Extended Near Wall Hindered Diffusion Theory for Nanoparticles Under Short and Long Range Interactions

Abstract

An extension of the near wall hindered diffusion theory of Brenner [1] is considered for spherical nano-particles undergoing Brownian motion under the influence of hydrodynamic drag and electrostatic interactions. Brenner’s theory is based on hydrodynamic interactions between a levitating particle and the wall and does not consider short range interactions (like electrostatic force and van der Waals force). Recent experiments by Banerjee & Kihm [2] (henceforth referred to as BK05), with nano-particles of radii ≤ 500 nm show substantial discrepancy between the experimental and theoretical values of normal reduction coefficient (ratio of near wall normal diffusivity to bulk diffusivity). However, the experimentally measured lateral reduction coefficient (ratio of tangential diffusivity of the wall to bulk diffusivity) show good agreement with theory. It is conjectured that the absence of short range interactions become critical for particle radii ≤ 500 nm in the (sub-micron) near wall region. The current work extends Brenner’s analytical theory (henceforth referred to as B61) considering various short and long range interactions. An analytical expression is derived for hindered diffusivity of a particle normal to the wall under the influence of hydrodynamic drag and electrostatic interaction with a constant surface charge density. The theory is validated with experiments of BK05 and shows a better agreement with measured values of diffusion coefficients for particles of radii 50 and 100 nm. The dependence of electrolyte concentrations on electrostatic potential energy for spheres has also been studied. Increase in ionic strength of electrolyte concentration confirms the reduction of electrostatic potential energy for different sphere sizes. Electrostatic interaction has a significant contribution in overall potential energy of the sphere in sub-micron near wall region when wall and sphere surface charge potentials are increased.