Viscoelectric Effect Research Articles

Analytical solutions for viscoelectric effects in electrokinetic nanochannels.

Understanding electrokinetic transport in nanochannels and nanopores is essential for emerging biological and electrochemical applications. The viscoelectric effect is an important mechanism implicated in the increase of local viscosity due to the polarization of a solvent under a strong electric field. However, most analyses of the viscoelectric effect have been limited to numerical analyses. In this work, we present a set of analytical solutions applicable to the physical description of viscoelectric effects in nanochannel electrokinetic systems. To achieve such closed-form solutions, we employ the Debye-Hückel approximation of small diffuse charge layer potentials compared to the thermal potential. We analyze critical parameters, including electroosmotic flow profiles, electroosmotic mobility, flow rate, and channel conductance. We compare and benchmark our analytical solutions with published predictions from numerical models. Importantly, we leverage these analytical solutions to identify essential thermophysical and nondimensional parameters that govern the behavior of these systems. We identify scaling parameters and relations among surface charge density, ionic strength, and nanochannel height.

Viscoelectric effect on the chemiosmotic flow in charged soft nanochannels

The charged nanochannel surface and pH-sensitive grafted polyelectrolyte layer (PEL) play a critical role in the design of devices aimed at controlling nanofludic flow. They enable the manipulation of ionic transport by influencing the electric-double (EDL) layers that overlap. Additionally, the viscoelectric effect, amplified by a strong EDL electric field, may enhance the activation energy and viscosity of liquids. Motivated by this, we conducted a numerical investigation using a finite element method-based solver, COMSOL, to examine the effects of the viscoelectric effect on concentration-gradient-driven chemiosmotic flow in a charged soft nanochannel with grafted pH-sensitive polyelectrolyte layer on the inner wall surfaces. It is important to note that the nanochannel is positioned between two reservoirs with different pH values and bulk-ionic concentrations. The PEL is sensitive to protonic association–dissociation due to the presence of carboxylic and amine groups in monomeric units. In our study, we comprehensively demonstrate variations in key variables characterizing the underlying flow. These variations include changing the solute concentration in the left side reservoir within the range of 0.1–5 mol m−3, adjusting the pH of the right-side reservoir (pHR) within the range of 3–10, and varying the viscoelectric coefficient. The viscoelectric effect significantly raises viscosity near the wall due to the stronger EDL electric field generated at the left-side reservoir resulting from the higher solute concentration. On the other hand, viscosity tends to decrease with lower pHR values and remains unaffected by changes at higher pHR values. The average flow velocity shows an increasing–decreasing pattern as the concentration of the right-side reservoir is enhanced. Additionally, the decrease in flow velocity becomes noticeably more pronounced with higher solute concentrations in the right-side reservoir when accounting for the viscoelectric effect. The findings of the present study have practical implications for novel nanofluidic devices, frequently employed in various engineering applications to control flow.

Viscoelectric effect analysis in an electroosmotic flow with microchannel wall slip

In the present work, we developed a numerical analysis for an electroosmotic flow circulating in a rectangular microchannel considering electrolyte viscosity as a function of the induced electric field; which is also reflected in the slip condition imposed on the system walls, since the slip length is a function of the fluid viscosity. It should be clarified this is an entirely hydrodynamic problem, and for this reason there are no induced pressure gradients, because we are in the presence of a purely electroosmotic flow, where the fluid motion is due only to electrokinetic forces. Based on these comments, the problem is centered on high induced potentials, enabling viscoelectric effect analysis in the electroosmotic flow, which leads to significant increases in velocity and volumetric flow profiles compared to the case where the viscosity is a constant and there is no slip condition. Due to analytical analysis limitations, we implemented a dimensionless equation scheme defined by the continuity equation, the momentum equations in the x and y direction, the Poisson-Boltzmann equation, and the charge conservation equation to obtain the velocity and volumetric flow rate profiles mentioned above. This model is described in its variational form in order to implement the finite element technique using free software, FreeFem++. The results obtained show how the viscoelectric effect is relevant when working with high induced potentials; that is, for values of , when the dimensionless viscoelectric parameter increases, there is a significant decrease in the velocity profiles u, a situation that is not observed when , where there are low induced potentials, and for this reason, as the dimensionless parameter increases, the velocity profiles remain constant. This condition is preserved for different values of the slip length .

Mass transport in oscillatory electroosmotic viscoelectric flow in a hydrophobic microchannel with steric effect

We conduct a numerical study of viscoelectric and steric effects on an oscillatory electroosmotic flow (OEOF) and their impact on the mass transport of a passive solute through a hydrophobic microchannel. In many applications of electroosmosis, zeta potentials as high as 100–200 mV can be found; in such a situation, the Debye–Hückel approximation is no longer valid, and the steric effect must be considered because the crowding of finite-sized ions close to the microchannel walls. In addition to the previous effect, the local viscosity can be increased due to the viscoelectric effect for strong electric potentials induced in the electric double layer. Earlier works have studied the mass transfer caused by an OEOF; however, the combined effects’ influence has not been considered. This research suggests that under an appropriate combination of the viscoelectric and steric effects, together with the microchannel hydrophobicity, the mass transport can be controlled and notably enhanced compared with the case where such effects are disregarded. An interesting behavior occurs for relatively high values of the steric factor ν, where there is a linear dependence between the mass transport and the viscoelectric factor ; in contrast, for low values of ν, the relationship is non-linear.

Influence of viscoelectric effect on diffusioosmotic transport in nanochannel.

We have investigated the role of viscoelectric effect on diffusioosmotic flow (DOF) through a nanochannel connected with two reservoirs. The transport equations governing the flow dynamics are solved numerically using the finite element technique. We have extensively analyzed the variation of induced field due to electric double layer (EDL) phenomenon, relative viscosity as modulated by the viscoelectric effect as well as reservoir's concentration difference, and their eventual impact on the underlying flow characteristics. It is revealed that the induced electric field in the EDL enhances fluid viscosity substantially near the charged wall at a higher concentration. We have shown that neglecting viscoelectric effect in the paradigm of diffusioosmotic transport overestimates the net throughput, particularly at a higher concentration difference. Furthermore, we show that pertaining to chemiosmosis dominated regime, the average flow velocity modifies with the increase in concentration difference up to a critical value. In comparison, the rise in the strength of resistive electroosmotic actuation by the accumulation of anions in the upstream reservoir reduces the average flow velocity at a higher concentration difference. We have reported a reduction in critical concentration with the increase in viscoelectric effect. The inferences of this analysis are deemed pertinent to reveal the bearing of viscoelectric effect as a flow control mechanism pertaining to DOF at nanoscale.

Direct measurement of the viscoelectric effect in water

The viscoelectric effect concerns the increase in viscosity of a polar liquid in an electric field due to its interaction with the dipolar molecules and was first determined for polar organic liquids more than 80 y ago. For the case of water, however, the most common polar liquid, direct measurement of the viscoelectric effect is challenging and has not to date been carried out, despite its importance in a wide range of electrokinetic and flow effects. In consequence, estimates of its magnitude for water vary by more than three orders of magnitude. Here, we measure the viscoelectric effect in water directly using a surface force balance by measuring the dynamic approach of two molecularly smooth surfaces with a controlled, uniform electric field between them across highly purified water. As the water is squeezed out of the gap between the approaching surfaces, viscous damping dominates the approach dynamics; this is modulated by the viscoelectric effect under the uniform transverse electric field across the water, enabling its magnitude to be directly determined as a function of the field. We measured a value for this magnitude, which differs by one and by two orders of magnitude, respectively, from its highest and lowest previously estimated values.

Analysis of thermal transport and entropy generation characteristics for electroosmotic flow through a hydrophobic microchannel considering viscoelectric effect

We investigate the thermo-fluidic and entropy generation characteristics for electroosmotic flow through a hydrophobic microchannel with the consideration of viscoelectric effect. A closed form expression for the velocity is obtained from the analytical solution of the momentum and continuity equations together with the Poisson-Boltzmann equation and thereafter the temperature field is computed numerically. The flow velocity, flow rate, average Nusselt number, and average total entropy generation are computed by varying the slip coefficient, viscoelectric coefficient (f), Brinkman number (Br), and thermal Peclet number(Pe). Results reveal that the viscoelectric effect decreases the flow velocity and percentage decrement in flow rate due to the viscoelectric effect is larger for the slip case and reaches up to 40.09%. The value of the average Nusselt number decreases with f at lower value of Br, and the effect is opposite at higher values of Br. Although the heat transfer enhancement is more with the interfacial slip, the augmentation decreases with f and increases with Pe. The value of average total entropy generation decreases with the increase in f, and decrement is substantial at higher values of Br.

Slip Effects on Ionic Current of Viscoelectric Electroviscous Flows through Different Length Nanofluidic Channels

The pressure driven slip flow of an electrolyte solution is studied through different nanofluidic channel lengths at varying salt concentrations. The viscous-thickening due to the electrostatic interactions within the electric double layer and the reverse ionic transport due to the streaming potential are developed. The influence of the Navier slip boundary condition is described under both electroviscous and viscoelectric effects with a surface charge regulation (CR) model while the observed behavior is compared and validated with molecular dynamic (MD) calculations from multiple studies. Results show that electroviscous and viscoelectric effects decrease transport. Earlier studies at the no slip boundary presented an increase of ionic current by increasing salt concentration and decreasing channel length. In contrast, our study found that the ionic current occurred almost independent of both salt concentration and channel length, except for very short channels and very low salt concentrations, when electroviscous and viscoelectric effects were considered. In the case of the constant slip length condition, ionic conduction was enhanced, but velocity slip developing on surfaces showed significant variation based on the salt concentration and channel length. This is due to the natural CR behavior enhancing the surface charge and consequential near surface electrohydrodynamics as a result of increase in salt concentration and/or decrease of channel length. Considering that the electroviscous effect alone creates up to 70% lower velocity slips than Poiseuille flow predictions, while further including the viscoelectric effect, results in an almost no-slip condition at high salt concentrations and/or short channels. As a result, the ionic current of a viscoelectric electroviscous slip flow is found to be equal to 1/3 of an electroviscous slip flow and to decrease with a decrease in the channel length.

Combined viscoelectric and steric effects on the electroosmotic flow in nano/microchannels with heterogeneous zeta potentials

The present study analyzes the combined viscoelectric and steric effects on the electroosmotic flow of Newtonian fluids in nano/microchannels. The governing equations that describe the flow field are the modified Poisson-Boltzmann equation for the electric potential, the mass conservation and momentum equations, which are solved numerically. On the channel walls, arbitrary and heterogeneous zeta potentials modulated via sinusoidal functions are imposed, being controlled by a phase angle, an amplitude and a wave number. The use of arbitrary zeta potentials leads to the study of the viscoelectric effect due to the fact that the viscosity near the walls of the channel increases drastically. Also, the presence of high ionic concentrations and large effective ionic sizes causes an excluded volume of the crowding of ions into the electric double layer; in this manner, the study of the steric effect is relevant in the present work. The results show that the viscoelectric effect produces a reduction in the magnitude of the velocity profiles when zeta potentials are magnified. On the contrary, the steric effect counteracts the aforementioned effect, increasing the velocity of the flow. In addition, the heterogeneous zeta potentials at the walls generate an induced pressure and recirculations on the flow. In particular, when the wave number is even leads to a condition with null volumetric flow rate; while for an odd wave number, a favorable volumetric flow rate is generated. This study extends the knowledge of electroosmotic flows under field effects for future mixing applications.

Combined viscoelectric and steric effects on the electroosmotic flow in a microchannel under induced high zeta potentials

Although the concepts of steric and the viscoelectric effects in the analysis of electrokinetic flows have been studied previously in nanochannels (Hsu et al., 2016), in the present work, their influence is extended to microchannels. The governing equations of Bikerman's Modified Poisson–Boltzmann (MPB) equation and the momentum conservation equation are solved numerically for an electroosmotic flow of a Newtonian fluid in a microchannel. Here, the excluded volume of the crowding of ions via steric factor is considered when high ionic concentration and large effective ionic size of the buffer solution are taken into account; also, the viscoelectric effect is present when high zeta potentials are induced and controlled by shielding electrodes at the walls of the microchannel. The results show a significant competition of the studied effects within the thin electric double layer, modifying the predictions from the classical velocity profiles of electroosmotic flows where the mentioned effects are not considered. It is reported that increasing the magnitude of the zeta potentials does not necessarily increase the volumetric flow rate as determined from the classical Poisson–Boltzmann (PB) theory. To validate the numerical solution, an approximate analytical solution for the velocity field for slightly high zeta potentials was determined.

On the oxygen reduction reaction in phosphoric acid electrolyte: Evidence of significantly increased inhibition at steady state conditions

In the presented work, we investigate the oxygen reduction reaction (ORR) in half-cell measurements employing different electrolytes. The aim is to compare the ORR inhibition due to anion adsorption at transient as well as steady state conditions. It is found that the ORR inhibition at the platinum − phosphoric acid electrolyte interface is a relative slow, time dependent process. The major inhibition is not observed in transient polarization curves but only under steady state conditions. This observation is in contrast to the typical ORR inhibition due to anion adsorption as observed for example in sulfuric acid electrolyte. In sulfuric acid the inhibition is fast and then stays more or less constant in time. As a consequence of our findings, common transient measurements of the ORR activity might not be sufficient to investigate suitable mitigation strategies for the ORR inhibition in phosphoric acid electrolyte. Such strategies need to take steady state conditions into account.In order to explain the slow ORR inhibition in phosphoric acid electrolyte, two possible explanations are discussed. Either the adsorption of phosphate is a slow, complex process, where a fast adsorption step is followed by a consecutive filling of the surface, or a mass transfer barrier develops at the polarized phosphoric acid–electrode interface. The latter might be the viscoelectric effect that is known from colloidal science.

Viscoelectric effect on electroosmotic flow in a cylindrical microcapillary

Electroosmotic flow, under the Debye–Hückel approximation, has been widely analyzed in the specialized literature. This is a severe restriction in practice, where zeta potentials as high as 100–200 mV are encountered frequently. Under this condition, the variation of the viscosity with the electric field in the electric double layer (EDL), known as the viscoelectric effect, can lead to a considerable variation in comparison to the Helmholtz–Smoluchowsky equation for the electroosmotic velocity. The objective of this work is to analyze the electroosmotic flow in a cylindrical capillary at high zeta potentials in the thin EDL approximation, taking into account the viscoelectric effect. In order to obtain the potential distribution, the Poisson–Boltzmann equation was solved by using the matched asymptotic expansions method, and then, by applying the same technique, the flow field was determined from the momentum equation by considering that the viscosity of the electrolyte changes according to the relationship , where is the viscosity evaluated in the absence of an electric field, f is the viscoelectric constant and E is the intrinsic electric field in direction transversal to the EDL. For asserting the correctness of the asymptotic solution, this result was compared against a numerical solution, and a very good agreement between them was found. The results show that the viscoelectric effect has a noticeable influence by reducing the electroosmotic flow velocity in about 10% in comparison to the standard Helmholtz–Smoluchowski velocity.

Regimes of streaming potential in cylindrical nano-pores in presence of finite sized ions and charge induced thickening: An analytical approach

We obtain approximate analytical expressions for the streaming potential and the effective viscosity in a pure pressure-driven flow through a cylindrical pore with electrokinetic interactions, duly accounting for the finite size effects of the ionic species (steric effects) and charge-induced thickening. Our analytical results show a remarkable agreement with the numerical solution even for high surface potentials and small channel radii. We demonstrate a consistent increment in the predicted value of the streaming potential and effective viscosity when finite size effects of the ionic species are accounted for. In addition to this, we account for the radial variation of in the viscosity of the fluid due to charge-induced thickening. We show that this so-called viscoelectric effect leads to a decrease in the induced streaming potential especially at high steric factors and high surface potentials. However, the viscoelectric effect, which is prominent at high zeta potential and narrow channels, does not cause significant changes in the electrokinetic conversion efficiency. These results shed light on the interesting confluence of the steric factor, the channel radius, the electrical double layer screening length, and the surface charge density in conjunction with the charge induced thickening, and thus provide ion-size dependent analytical framework for accurate system design and better interpretation of electrokinetic data.

Modelling of EDL effect on chloride migration in cement-based materials

The shortcomings of the geometrical approach for studying the chloride ingress through cement-based material have been highlighted previously. Improving this approach requires taking into account the electrical double layer (EDL) occurring at the interface between the pore walls and the pore solution. This is the aim of the present work. First, it is shown that the viscoelectric effect of EDL depends on pore diameter and zeta potential. Second, the decelerating effect of EDL is seen to induce a decrease in co-ions flux and an increase in counter-ions flux. Finally, the proposed macroscopic model is validated through monitoring of current densities during chloride migration tests carried out on cement mortars. Simulated current densities are found to be in good agreement with measured values.

Shortcomings of geometrical approach in multi-species modelling of chloride migration in cement-based materials

Chloride migration tests and chronoamperometries were carried out on three cement mortars with different water/cement (w/c) ratios. The electrical current of the chloride migration is simulated with a multi-species model, which takes into account the geometrical properties of the pore structure throughout the diffusibility ratio. The comparison between the measured and the simulated currents shows a significant difference: systematically, simulated currents evolve faster than those measured. From these results, it appears that the purely geometrical approach alone is insufficient correctly to describe the transport of ionic species in cement-based materials. Finally, it is shown that the introduction of a ‘viscoelectric effect’, which conveys the electrical double-layer effect (EDL), improves the results of the model. As a first approach the EDL is taken into account empirically by considering a reducing factor 1/rD applied to the effective diffusion coefficients of the cations. This factor is deduced from Truc's work.

On the slip process in electrokinetics

The slip process in electrokinetics is reconsidered in terms of recent insights into the structure of water near surfaces. There is an apparent stagnant layer on the surface, but this observation is not in conflict with substantial tangential conduction in that layer. Zeta potentials, computed for a limited number of well-defined systems, after correction for surface conduction, level off at plateaux below that corresponding to about 2.5 μC cm −2 of electrokinetic charge. The plateaux are almost independent of the nature of the surface and may be explained in terms of the viscoelectric effect. The desirability of further systematic studies is stressed.

Electrorheological effects and gating of membrane channels

A hypothesis is presented on the gating of ion channels. This is considered as a consequence, in part, of a large increase in viscosity of the water in the "vestibule" region of the channel in the high field present when the channel is not conducting. This part of gating amounts to "melting" of the high viscosity part of the water upon release of the field. The resulting model accounts qualitatively for a number of phenomena in the literature, including the steepness of the voltage dependence of gating, the slowing of gating upon substitution of D2O for H2O, and the pressure dependence of the gating kinetics. The viscosity increase with field is well known in the literature; several forms of electroviscous effects, a viscoelectric effect, and a generalized electrorheological effect have been described. This model appears closest to an electrorheological effect in which boundary water out to a few molecular diameters is structured in the presence of a high field, while the boundary (here, protein) moves. The size of the channel entrance is small enough for this effect to prevent conductivity. The remainder of the gating current, which occurs at more polarized potentials, is attributed to protein motion. Some consequences of the model are discussed. Qualitative comparison with published data is included.

Constant pressure viscometer to measure viscoelectric effect based on a drop counter

We describe a viscometer based on the fact that a succession of drops created at constant pressure and temperature exhibit equal weights. This viscometer was used to detect small flow changes due to the presence of an electric field applied transversally to the liquid flow.

Viscoelectric effects in reverse osmosis

The equations of motion and conservation, which include the effect of the electric field, together with the Poisson equation, have been solved for a single charged cylindrical pore, over a wide range of conditions, to compute the flow rate of water as well as the fluxes of salt and the rejection coefficient. The calculations have been carried out for both constant surface potential and constant surface charge. At constant surface potential and if the surface potential is sufficiently large, the flow of water is decreased by the electrical field by a large amount. For instance, the decrease can be as large as 90% for a surface potential of 75 mV. At constant surface charge, the decrease is about 20% for a surface charge of 10 4 esu/cm 2. The rejection coefficient is somewhat lower when the viscoelectric effect is taken into account. A membrane can reject salt, only up to a maximum value for a given set of conditions. This maximum is primarily determined by the electrical properties of the pore walls, and to a very large extent by the diffusivities of the co-ions and counterions. Besides the numerical calculations, some approximate analytical solutions are also presented.

Rheological electrokinetic phenomena in a single capillary

A numerical simulation of rheological electrokinetic phenomena in a rectangular capillary slit is reported. The theological state of the vicinity water in the capillary is based on the Babchin—Piliavin—Levich model of the viscoelectric effect. The electrical field of the diffuse double layer is considered as the cause for the non-Newtonian behaviour of the interface water layers. A special numeric procedure is suggested to solve the closed system of equations which describe the generalized flows through the capillary. The solution for a particular case (10 −5 N KCl water solution, 2 μm x 0.6 cm x 1 cm capillary slit) is presented and discussed. An approximate linear relation between the driving forces and the total current and volume fluxes is obtained and used to determine the phenomenological kinetic coefficients. The electrokinetic ζ-potentials which are functions of the surface charges (potentials) and external conditions are predicted. It is found that ζ-potentials may be different for different electrokinetic experiments. The results are compared with predictions based on a classical viscous flow model.