Particle tracking model for colloid transport near planar surfaces covered with spherical asperities

This paper proposes a Lagrangian particle tracking model (PTM) for predicting colloid transport near a planar substrate containing protruding spherical asperities in the presence of shear flow. The fluid flow field around such a physically heterogeneous substrate is obtained from a numerical solution of the Stokes equations. A simple approximation of the particle-substrate hydrodynamic interactions is developed based on the universal hydrodynamic correction functions. The model is employed to quantitatively predict how the presence of a spherical asperity on a macroscopically planar substrate can influence deposition of particles on the substrate in shear flow. Some simulation results depicting the deposit morphologies on an array of spherical asperities are also presented. Results from the PTM reveal that (i) asperities act as attractive "beacons", pulling particles closer to the composite substrate regardless of whether or not it is favorable to deposition; (ii) asperities can also act as additional collectors, increasing the available surface area onto which particles can deposit; and (iii) particles deposit on the "peaks" of the asperities under favorable conditions. From a mainly hydrodynamic standpoint, these observations indicate that physical heterogeneity on surfaces can have significant influence on particle deposition. The modification of the flow field due to the substrate's geometry, coupled with the modifications due to hydrodynamic retardation of the particle, lead to large variations of deposition probabilities. Therefore, assuming perfectly smooth collectors to compute the flow field may lead to errors in predicting deposition phenomena on physically heterogeneous collectors.