Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation
Abstract
The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pairlevel interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, manybody interactions must be considered. Prior analytical approaches to capturing such interactions such as meanfield approaches replace detailed interactions with averaged approximations. However, longrange coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261–290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16–29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for lowReynoldsnumber hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluidmore »
 Authors:

 Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853 (United States)
 Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
 Publication Date:
 OSTI Identifier:
 22493330
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 143; Journal Issue: 22; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00219606
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ABUNDANCE; COLLOIDS; CONCENTRATION RATIO; LIQUIDS; MANYBODY PROBLEM; MEANFIELD THEORY; MICROSTRUCTURE; MOBILITY; PARTICLE SIZE; PARTICLES; PHASE TRANSFORMATIONS; RENORMALIZATION; REYNOLDS NUMBER; ROTATION; SAMPLING; SOLUTIONS; STOCHASTIC PROCESSES; SUSPENSIONS; TORQUE
Citation Formats
Zia, Roseanna N., Email: zia@cbe.cornell.edu, Su, Yu, and Swan, James W. Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation. United States: N. p., 2015.
Web. doi:10.1063/1.4936664.
Zia, Roseanna N., Email: zia@cbe.cornell.edu, Su, Yu, & Swan, James W. Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation. United States. doi:10.1063/1.4936664.
Zia, Roseanna N., Email: zia@cbe.cornell.edu, Su, Yu, and Swan, James W. Mon .
"Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation". United States. doi:10.1063/1.4936664.
@article{osti_22493330,
title = {Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation},
author = {Zia, Roseanna N., Email: zia@cbe.cornell.edu and Su, Yu and Swan, James W.},
abstractNote = {The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pairlevel interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, manybody interactions must be considered. Prior analytical approaches to capturing such interactions such as meanfield approaches replace detailed interactions with averaged approximations. However, longrange coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261–290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16–29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for lowReynoldsnumber hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375–400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1–29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction ϕ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ ϕ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to ϕ ≤ 0.4, the relative mobility does not reached the farfield value even beyond separations of many particle sizes. In the case of ϕ = 0.5, the farfield asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquidlike structural effects on pair mobility at close separations. These results confirm that longrange manybody hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes.},
doi = {10.1063/1.4936664},
journal = {Journal of Chemical Physics},
issn = {00219606},
number = 22,
volume = 143,
place = {United States},
year = {2015},
month = {12}
}