Mean first passage times for bond formation for a Brownian particle in
linear shear flow above a wall

C.B. Korn and U.S. Schwarz

J. Chem. Phys. 126: 095103 (2007)

Motivated by cell adhesion in hydrodynamic flow, here the authors
study bond formation between a spherical Brownian particle in linear
shear flow carrying receptors for ligands covering the boundary
wall. They derive the appropriate Langevin equation which includes
multiplicative noise due to position-dependent mobility functions
resulting from the Stokes equation. They present a numerical scheme
which allows to simulate it with high accuracy for all model
parameters, including shear rate and three parameters describing
receptor geometry (distance, size, and height of the receptor
patches). In the case of homogeneous coating, the mean first passage
time problem can be solved exactly. In the case of position-resolved
receptor-ligand binding, they identify different scaling regimes and
discuss their biological relevance.