Study of Drafting, Kissing and Tumbling Process of two Particles with different Densities using Immersed Boundary Method in a Confined Medium

Abstract

This paper numerically demonstrates the Drafting, Kissing and Tumbling (DKT) phenomenon between two interacting circular, impermeable particles with same Diameter (D) but with di?erent densities in a confined medium using Immersed Boundary (IB) method in two-dimensions. Two cases were considered for this particular scenario, Case 1 where the trailing particle’s density is considered higher than the leading particle and in Case 2 it is vice-versa. In Case 1, the particles undergo DKT phase. But the pattern observed is not uniform for all density di?erences. For some values of density di?erences, the particles experience one phase of DKT and for some other values of density di?erences, the particles experience two phase of DKT. In Case 2, for some values of density di?erences they part away from each other without experiencing DKT process and for some other values they experience DKT. The paper has further studied the e?ect of the vertical initial distance between two interacting particles for a specific density di?erence. For the range of initial vertical distance [2D, 4D] chosen, it was observed that the hydrodynamic interaction (in terms of DKT) between the particles remain the same irrespective of the initial vertical distance. The paper in the end performed convergence studies. Settling velocities of the particles was chosen as representative for determining convergence rate. The study done suggested that the implementation of the IB method is close to the expected first-order accuracy in space.