Abstract
An electrokinetic (zeta) potential of charged permeable porous films on solid supports generally exceeds their surface potential, which often builds up to a quite high value itself. Recent work provided a quantitative understanding of zeta potentials of thick, compared to the extension of an inner electrostatic diffuse layer, porous films. Here, we consider porous coatings of thickness comparable to or smaller than that of the inner diffuse layer. Our theory, which is valid even when electrostatic potentials become quite high and accounts for finite hydrodynamic permeability of the porous materials, provides a framework for interpreting the difference between values of surface and zeta potentials in various situations. Analytic approximations for the zeta potential in the experimentally relevant limits provide a simple explanation of transitions between different regimes of electro-osmotic flows and also suggest strategies for its tuning in microfluidic applications.
Highlights
A century ago, von Smoluchowski1 proposed an equation to describe a plug electro-osmotic flow in a bulk electrolyte that emerges when an electric field E is applied at tangent to a charged solid surface
Some authors concluded that the zeta potential “loses its significance,”25 “irrelevant as a concept”32 or “is undefined and nonapplicable,”28 while others reported that Z typically exceeds Ψs33,34 but did not attempt to relate their results to the inner flow and emerging liquid velocity at the porous surface. This was taken up only recently in the paper by Vinogradova et al.,15 who carried out calculations of the zeta potential for thick coatings of both an arbitrary volume charge density and a finite hydrodynamic permeability. These authors predicted that Z is generally augmented compared to the surface electrostatic potential, thanks to a liquid slip at their surface emerging due to an electro-osmotic flow in the enriched by counter-ions porous films
We have presented a theory of surface and zeta potentials of non-thick porous coatings, i.e., those with thickness H comparable to or smaller than that of the inner diffuse layer, of a finite hydrodynamic permeability
Summary
A century ago, von Smoluchowski proposed an equation to describe a plug electro-osmotic flow in a bulk electrolyte that emerges when an electric field E is applied at tangent to a charged solid surface. This was taken up only recently in the paper by Vinogradova et al., who carried out calculations of the zeta potential for thick coatings of both an arbitrary volume charge density and a finite hydrodynamic permeability These authors predicted that Z is generally augmented compared to the surface electrostatic potential, thanks to a liquid slip at their surface emerging due to an electro-osmotic flow in the enriched by counter-ions porous films. When κH(1 + ρ2)1/4 ≫ 1, the film becomes thick compared to the inner diffuse layer, with an extended “bulk” electro-neutral region (where the intrinsic coating charge is completely screened by the absorbed electrolyte ions) The potential in this region is usually referred to athsatthψe DD=onanrsainnhp(oρt)e,nstiinacl,eψinD.tNheoeteletchtarot -Enqe.u(t5r)alimarmeae,dψiai′′tevlaynsiushgegse.sAts systematic treatment of the influence of the Brinkman length on the zeta potential of thick films was described in a paper published by Vinogradova et al.. Substitution of Eqs. (37) and (38) into (19) for KH ≫ 1 leads to ζ
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