Brady, John F. (1994) The longtime selfdiffusivity in concentrated colloidal dispersions. Journal of Fluid Mechanics, 272 . pp. 109134. ISSN 00221120. http://resolver.caltech.edu/CaltechAUTHORS:20120229143202470

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Abstract
The longtime selfdiffusivity in concentrated colloidal dispersions is determined from a consideration of the temporal decay of density fluctuations. For hydrodynamically interacting Brownian particles the longtime selfdiffusivity, D^s_∞, is shown to be expressible as the product of the hydrodynamically determined shorttime selfdiffusivity, D^s_0(φ), and a contribution that depends on the distortion of the equilibrium structure caused by a diffusing particle. An argument is advanced to show that as maximum packing is approached the longtime selfdiffusivity scales as D^s_∞(φ)~ D^s_0(φ)/g(2;φ), where g(2;φ) is the value of the equilibrium radialdistribution function at contact and φ is the volume fraction of interest. This result predicts that the longtime selfdiffusivity vanishes quadratically at random close packing, φ_m ≈ 0.63, i.e. D^s_∞D_0(1φ/φ_m)^2 as φ → φ_m, where D_0 = kT/6πηα is the diffusivity of a single isolated particle of radius α in a fluid of viscosity η. This scaling occurs because Ds_0(φ) vanishes linearly at random close packing and the radialdistribution function at contact diverges as (1 φ/φ_m)^(−1). A model is developed to determine the structural deformation for the entire range of volume fractions, and for hard spheres the longtime selfdiffusivity can be represented by: D^s_∞(φ) = D^s_∞(φ)/[1 + 2φg(2;φ)]. This formula is in good agreement with experiment. For particles that interact through hardspherelike repulsive interparticle forces characterized by a length b(> α), the same formula applies with the shorttime selfdiffusivity still determined by hydrodynamic interactions at the true or ‘hydrodynamic’ volume fraction φ, but the structural deformation and equilibrium radialdistribution function are now determined by the ‘thermodynamic’ volume fraction φ_b based on the length b. When b » α, the longtime selfdiffusivity vanishes linearly at random close packing based on the ‘thermodynamic’ volume fraction φ_(bm). This change in behaviour occurs because the true or ‘hydrodynamic’ volume fraction is so low that the shorttime selfdiffusivity is given by its infinitedilution value D_0. It is also shown that the temporal transition from short to longtime diffusive behaviour is inversely proportional to the dynamic viscosity and is a universal function for all volume fractions when time is nondimensionalized by α^2/D^s_∞(φ).
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Additional Information:  © 1994 Cambridge University Press. Received 5 July 1993 and in revised form 9 February 1994. Published online: 26 April 2006. This work was supported in part by Grant No. CTS9020646 from the National Science Foundation.  
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Record Number:  CaltechAUTHORS:20120229143202470  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20120229143202470  
Official Citation:  The longtime selfdiffusivity in concentrated colloidal dispersions preview John F. Brady Journal of Fluid Mechanics / Volume 272 / pp 109  134 1994 Cambridge University Press Published online: 26 April 2006 DOI:10.1017/S0022112094004404  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  29531  
Collection:  CaltechAUTHORS  
Deposited By:  Ruth Sustaita  
Deposited On:  29 Feb 2012 23:41  
Last Modified:  26 Dec 2012 14:54 
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