(322e) Measurement of Shear-Induced Diffusivity of a Dilute Suspension in the Vicinity of Walls

The unexpectedly large shear-induced self-diffusivity of a dilute suspension of spheres measured by Zarraga & Leighton, 2002 and Beimfohr et. al, 1993 was explained by the wall reflection mechanism suggested by Zurita-Gotor et. al, 2007. It was shown that the presence of a no-slip boundary leads to a class of open ?flipping? trajectories which are capable of producing dispersion, and this mechanism was demonstrated to be the dominant source of shear induced self-diffusivity in dilute suspensions. According to this mechanism, the shear-induced self-diffusivity and fluid dispersivity should depend on the distance from the two walls. The self-diffusivity measurements made previously for dilute suspensions (Leighton & Acrivos, 1987, Beimfohr et. al, 1993, Zarraga & Leighton, 2001) have focused on a limited region at the mid point between the two walls, specifically to avoid wall effects.

In addition to the self-diffusivity, the particle-wall interaction in a shear flow also leads to a fluid tracer diffusivity which may have significant consequences in mass transfer to surfaces in microfluidic devices (e.g., Lopez & Graham, 2008). Theoretical calculations indicate that the fluid tracer and self-diffusivities arising from the wall reflection mechanism should be identical in the far-field, and should also be a function of position in a bounded geometry.

In this work, we measure shear-induced random walk self-diffusivities and fluid dispersivities as a function of position between the walls for a dilute suspension of spheres. A density and refractive index matched suspension of acrylic spheres in a ternary mixture of water, ZnCl2 and Triton X-100 is sheared in a parallel plate geometry under steady and oscillatory shear flow. Tracking the motion of a small fraction of marked particles in steady flow and the dispersion of a line of dye in oscillatory shear flow permits the measurement of fluid and self-diffusivities as a function of distance from the walls. For steady shear, diffusivities in the flow gradient direction are obtained using a modification of the orbit-time technique developed by Leighton & Acrivos, 1987. Fluid and self-diffusivities are determined from the spread of a line of dye and marked particles in the flow direction due to Taylor-Aris dispersion in oscillatory flow. The measurements indicate that fluid dispersivity and self-diffusivity scale linearly with concentration as expected from the wall reflection mechanism. The measured self-diffusivity vanishes close to the walls as predicted by Zurita-Gotor et. al, 2007.

References: Beimfohr, S., Looby, T., Leighton, D. T., Measurement of the shear-induced coefficient of self-diffusion in dilute suspensions, in Proceedings of the DOE/NSF Workshop on Flow of Particles and Fluids, Ithaca, NY, 1993.

Leighton, D. T., Acrivos, A., Measurement of shear-induced self-diffusion in concentrated suspensions of spheres, J. Fluid Mech., 177, 109-131, 1987.

Lopez, M., Graham, M. D., Enhancement of mixing and adsorption in microfluidic devices by shear-induced diffusion and topography-induced secondary flow, Phys. Fluids, 20, 053304, 2008.

Zarraga, I.E., Leighton, D.T., Measurement of an unexpectedly large shear-induced self-diffusivity in a dilute suspension of spheres, Phys. Fluids, 14(7), 2194-2201, 2002.

Zurita-Gotor, M., Blawzdziewicz, J., Wajnryb, E. Swapping Trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres, J. Fluid. Mech. 592, 447-469, 2007.

Figure 1: Measured self-diffusivities as a function of position from one wall for φ = 0.03 with a gap width of H/d = 18.2. This is compared to the numerical prediction by Zurita-Gotor et. al, 2007 and the far-field analytical estimate of self-diffusivity for infinite dilution.