382895 Does Macromolecular Crowding Screen Hydrodynamic Interactions?
The formulation of detailed models for the dynamics condensed soft matter including: glasses, gels, polymer melts and micellar solutions, hinges on accurate description of the physical forces between microstructural constituents. A common approximation is to neglect fluid mediated interactions and to introduce an effective viscosity or diffusivity as a proxy for long-ranged hydrodynamic forces. This approach is rationalized by the claim that hydrodynamic interactions are screened in slowly evolving, concentrated materials. We use Accelerated Stokesian Dynamics simulations of concentrated suspensions to test this claim.
Resistance and mobility functions describe linear relationships 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 definitively by Jeffrey and Onishi (JFM, 1984). These are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions. We utilize a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two spheres immersed in a suspension of other identical particles. These mobility functions are exactly what is required to model the near equilibrium dynamics of concentrated dispersions, for instance: linear viscoelasticity and long-time diffusion. If hydrodynamic interactions are screened, then the mobility functions coupling motion of one particle to moments of the traction on another should show a more rapid decay than the dilute limit results of Jeffrey and Onishi, which are unscreened.
Our measurements demonstrate that the mobility is unscreened at the pair level, even in suspensions of high concentration. These results confirm that hydrodynamic interactions are an essential part of the dynamics of macromolecular systems and cannot be neglected in favor of simple renormalization schemes. We demonstrate how some of our pair mobility functions in concentrated suspensions can be modeled accurately through a straightforward rescaling of those for two isolated spheres. Additionally, we compare our results for the hydrodynamic interactions between suspended particles to predictions from two-point microrheology. This technique can be used to infer the complex viscosity from long-ranged decay of the pair mobility in viscoelastic materials. Its validity when not in the continuum limit is addressed.
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