Many-body microhydrodynamics of colloidal particles with active boundary layers

摘要

Colloidal particles with active boundary layers - regions surrounding theparticles where nonequilibrium processes produce large velocity gradients - arecommon in many physical, chemical and biological contexts. The velocity orstress at the edge of the boundary layer determines the exterior fluid flowand, hence, the many-body interparticle hydrodynamic interaction. Here, wepresent a method to compute the many-body hydrodynamic interaction between $N$spherical active particles induced by their exterior microhydrodynamic flow.First, we use a boundary integral representation of the Stokes equation toeliminate bulk fluid degrees of freedom. Then, we expand the boundaryvelocities and tractions of the integral representation in aninfinite-dimensional basis of tensorial spherical harmonics and, on enforcingboundary conditions in a weak sense on the surface of each particle, obtain asystem of linear algebraic equations for the unknown expansion coefficients.The truncation of the infinite series, fixed by the degree of accuracyrequired, yields a finite linear system that can be solved accurately andefficiently by iterative methods. The solution linearly relates the unknownrigid body motion to the known values of the expansion coefficients, motivatingthe introduction of propulsion matrices. These matrices completely characterizehydrodynamic interactions in active suspensions just as mobility matricescompletely characterize hydrodynamic interactions in passive suspensions. Thereduction in the dimensionality of the problem, from a three-dimensionalpartial differential equation to a two-dimensional integral equation, allowsfor dynamic simulations of hundreds of thousands of active particles onmulti-core computational architectures.