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Hydrodynamic diffusion near solid boundaries with applications to heat and mass transport into sheared suspensions and fixed-fibre beds

Published online by Cambridge University Press:  26 April 2006

Donald L. Koch
Donald L. Koch
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

Heat and mass transport in the bulk of a suspension or fixed bed in the limit of high Péclet number is controlled by hydrodynamic diffusion. This hydrodynamic diffusion is caused by the stochastic velocity field induced by the randomly distributed particles. However, the no-slip boundary conditions require that the hydrodynamic diffusivity vanish at boundaries of the medium. Thus, molecular diffusion must aid the transport in a thin boundary layer near the solid boundary. Quantitative results are derived for the hydrodynamic diffusivity, boundary layer thickness, and net resistance to transport across a dilute fixed fibrous bed in the direction transverse to the mean flow. A scaling analysis is presented for transport in the direction of the gradient of the mean velocity in a sheared suspension of neutrally buoyant spheres. This scaling analysis is able to explain the qualitative variations of the transport resistance with the Péclet number and the ratio of the suspension thickness to the particle radius.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 318 , 10 July 1996 , pp. 31 - 47
Copyright
© 1996 Cambridge University Press

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References

Bonnecaze, R. T. & Brady, J. F. 1991 The effective conductivity of random suspensions of spherical particles. Proc. R. Soc. Lond. A 432, 445.Google Scholar
Bossis, G. & Brady, J. F. 1987 Self-diffusion of Brownian particles in concentrated suspensions under shear. J. Chem. Phys. 87, 5437.Google Scholar
Brady, J. F. & Phung, T. 1992 Microstructure fluids: Structure, diffusion and rheology of colloidal dispersions. In Proc 1st Tohwa Symposium: Slow Dynamics in Condensed Matter (ed. K. Kawasaki, M. Tokuyama & T. Kawakatsu). AIP Conf. Proc. Vol. 256, p. 391.
Cheng, P. & Zhu, H. 1987 Effects of radial thermal dispersion on fully-developed forced convection in cylindrical packed tubes. Intl J. Heat Mass Transfer 30, 2373.Google Scholar
Eckert, E. R. G. & Drake, R. M. 1972 Analysis of Heat and Mass Transfer. McGraw-Hill.
Fried, J. J. & Combarnous, M. A. 1971 Dispersion in porous media. Adv. Hydrosci. 7, 169.Google Scholar
Howells, I. D. 1974 Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects. J. Fluid Mech. 64, 449.Google Scholar
Koch, D. L. & Brady, J. F. 1985 Dispersion in fixed beds. J. Fluid Mech. 154, 399.Google Scholar
Koch, D. L. & Brady, J. F. 1986 The effective diffusivity of fibrous media. AIChE J. 32, 575.Google Scholar
Koch, D. L. & Brady, J. F. 1987 A non-local description of advection-diffusion with application to dispersion in porous media. J. Fluid Mech. 180, 387.Google Scholar
Larson, R. E. & Higdon, J. J. L. 1986 Microscopic flow near the surface of two-dimensional porous media. Part 1. Axial flow. J. Fluid Mech. 166, 449.Google Scholar
Larson, R. E. & Higdon, J. J. L. 1987 Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow. J. Fluid Mech. 178, 119.Google Scholar
Leighton, D. & Acrivos, A. 1987 Measurement of self-diffusion in concentrated suspensions. J. Fluid Mech. 177, 109.Google Scholar
Meredith, R. E. & Tobias, C. W. 1961 Conductivities in emulsions, J. Electrochem. Soc. 108, 286.Google Scholar
Sangani, A. S. & Behl, S. 1989 The planar singular solutions of Stokes and Laplace equations and their application to transport processes near porous surfaces. Phys. Fluids A 1, 21.Google Scholar
Shaqfeh, E. S. G. 1988 A nonlocal theory for the heat transport in composites containing highly conducting fibrous inclusion. Phys. Fluids 31, 2405.Google Scholar
Sohn, C. W. & Chen, M. M. 1981 Microconvective thermal conductivity in disperse two-phase mixtures as observed in a low velocity Couette flow experiment. J. Heat Transfer 103, 47.Google Scholar
Spielman, L. & Goren, S. L. 1968 Model for predicting pressure drop and filtration efficiency in fibrous media. Envir. Sci. Tech. 2, 279.Google Scholar
Wang, N.-H. L. & Keller, K. H. 1985 Augmented transport of extracellular solutes in concentrated erythrocyte suspensions in Couette flow. J. Colloid Interface Sci. 103, 210.Google Scholar
Wang, Y., Mauri, R. & Acrivos, A. 1995 Transverse shear-induced diffusion of spheres in a dilute suspension. J. Fluid Mech. (submitted).Google Scholar
Zydney, A. L. & Colton, C. K. 1988 Augmented solute transport in the shear flow of a concentrated suspension. Physico-Chem. Hydrodyn. 16, 77.Google Scholar