Modeling of Sedimentation of Particles near Corrugated Surfaces by the Meshless Method of Fundamental Solutions

The velocity and trajectory of particles moving along the corrugated (rough) surface under the action of gravity is obtained by a modified Method of Fundamental Solutions (MFS). 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’s function for Stokeslets. In the present study, the velocity of a moving particle under the action of the gravity force is not known and becomes a part of the MFS solution. This requires an adjustment of the matrix of the MFS linear system to include the unknown particle velocity and incorporate in the MFS the balance of hydrodynamic and gravity forces acting on the particle. The study explores the combination of the regularization of Stokeslets and placement of Stokeslets outside the flow domain to ensure the accuracy and stability of computations for particles moving in proximity to the wall. The MFS results are compared to prior published approximate analytical and experimental results to verify the effectiveness of this methodology to predict the trajectory of particles, including their deviation from the vertical trajectory, and select the optimal set of computational parameters. The developed MFS methodology is then applied to the sedimentation of a pair of two spherical particles in proximity to the corrugated wall, in which case, the analytical solution is not available. The MFS results show that particles in the pair deviate from the trajectory of a single particle: the particle located below moves farther away from vertical wall, and the particle located above shifts closer to the wall.