Abstract
We discuss an electro-osmotic flow near charged porous coatings of a finite hydrodynamic permeability, impregnated with an outer electrolyte solution. It is shown that their electrokinetic (zeta) potential is generally augmented compared to the surface electrostatic potential, thanks to a large liquid slip at their surface emerging due to an electro-osmotic flow in the enriched by counter-ion porous films. The inner flow shows a very rich behavior controlled by the volume charge density of the coating, its Brinkman length, and the concentration of added salt. Interestingly, even for a relatively small Brinkman length, the zeta-potential can, in some cases, become huge, providing a very fast outer flow in the bulk electrolyte. When the Brinkman length is large enough, the zeta-potential could be extremely high, even at practically vanishing surface potential. To describe the slip velocity in a simple manner, we introduce a concept of an electro-osmotic slip length and demonstrate that the latter is always defined by the hydrodynamic permeability of the porous film and also, depending on the regime, either by its volume charge density or by the salt concentration. These results provide a framework for the rational design of porous coatings to enhance electrokinetic phenomena, and for tuning their properties by adjusting bulk electrolyte concentrations, with direct applications in microfluidics.
Highlights
When an electric field E is applied tangent to a charged surface, an electro-osmotic flow of an electrolyte solution is induced.1 The successful understanding of electro-osmosis, due to Smoluchowski,2 was a triumph of 20th century colloid physics
To describe the slip velocity in a simple manner, we introduce a concept of an electro-osmotic slip length and demonstrate that the latter is always defined by the hydrodynamic permeability of the porous film and depending on the regime, either by its volume charge density or by the salt concentration. These results provide a framework for the rational design of porous coatings to enhance electrokinetic phenomena, and for tuning their properties by adjusting bulk electrolyte concentrations, with direct applications in microfluidics
Our results provide new insight into the physics of electro-osmosis, the zeta-potential, and the nature of electro-osmotic slip at the porous interface
Summary
When an electric field E is applied tangent to a charged surface, an electro-osmotic flow of an electrolyte solution is induced. The successful understanding of electro-osmosis, due to Smoluchowski, was a triumph of 20th century colloid physics. Brinkman proposed a modification of the Darcy law to accommodate situations involving shear rates of an outer fluid at the surface of the porous medium This led to the generalized Stokes equation for a (tangent) pressuredriven flow and to the concept of the Brinkman screening length, Λ, defined as the square root of the hydrodynamic (Darcy) permeability of the medium. Neither paper addresses itself to the issues of the surface slip This was taken up only recently in the paper by Silkina, Bag, and Vinogradova who carried out calculations in the limit of infinite Brinkman length, Λ → ∞, in an attempt to obtain a proper understanding of an upper bound on achievable zeta-potential. VI with a further discussion of our results and their possible relevance for electro-kinetic experiments
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