## Lift-off of a single particle in Newtonian and viscoelastic fluids by
direct numerical simulation

#### *N. A. Patankar, P. Y. Huang, T. Ko and D. D. Joseph*

#### Abstract

In this paper we study the lift-off to equilibrium of a single circular
particle in Newtonian and viscoelastic fluids by direct numerical simulation. A
particle heavier than the fluid is driven forward on the bottom of a channel by
a plane Poiseuille flow. After a certain critical Reynolds number the particle
rises from the wall to an equilibrium height at which the buoyant weight just
balances the upward thrust from the hydrodynamic force. The aim of the
calculation is the determination of the critical lift-off condition and the
evolution of the height, velocity and angular velocity of the particle as a
function of the pressure gradient and material and geometric parameters. The
critical Reynolds number for lift-off is found to be larger for a heavier
particle whereas it is lower for a particle in a viscoelastic fluid. The
equilibrium height increases with the Reynolds number, the fluid elasticity and
the slip angular velocity of the particle. Simulations of single particle
lift-off at higher Reynolds numbers in a Newtonian fluid show multiple steady
states and hysteresis loops. This is shown to be due to the presence of two
turning points of the equilibrium height as a function of the Reynolds number.
A general data structure for the interrogation of direct numerical simulations
for information necessary for the evaluation of models of lift is proposed.
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February 2000. Contact N.A.
Patankar for questions about this article.

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