Electroviscous effect for a confined nanosphere in solution

Abstract

A charged colloidal particle suspended in an electrolyte experiences electroviscous stresses arising from motion-driven electrohydrodynamic phenomena. Under certain conditions, the additional contribution from electroviscous drag forces to the total drag experienced by the moving particle can lead to measurable deviations of particle diffusion coefficients from values predicted by the well known Stokes-Einstein relation that describes diffusive behavior of small particles in an unbounded charge-free fluid. In this study, we investigate the role of electroviscous stresses on nanoparticle diffusion in confined geometries using both simulations and experiment. We compare our experimental measurements with the results of a numerically solved continuum model based on the Poisson-Nernst-Planck-Stokes system of equations and find good agreement between experiment and theory. Depending on the radius of the counterion species in solution and the degree of confinement, we find that the viscous drag on polystyrene nanoparticles can be augmented by approximately 10-25% compared to the values predicted by pure hydrodynamic models in the absence of free charge in the fluid. This enhancement corresponds approximately to a 5-10% increase compared to the electroviscous contribution for a charged particle in an unbounded fluid. Contrary to recent reports in the experimental literature, we find neither experimental nor theoretical evidence of an anomalously large enhancement of electroviscous forces on a confined charged nanoparticle in solution.

Particle/wall electroviscous effects at the micron scale: comparison between experiments, analytical and numerical models

“…The simplicity of equation ( 6) allow us to see the main characteristics of EVE's: it predicts an increase of the apparent viscosity as h decreases. As explained by Behjatian et al [36], this behavior is attributed to a higher deformation (compression) of the EDL as the particle approaches the wall or when confinement is more severe. Secondly, the increase of μ app is influenced by a second order degree in ζ; this dependance was early explained by Ohshima et al [17] and it is due to the fact that the particle charge and its interaction with the asymmetrical electric field arising from the distorted EDL, both have magnitude of order ζ. Thirdly, μ app decrease as the conductivity of the medium increases; this dependance is due to two reasons: since λ = 2c ∞ Λ, where Λ is the mean molar conductivity of the medium, an increase in λ could mean an increase of the ion concentration c ∞ but at the same time a decrease of the EDL thickness due to equation (4).…”

“…Apart from comparing our experimental results with the theoretical equations ( 1) and ( 7) or (11), we also analyzed and compare our data with computational models obtained by solving numerically the electrokinetic equations (Poisson-Nernst-Planck-Stokes model, PNPS) in 2D using a similar scheme as that described by Behjatian et al [36] in order to assess the effects when the particle approaches the wall. The system of equations to solve are therefore the Stokes equations for an incompressible and stationary slow flow:…”

“…One exception to the rule were the experiments reported by Faucheux et al [35], who observed good agreement with hydrodynamic theory even though their system consisted in the same confined configuration with no added salt. Recent experiments on EVE's have been performed in confined nanoparticles [36][37][38] and confined quantum dots [39]. Although all these observations are consistent with the fundamentals of EVE's mechanisms, lack of quantitative agreement between experiments and theory has been generally obtained, partly because the theory is based on asymptotic expansions of the EDL thickness [23,40] and partly because the experiments usually do not show the increase of the drag factor as a function of the particle/wall separation distance.…”

Direct measurement of the viscoelectric effect in water

“…The inertial term (where m ∼2 gm is the mass of the lower lens) is readily shown to be negligible compared to the other terms ( 33 ). In this study, the electroviscous effect ( 34 – 37 ), which describes the resistance to the flow of the counterions in the diffuse double layers adjacent to the gold and mica surfaces (and should not be confused with the viscoelectric effect, which is the subject of our study), is negligible because of the low ion concentration and may therefore be safely ignored in the hydrodynamic resistance term ( SI Appendix , Section 4 ). The electric field in the gap E ( D ) can be evaluated by the PB equation for given ψ gold and σ mica .…”

Modeling charge separation in charged nanochannels for single-molecule electrometry

“…Both surfaces of the slit channel are kept at the same constant surface potential (voltage), and the solute molecules that are transported by convection and diffusion bear the electric charge q. For the sake of simplicity, we consider the case where the ratio of solute size to channel width is small enough to ignore Faxén's correction factors for the drag coefficient, or of any electroviscous effects 40 . This assumption holds true for the majority of biomolecules of interest that are smaller than or equal to 10 nm in diameter inside a slit with a width in the order of 100 nm.…”