Year: 2026
Type: article
Abstract: When a non-spherical particle sediments, its velocity generally changes in time as the particle orientation changes in time. This gives extra dispersion of the particle position in addition to the thermal Brownian motion. Brenner ( J. Colloid Interf. Sci. , vol. 71, 1979, pp. 189–208) studied this effect and formulated how to calculate the gravity-induced dispersion (called Taylor dispersion in sedimentation). However, he conducted the explicit calculation only for torque-free particles which keep an isotropic orientational distribution in the steady-state. In this paper, we study the effect of the gravitational torque on the Taylor dispersion. We limit the analysis to particles having uniaxial symmetry. In this case, the gravitational torque is caused by the offset l Subscript c l c $l_{{c}}$ , the distance between the hydrodynamic centre and the gravitational force centre. The effect of the gravitational torque is represented by a dimensionless parameter alpha α $\alpha$ (called the Langevin parameter by Brenner) which is proportional to l Subscript c l c $l_{{c}}$ . We obtain analytical expressions for the Taylor diffusivity for the two limits alpha much less than 1 α ≪ 1 $\alpha \ll 1$ and alpha much greater than 1 α ≫ 1 $\alpha \gg 1$ . We show that the offset gives a significant effect on the diffusivity and changes the classical scaling of the Taylor dispersion at a large Péclet number. We also analyse the transient regime of the mean square displacement and show how the crossing time from the ballistic regime to the diffusive regime depends on the gravitational torque.
Source: Journal of Fluid Mechanics
Authors: Zhongqiang Xiong, Ryohei Seto, Masao Doi
Language: English
Subfield: Ocean Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7165031176