Sedimentation of Microscale Particles near Corrugated Wall Using Method of Fundamental Solutions

Sedimentation of particles along the corrugated surface under action of gravity is obtained by meshless 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 is not known and becomes a part of the MFS solution. This requires an adjustment of the matrix of MFS linear system to include the unknown particle velocity and incorporate the balance of hydrodynamic and gravity forces acting on the particle in the MFS. Combination of regularization of Stokeslets and placement of Stokeslets outside flow domain is implemented 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 methodology is applied to sedimentation of two spherical particles in proximity for which case the analytical solution is not available. The MFS results show that particles in tandem deviate from trajectory of a single particle where the forward particle is moving farther away from vertical corrugated wall and the back particle is shifted closer to the wall.