Modeling of Sedimentation of Particles near Corrugated Surface by Boundary Singularity Method

The velocity and trajectory of particle moving along the corrugated (rough) surface under action of gravity is obtained by meshless Boundary Singularity Method (BSM). This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with no-slip boundary conditions are solved using the Green function for Stokeslets. In the present study, the velocity of a moving particle is not known and becomes a part of the BSM solution. This requires an adjustment of the matrix of BSM linear system to include the unknown particle velocity and incorporate in the BSM the balance of hydrodynamic and gravity forces acting on the particle. Combination of regularization of Stokeslets and placement of Stokeslets outside flow domain was explored to ensure accuracy and stability of computations. Comparison has been made to prior published approximate analytical and experimental results to verify the effectiveness of this methodology to predict the trajectory of particle including its deviation from vertical trajectory and select the optimal set of computational parameters. The developed BSM methodology is applied to sedimentation of two spherical particles in proximity for which the analytical solution is not available.