Tangential velocity profile for pseudoplastic power-law fluids in the hydrocyclone — A theoretical derivation

The tangential velocity profile for pseudoplastic power-law fluids in a hydrocyclone is determined with an analytical solution to a simplified momentum balance equation by the method of perturbation. A numerical solution of the non-linear two-point boundary-value problem by the finite-difference method provides a verification of the perturbation solution. The tangential velocity is found to be controlled by a modified Reynolds number involving the radial velocity at the outer radius of the hydrocyclone and the consistency and flow-behavior indices of the fluid. The radial position of the maximum tangential velocity decreases with an increase in the modified Reynolds number and/or the degree of pseudoplasticity of the fluid. This analysis suggests that improved performance of hydrocyclones may be possible for pseudoplastic fluid systems as the tangential velocity profiles are steeper and the free-vortex zone is extended inwards.