# Massive distributed computational algorithm for simulating many-body hydrodynamic interactions

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Complex fluids comprise two phases of materials: a solvent phase and a non-continuum phase such as microscopic particles or polymers. Suspensions of colloids -- microscopic particles small enough to undergo Brownian motion -- are an important example and model system for understanding general complex fluids. The particles are distributed in the suspending solvent, forming a "microstructure". 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, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as mean-field approaches replace detailed interactions with averaged approximations. However, long-range 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, Kim and Karrila, and Jeffrey. Along with pioneering work by Batchelor and Green, 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. The Reynolds number, Re, is the dimensionless strength of flow inertia relative to viscous stress,

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Bindel, David S.