TY - JOUR

T1 - Cooperative motion of spheres arranged in periodic grids between two parallel walls

AU - Bhattacharya, Sukalyan

PY - 2008

Y1 - 2008

N2 - In this article, we analyze the collective motion of a two-dimensional periodic array of spheres in a slit-pore confined by two parallel planar walls. We determine the friction coefficient of the spheres when all particles move with the same velocity along a particular direction and cooperate with each other in their motion. In order to solve this many-body problem, we use Stokesian dynamics algorithm and resolve multiparticle hydrodynamic interactions in wall-bounded geometry. Apart from particle-particle interactions, we also recognize that the aforementioned collective motion of all particles creates a cumulative effect on the fluid medium. This effect is manifested as either a net induced flow for a periodic pressure field or an additional pressure gradient for quiescent fluid. In our analysis, we focus on both periodic pressure and no-flow conditions. For both cases, the hydrodynamic friction on the translating particles is calculated using our multiparticle Stokesian dynamics simulation. The simulation for the no-flow condition is relatively straightforward-we only need to compute the multiparticle hydrodynamic interactions in quiescent fluid. However, for the periodic pressure condition, the net induced flow dragged by the particles has to be evaluated also. We express this net induced flow in terms of an additional pressure-driven velocity field. We present the hydrodynamic friction as a function of the dimensions of the two-dimensional periodic lattice. For closely packed arrays, the results show a considerable reduction in friction coefficients that usually increase with interparticle distance. Hence, our work renders the theoretical justification for other recent findings that indicate the importance of interparticle mutual cooperation.

AB - In this article, we analyze the collective motion of a two-dimensional periodic array of spheres in a slit-pore confined by two parallel planar walls. We determine the friction coefficient of the spheres when all particles move with the same velocity along a particular direction and cooperate with each other in their motion. In order to solve this many-body problem, we use Stokesian dynamics algorithm and resolve multiparticle hydrodynamic interactions in wall-bounded geometry. Apart from particle-particle interactions, we also recognize that the aforementioned collective motion of all particles creates a cumulative effect on the fluid medium. This effect is manifested as either a net induced flow for a periodic pressure field or an additional pressure gradient for quiescent fluid. In our analysis, we focus on both periodic pressure and no-flow conditions. For both cases, the hydrodynamic friction on the translating particles is calculated using our multiparticle Stokesian dynamics simulation. The simulation for the no-flow condition is relatively straightforward-we only need to compute the multiparticle hydrodynamic interactions in quiescent fluid. However, for the periodic pressure condition, the net induced flow dragged by the particles has to be evaluated also. We express this net induced flow in terms of an additional pressure-driven velocity field. We present the hydrodynamic friction as a function of the dimensions of the two-dimensional periodic lattice. For closely packed arrays, the results show a considerable reduction in friction coefficients that usually increase with interparticle distance. Hence, our work renders the theoretical justification for other recent findings that indicate the importance of interparticle mutual cooperation.

UR - http://www.scopus.com/inward/record.url?scp=39749114610&partnerID=8YFLogxK

U2 - 10.1063/1.2830713

DO - 10.1063/1.2830713

M3 - Article

C2 - 18298166

AN - SCOPUS:39749114610

VL - 128

JO - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

SN - 0021-9606

IS - 7

M1 - 074709

ER -