Normal modes of weak colloidal gels
Name
PhysRevE.97.012608.pdf
Size
2.08 MB
Format
Adobe PDF
Checksum (MD5)
944076295e5f53c54129a1a521f93e96
Author(s)
Varga, Zsigmond
Swan, James W
Date Issued
January 2018
Journal
Physical Review E
Publisher
American Physical Society
Citation
Varga, Zsigmond, and James W. Swan. “Normal Modes of Weak Colloidal Gels.” Physical Review E, vol. 97, no. 1, Jan. 2018. © 2018 American Physical Society
Version
Final published version
Abstract
The normal modes and relaxation rates of weak colloidal gels are investigated in calculations using different models of the hydrodynamic interactions between suspended particles. The relaxation spectrum is computed for freely draining, Rotne-Prager-Yamakawa, and accelerated Stokesian dynamics approximations of the hydrodynamic mobility in a normal mode analysis of a harmonic network representing several colloidal gels. We find that the density of states and spatial structure of the normal modes are fundamentally altered by long-ranged hydrodynamic coupling among the particles. Short-ranged coupling due to hydrodynamic lubrication affects only the relaxation rates of short-wavelength modes. Hydrodynamic models accounting for long-ranged coupling exhibit a microscopic relaxation rate for each normal mode, λ that scales as l[superscript −2], where l is the spatial correlation length of the normal mode. For the freely draining approximation, which neglects long-ranged coupling, the microscopic relaxation rate scales as l[superscript −γ], where γ varies between three and two with increasing particle volume fraction. A simple phenomenological model of the internal elastic response to normal mode fluctuations is developed, which shows that long-ranged hydrodynamic interactions play a central role in the viscoelasticity of the gel network. Dynamic simulations of hard spheres that gel in response to short-ranged depletion attractions are used to test the applicability of the density of states predictions. For particle concentrations up to 30% by volume, the power law decay of the relaxation modulus in simulations accounting for long-ranged hydrodynamic interactions agrees with predictions generated by the density of states of the corresponding harmonic networks as well as experimental measurements. For higher volume fractions, excluded volume interactions dominate the stress response, and the prediction from the harmonic network density of states fails. Analogous to the Zimm model in polymer physics, our results indicate that long-ranged hydrodynamic interactions play a crucial role in determining the microscopic dynamics and macroscopic properties of weak colloidal gels.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.97.012608
