Brownian simulations of probability distribution functions (PDF) for rod like particles near a solid surface

Full text.Simulations for the joint probability distribution functions PDF (ξ, θ) have been constructed as a function of their centre of mass from a solid surface boundary, ξ, and of their average orientations, θ, for a macromolecular rod like particles in a dilute solution under hydrodynamic flow. These simulations are constructed for a wide range of the quantity ξ □□ which depicts the ratio of the hydrodynamic shear rate to the rotational Brownian diffusion coefficient. The notion of restitution is introduced to develop an algorithm for the consequences of the Brownian and hydrodynamic collisions of the macromolecules with the impenetrable solid surface boundaries. This restitution applies for a wide range of solid surfaces and macromolecules. In particular, simulation results are presented for these distributions in the neighbourhood of a solid surface boundary, and for a confined space between two such boundaries. The distributions are given for typically low and high hydrodynamic flow conditions and their properties are discussed. In Fig.1 we present the normalized PDF P(θ) for a high value of the shear to rotational diffusion ratio, α=γ/Drot=100. This ratio characterizes the coupling of the stochastic thermal diffusion of the macromolecular particles in their motion in teh hydrodynamic flow. The exact numerical solution of the Boeder differential equation (BDE), is the continuous curve in Fig. 1, whereas the Brownian simulations are presented in comparison, for the same value of α, and for typically N = 108 events per simulation, as the dots with error bars. Faced with little information in the literature concerning the detailed Brownian 'collision' mechanisms between macromolecules and an impenetrable solid surface, we have introduced the notion opf geometrical restitution per collision event to develop a novel algorithm. Our approach is shown to render intelligible some previous simulation results, where one is often led to making unverifiable assumptions concerning the molecule-surface collisions. In Fig. 2, we present results for the folded P(ξ), summing over θ, for the case of macromolecular rod particles in a static liquid and for high values of α. Our simulation model is seemingly the best available at present to explain the decrease of the macromolecular PDF in the depletion layer with increasing hydrodynamic flux. Using optical experimental techniques we have been able to show for non-Brownian microscopic rod like particles present in flowing dilute solutions, their behaviour when colliding with solid surface boundaries. This is in quantitative agreement with our simulation model