The transverse migration of particles in the presence of a shear flow is a phenomenon which has attracted a great deal of attention ever since the landmark experiments of Segré and Silberberg.^1,2 Past studies in bounded geometries, which have been primarily focused on steady flow, demonstrate that the “tubular pinch” effect is expected to occur when finite inertial effects exist in a system (see, for example, Ho and Leal³ or Vassuer and Cox⁴).  The equilibrium position of a non-neutrally buoyant particle in a horizontal tube will be governed by a balance between gravitational and inertial forces.⁵  In gravitational field flow fractionation, for example, such a balance of forces determines the mobility of a particle in the analogous channel flow problem.⁶ It is reasonable to expect that oscillatory flow will affect particles in a similar way, particularly at low frequencies (i.e. low Womersly number).  Bubbles, though fundamentally different, will behave like solid particles if they remain spherical (i.e. low Capillary number).

In this work, we experimentally examined the dimensionless mobility Dx_p/Dx_o of solid polymethylmethacrylate particles and air bubbles which were subjected to oscillatory flow in a glass capillary tube.  In water, we observed the mobility of both particles and bubbles to exhibit behavior consistent with well known inertial lift mechanisms derived for steady flow; that is, the amplitude of motion was a function of Re_p²/Re_s (the ratio of inertial to gravitational forces⁷) for a wide range of frequencies.  In a more viscous fluid, the mobility of the particles at high frequencies deviated from the simple Re_p²/Re_s dependence.  This departure occurred as the frequency time scale became comparable to the sedimentation time scale.  Bubbles were found to have a more complex behavior in the more viscous fluid originating from the competition between two migration mechanisms: inertial lift and deformation induced lift.  The inertial lift tends to drive the bubble to an equilibrium position between the tube wall and center while the deformation induced lift drives the bubbles towards the centerline.⁸

The migration behavior observed for symmetric oscillatory flow suggested a methodology for extracting or separating particles/bubbles in confined geometries, such as those commonly found in microfluidic devices.  By applying a zero-mean asymmetric oscillatory flow, particles and bubbles in a capillary tube were given a net drift with each stroke.  The direction and speed of the drift were shown to depend on the ratio of the frequencies in the forward and reverse direction and corresponded well with displacements predicted from the experiments performed using symmetric oscillatory flow.

(1)        Segré, G.; Silberberg, A. Journal of Fluid Mechanics 1962, 14, 115-135.

(2)        Segré, G.; Silberberg, A. Journal of Fluid Mechanics 1962, 14, 136-157.

(3)        Ho, B. P.; Leal, L. G. Journal of Fluid Mechanics 1974, 65, 365-400.

(4)        Vasseur, P.; Cox, R. G. Journal of Fluid Mechanics 1976, 78, 385-413.

(5)        Yang, B. H.; Wang, J.; Joseph, D. D.; Hu, H. H.; Pan, T. W.; Glowinsk, R. Journal of Fluid Mechanics 2005, 540, 109-131.

(6)        Williams, P. S.; Lee, S. H.; Giddings, J. C. Chemical Engineering Communications 1994, 130, 143-166.

(7)        King, M. R.; Leighton, D. T. Physics of Fluids 1997, 9, 1248-1255.

(8)        Chan, P. C. H.; Leal, L. G. Journal of Fluid Mechanics 1979, 92, 131-170.