A Flow Model for the Settling Velocities of non Spherical Particles in Creeping Motion

This paper undertakes a critical examination of Stokes’ law in its final form. The examination and insights of the viscosity principle substantiate grounds to suspect that the controlling dynamics are viscous shear rates across a geometry set by solid boundaries only. The examination sets grounds to conduct an analysis of the dynamics based on the viscosity principle alone and a flow model is derived. Based on the relationship between the pressure gradient and the shear forces as mandated by the viscosity principle the analysis suggests that the pressure gradient surrounding settling particles can be computed, is a single value and expands as required to mobilize a force equal to the driving force. In this context, the pressure gradient arises as a consequence of the contest between body forces in the fluid and the shear forces promoted by shear rates. The flow model suggests that Stokes’ law may be missing important information. An analysis is conducted for the settling velocity of non spherical particles based on the same dynamics and a mathematical solution is reached. The solution is in good agreement with published measured values and defines the influence of particle shape in settling phenomena.

Keywords:

Sedimentation , Tributary volume , Wall shear , Expansion , Stokes’ law , Aspect ratio