History force on an asymmetrically rotating body in Poiseuille flow inducing particle migration across a slit pore

Abstract

Experimental evidence shows that suspended particles preferentially migrate away from confining boundaries due to the effect of a shear flow. In this paper, we consider an asymmetric particle in Poiseuille flow and determine an inertial lift force which can contribute to the particle migration. Under the influence of Poiseuille flow in a slit pore, an arbitrary particle undergoes periodic rotation which is described by Jeffery’s orbit [G. Jeffery, Proc. R. Soc. London, Ser. A 102, 161 (1922)]. In the absence of rotational symmetry, a rotating particle produces an unsteady scattered field. The fluid inertia due to the unsteadiness causes an inertial force on the rotating body if the Reynolds number Re and the temporal variation in viscous force on the particle are nonzero. The resulting effect of this force on the particle migration can be significant especially for microfluidic systems, where gravitational contribution is negligible. In this paper, we consider two systems where the Reynolds number is assumed to be small but finite. In the first problem, we analyze the inertial force on a body asymmetrically rotating around its fixed center. In the second case, we focus on a freely suspended heavy particle which is considerably denser than the solvent so that the product of Re and the particle-solvent density ratio is greater than unity. For both systems, the Reynolds number and the temporal variation in viscous force are significant enough to produce a considerable inertial force on the particle. Our results indicate that the mean of this inertial component perpendicular to the boundaries is nonzero and acts in the direction away from the wall. The magnitude of this force is relatively larger near the wall and gradually decays as the particle-wall distance increases. Hence, we conclude that the discussed effect influences the preferential particle migration in conjunction with other factors.