Brownian dynamics method for simulation of binding kinetics of patterned colloidal spheres with hydrodynamic interactions

We develop a Brownian dynamics simulation method with full hydrodynamic interactions (HI) to study the recognition kinetics between two patterned colloidal spheres. We use a general resistance matrix (12*12) to describe both the far and near-field hydrodynamics of translation, rotation, and translation-rotation coupling between the two spheres, adopted from Jeffrey and Onishi [J. Fluid Mech. 139, 261 (1984)]. We apply the method to the specific binding of "patchy" spheres, including effects of depletion attraction and orientation-specific binding, as are present in "Janus" spheres whose surfaces contain hydrophobic and hydrophilic faces [Q. Chen, S. C. Bae, and S. Granick, Nature (London) 469, 381 (2011)]. The binding times obtained between two non-patterned spheres (of equal or unequal diameter) with or without HI extrapolated to infinite dilution are shown to be in good agreement with theoretical predictions of the Smoluchowski equation. In addition, the binding times for pairs of spheres for three cases of surface patterning of the two spheres (uniform-uniform, uniform-Janus, and Janus-Janus) are compared with or without rotational motion. (C) 2013 AIP Publishing LLC.