Journal of Fluid Mechanics

Dynamic simulation of hydrodynamically interacting suspensions

John F.  Brady a1, Ronald J.  Phillips a2, Julia C.  Lester a1 and Georges  Bossis a3
a1 Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
a2 Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
a3 Laboratoire de Physique de la Matière Condensée, Université de Nice, Parc Valrose, 06034 Nice Cedex, France

Article author query
brady jf   [Google Scholar] 
phillips rj   [Google Scholar] 
lester jc   [Google Scholar] 
bossis g   [Google Scholar] 


A general method for computing the hydrodynamic interactions among an infinite suspension of particles, under the condition of vanishingly small particle Reynolds number, is presented. The method follows the procedure developed by O'Brien (1979) for constructing absolutely convergent expressions for particle interactions. For use in dynamic simulation, the convergence of these expressions is accelerated by application of the Ewald summation technique. The resulting hydrodynamic mobility and/or resistance matrices correctly include all far-field non-convergent interactions. Near-field lubrication interactions are incorporated into the resistance matrix using the technique developed by Durlofsky, Brady & Bossis (1987). The method is rigorous, accurate and computationally efficient, and forms the basis of the Stokesian-dynamics simulation method. The method is completely general and allows such diverse suspension problems as self-diffusion, sedimentation, rheology and flow in porous media to be treated within the same formulation for any microstructural arrangement of particles. The accuracy of the Stokesian-dynamics method is illustrated by comparing with the known exact results for spatially periodic suspensions.

(Published Online April 21 2006)
(Received October 8 1987)