformation forces are dominated by the thermal fluctuations associated with rotational and deformation Brownian motion. This numerical solution, obtained by including a large number of higher order hydrodynamic interactions (120 terms), describes the Brownian particle's long-time transport without resorting to ad hoc approximations, such as preaveraging the hydrodynamic force or incorporating only first-order hydrodynamic interaction effects (such as employing the Burgers-Oseen tensor). Separate analytical solutions, based on these respective approximations, are also presented and it is concluded that in the limit of "long tethers," where the ratio of tether length to sphere size is greater than seven, no more than 15% error is introduced by neglecting higher-order hydrodynamic interactions. Similarly, the preaveraging approximation introduces no more than a few percent error in the limit of "almost-rigid" dumbbells, where the ratio of tether length to sphere size is less than three. For tethers of "intermediate" length, the full numerical solution must be employed.