Simulations of distribution functions for rod-like macromolecules in linear flow near solid surfaces

Brownian two-dimensional simulations are constructed to calculate the probability distribution functions (PDFs), for macromolecular rod-like particles in a flowing solution near solid surfaces. This is done for a wide range of α=γ̇/Drot, where γ̇ is the constant shear rate of the linear hydrodynamic flow and Drot is the diffusion coefficient for the molecular Brownian rotational motion. The surface simulations are developed on the basis of bulk simulations that are in agreement with the exact numerical solutions of the bulk Boeder differential equation (BDE). This procedure ensures an appropriate limit for the surface simulations. Surface restitution is introduced for Brownian and hydrodynamic events to develop an algorithm for the surface collisions of the macromolecules. The surface PDFs, given as a function of spatial and angular co-ordinates, are calculated for the possible range of restitution coefficients that model interactions between molecular species and surface topographies. These PDFs are consistently concave in the depletion layer as is physically expected. For small α or low flow conditions, the surface spatial PDF are shown to be the result of a dynamic balance between competing Brownian and hydrodynamic collisions restitution. For large α, the rod-like macromolecules are shown to be evacuated from the depletion layer by the dominant hydrodynamic collisions restitution. This is consistent with experimental observations. The surface angular PDF for the depletion layer are also calculated, showing marked differences from their bulk counterpart.