(440j) Segregation of Particles Undergoing Shear Flow in a Counter Rotating Plate Geometry

Recently there has been much interest in the use of inertial secondary currents driven by centrifugal forces to achieve particle separations. A key application is the separation between deformable and non deformable particles (eg. circulating tumor cells in blood). In a microfluidic geometry, for example, separation of tumor cells has been demonstrated in a gently curved large aspect ratio rectangular channel [1,2]. These separations rely on a complex interplay between inertial secondary currents, size exclusion, inertial lift, deformation-induced lift, sedimentation velocity and shear induced diffusion giving rise to cross-streamline segregation. This particle distribution then interacts with the inertial secondary current to yield the separation. In this study we focus on a related problem: particle migration in the classic von Karman geometry of counter rotating parallel plates. As is well known, when the plates are at precise counter rotation (s = -1) the radial secondary current is such that the flow is outward at both the rotating plates and inwards at the center [3]. For particles in this geometry, the mean shear causes both an inertial lift [4] and deformation induced lift [5] forcing particles towards the center of the gap. This migration is balanced by shear induced diffusion and, for non-neutrally buoyant particles, by sedimentation. For very dilute suspensions, the shear induced dispersivity is small, and the balance is primarily between the lift force and the sedimentation velocity of the particles. Because the lift scales with r², this balance gives rise to an equilibrium radial position at which point the radial convective flux is zero. Although weak, shear induced diffusion causes a radial spread in the particle distribution about the equilibrium location. In this paper we experimentally demonstrate the existence of such a band and show that the width is quantitatively consistent with shear induced dispersion. In addition, the location of this band is qualitatively consistent with the inertial lift mechanism of Ho & Leal [4]. At higher concentrations, a band is also shown to exist, however the situation is complicated by modification of the inertial secondary current due to viscosity variation arising from the non uniform concentration profile between the plates. In this higher concentration region of stronger shear induced dispersion, the phenomenon may be modeled in terms of an average radial flux and a shear-induced Taylor dispersivity.

References:

[1] Hou, H.W. et al. Isolation and retrieval of circulating tumor cells using centrifugal forces. Sci. Rep. 3, 1259; DOI:10.1038/srep01259 (2013).                                                                                                                   

[2] Bhagat, A. A. S. et al. Continuous particle separation in spiral microchannels using dean flows and differential migration. Lab Chip 8, 1906–1914 (2008)                                                                                         

[3] J.F. Brady and L. Durlofsky. On rotating disc flow. J. Fluid Mech. vol. 175, pp. 363-394, (1987).

[4] B. P. Ho and L. G. Leal. Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech., 65(2):365-400, (1974).    

[5] P.C. Chan and L.G. Leal. The motion of a deformable drop in a second-order fluid, J. Fluid Mech., 92(1):131-170, (1979).