  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.
