Interfacial Hydrodynamics – New Insight On the Drag Force Induced by Permeation Through a Membrane

Practical experience has shown that membrane surfaces are more prone to deposition and, consequently, foul more than other non-permeable surfaces. This is because solvent permeation creates a velocity component perpendicular to the surface, which results in a convective flux of material toward the membrane. A particle will translate towards the membrane at the same velocity as the background fluid; however, at close approach, particle interaction with the membrane creates additional forces, which depend on the particle size, surface charge and hydrophobicity in addition to membrane permeability, roughness, hydrophobicity and charge. In this work, we focus on the impacts of membrane permeability on the effective permeate drag force. An analytical asymptotic model is formulated, offering a clear and intuitive understanding of the permeation-induced force acting on a particle at close approach to a membrane. Quantitative assessment of this force is made accessible and is illustrated for realistic membrane permeabilities and particle sizes. Furthermore, extensions to the theory are made to allow for elastic interaction when the particle and/or surface are not completely rigid (e.g., soft polymer interfaces, bacteria cells, etc.). The model and model results will be presented and discussed along with additional contributions from factors such as surface roughness and velocity slip.