Multiple Particle Interaction at Intermediate Reynolds Numbers

The literature is rich with studies on particle interaction in Stokes flow. However, there are scant studies on particle interaction at intermediate Reynolds numbers. Here, we present a new computational scheme to simulate the dynamics of the particles coupled to the Naviers-Stokes solutions for the fluid. In order to understand the basic picture of particle-particle interactions in fluid, we investigate the dynamics of an array of freely falling cylinders with an initial spacing on the order of the particle diameter. We find that for a small number of particles ($n=3,~4$), there are two distinct falling configurations which depend on the parity of $n$. For $n>4$, the falling configuration is a mix of those previous modes. However, when the initial spacing between particles is below a threshhold, the array is separated into small clusters of $2$ or $3$ particles. We further quantify the interaction force between two falling particles as a function of their relative position, and compare them with results in the Stokes regime.