In this paper, we develop one of the first models for closed-form fully analytical solutions for describing the nonionic and ionic diffusio-osmotic (DOS) transport at interfaces grafted with a soft and porous polymeric film in the presence of a neutral solute concentration gradient (for nonionic diffusio-osmosis) and a salt concentration gradient (for ionic diffusio-osmosis). The nonionic DOS velocity depends on this solute concentration gradient and the drag force from the polymeric film. The ionic DOS transport is characterized by the diffusio-osmotically induced electric field and the diffusio-osmotically induced velocity field. This induced electric field is primarily dictated by the conduction of the mobile ion imbalance present within the electric double layer, induced at the charged solid, in the presence of the applied salt concentration gradient. The DOS velocity, on the other hand, is driven by a combination of the induced pressure gradient and an induced electro-osmotic body force (triggered by this induced electric field) and is opposed by the drag from the polymer layer. The result is a velocity field whose magnitude increases rapidly at near wall locations, decreases away from the wall, and depending on the salt concentration, may or may not increase outside the polymeric layer. This unique velocity profile ensures the presence of significant hydrodynamic shear stress across a wide zone extending from the wall in a non-confined fluidic system: This will ensure that finite-sized species (e.g., biological cells) can be conveniently made to access locations of large hydrodynamic stresses for a myriad of engineering and biological applications.
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