  In this paper, we describe the unification and extension of multiple
kinematic theories on the advection of colloidal particles through periodic
obstacle lattices of arbitrary geometry and infinitesimally small obstacle
size. We focus specifically on the particle displacement lateral to the flow
direction (termed "deterministic lateral displacement") and the
particle-obstacle interaction frequency, and develop novel methods for
describing these as a function of particle size and lattice parameters for
arbitrary lattice geometries for the first time in the literature. We then
demonstrate design algorithms for microfluidic devices consisting of chained
obstacle lattices of this type that approximate any lateral displacement
function of size to arbitrary accuracy with respect to multiple optimization
metrics, prove their validity mathematically, and compare the generated results
favorably to designs in the literature with respect to metrics such as
accuracy, device size, and complexity.
