  The general system of images for regularized Stokeslets (GSIRS) developed by
Cortez and Varela (2015) is used extensively to model Stokes flow phenomena
such as microorganisms swimming near a boundary. Our collaborative team uses
dynamically similar scaled macroscopic experiments to test theories for forces
and torques on spheres moving near a boundary and use these data and the method
of regularized Stokeslets (MRS) created by Cortez et al. (2015) to calibrate
the GSIRS. We find excellent agreement between theory and experiments, which
provides the first experimental validation of such series solutions for spheres
moving near an infinite plane boundary. We test two surface discretization
methods commonly used in the literature: the six-patch method and the spherical
centroidal Voronoi tessellation (SCVT) method. Our data show that the SCVT
method provides the most accurate results when the motional symmetry is broken
by the presence of a boundary. We use theory and the MRS to find optimal values
for the regularization parameter in free space and show that the optimal
regularization parameter values can be fit with simple formulae when using the
SCVT method, so that other researchers have an easy reference. We also present
a regularization function with higher order accuracy when compared with the
regularization function previously introduced by Cortez et al. (2005). The
simulated force and torque values compare very well with experiments and theory
for a wide range of boundary distances. But, we find the simulations lose
accuracy when the gap between the edge of the sphere and the wall is smaller
than the average distance between grid points using the SCVT method. Our
computational parameters and MATLAB and PYTHON implementations of the Lee and
Leal (1980) theory provide researchers with important resources to optimize the
numerical simulations of spheres moving near boundaries.
