Combined electroosmotically and pressure driven flow in soft nanofluidics

Electro-Osmotic Flow and Mass Transfer through a Rough Microchannel with a Modulated Charged Surface

In this paper, we investigate the electro-osmotic flow (EOF) and mass transfer of a Newtonian fluid propelled by a pressure gradient and alternating current (AC) electric field in a parallel microchannel with sinusoidal roughness and modulated charged surfaces. The two-wall roughness is described by in-phase or out-of-phase sine functions with a small amplitude δ. By employing the method of perturbation expansion, the semi-analytical solutions of the Poisson-Boltzmann (P-B) equation based on the Debye-Hückel approximation and the modified Navier-Stokes (N-S) equation are obtained. The numerical solution of the concentration equation is obtained by the finite difference method. The effects of sinusoidal roughness, modulated charged surface, and the AC electric field on the potential field, velocity field, and concentration field are discussed. Under the influence of the modulated charged surface and sinusoidal roughness, vortices are generated. The velocity oscillates due to the effect of the AC electric field. The results indicate that solute diffusion becomes enhanced when the oscillation Reynolds number is below a specific critical value, and it slows down when the oscillation Reynolds number exceeds this critical value.

Impact of hydrodynamics and rheology of the ion partitioning effect on electrokinetic flow through a soft annulus with a retentive and absorptive wall

The theoretical analysis for the mass transfer process of an oscillatory electroosmotic flow (EOF) in the fractional Jeffrey fluid model is studied through a polyelectrolyte layer (PEL) coated cylindrical annulus with reversible and irreversible wall reactions. The ion partitioning effect is observed due to the difference in permittivity of the PEL and the electrolyte solution, which is accounted for by the Born energy. Considering ion partitioning effects, analytical solutions for induced potential and axial velocity are presented, respectively in both the PEL and electrolyte region from the modified Poisson-Boltzmann equation and the Cauchy momentum equation with a proper constitutive equation, respectively. The Maxwell fluid and classical viscous Newtonian fluid models can be achieved separately by adjusting the relaxation and retardation time in the constitutive equation of this model. The analytical solution of the convection-diffusion equation for solute transport is established in the full domain. The separation of species is found to be dependent mainly on the Damköhler number, absorption parameter, phase partitioning coefficient, etc. It is observed that the osmotic pressure increases with the thickness and fixed charge density of the PEL. The velocity decreases with an increase in the permittivity difference of these layers. Our results suggest that the separation may be achieved through a difference in absorption kinetics.

Space Electroosmotic Thrusters in Ion Partitioning Soft Nanochannels

Space electroosmotic thrusters (EOTs) are theoretically investigated in a soft charged nanochannel with a dense polyelectrolyte layer (PEL), which is considered to be more realistic than a low-density PEL. When the PEL is dense, its permittivity is smaller than the one of the electrolyte solution layer, leading to rearrangement of ions in the channel, which is denoted as the ion partitioning effect. It is noted that fluid viscosity becomes high within the PEL owing to the hydration effect. An analytical solution for electroosmotic velocity through the channel is obtained by utilizing the Debye-Hückel linearization assumption. Based on the fluid motion, thruster performances, including thrust, specific impulse, thrust-to-power ratio, and efficiency, are calculated. The ion partitioning effect leads to enhancement of the thruster velocity, while increase of the dynamic viscosity inside the PEL reduces the flow rate of the fluid. Therefore, these performances are further impacted by the dense soft material, which are discussed in detail. Moreover, changes or improvements of the thruster performances from the dense PEL to the weak PEL are presented and compared, and distributions of various energy items are also provided in this study. There is a good result whereby the increase in electric double layer thickness promotes the development of thruster performances. Ultimately, the simulated EOTs produce thrust of about 0 to 20 μN and achieve thruster efficiency of 90.40%, while maintaining an appropriate thrust-power ratio of about 1.53 mN/W by optimizing all design parameters.

Electrokinetic ion transport and fluid flow in a pH-regulated polymer-grafted nanochannel filled with power-law fluid

In this article, we have discussed extensively electrokinetic ion transport and fluid flow through a slit polymer-grafted nanochannel filled with power-law fluid. The rigid walls of the channel are coated with the ion and fluid penetrable polymer layer containing a pH-regulated zwitterionic functional group (e.g., succinoglycan). The mathematical model is based on the non-linear Poisson-Boltzmann equation for electric double layer potential and the flow field within the polymer layer is governed by a modified Darcy-Brinkman equation; the Cauchy momentum equation governs the fluid flow outside of the polymer layer along with the equation of continuity for incompressible fluid. In order to consider a wide range of pertinent parameters, we adopt a finite difference based numerical tool to solve the coupled set of governing equations. We have analyzed several interesting features of electrokinetic transport phenomena through such a polymer-grafted nanochannel for a wide range of electrostatic and hydrodynamic properties of the polymer layer, parameters describing the non-Newtonian rheology of the background fluid, and the pH and concentration of the bulk electrolyte. In addition, we have also illustrated the ionic current across the undertaken nanochannel and observed that it can be either cation selective, anion selective or non-selective, depending on the critical choice of the pertinent parameters.

Mass transfer of a neutral solute in polyelectrolyte grafted soft nanochannel with porous wall

A soft nanochannel involves a soft interface that contains a polyelectrolyte layer (PEL) sandwiched between a rigid surface and a bulk electrolyte solution. Mass transfer of a neutral solute in a combined electroosmotic and pressure driven flow through a polyelectrolyte grafted charged nanochannel with porous wall is presented in this work. Assuming the PEL as fixed charged layer and PEL-electrolyte interface as a semi-penetrable membrane, analytical solutions were obtained for potential distributions (for small wall potential). Velocity profiles were also derived in the same domains, for both inside and outside the PEL. Convective-diffusive species balance equation was semi-analytically solved inside the PEL. Expression of length averaged Sherwood number was also obtained and effects of different parameters, namely, drag parameter (α), Debye parameter ( κ ¯ ) , and PEL thickness were studied in detail. The variation of permeate concentration and permeation flux across the porous wall was obtained.

Electrohydrodynamic transport of non-symmetric electrolyte through porous wall of a microtube

Transport of salt through the wall of porous microtube is relevant in various physiological microcirculation systems. Transport phenomena based modeling of such system is undertaken in the present study considering a combined driving force consisting of pressure gradient and external electric field. Transport of salt is modeled in two domains, in the flow conduit and in the pores of porous wall of the microtube. The solute transport in the microtube is presented by convective-diffusive mass balance and it is solved using integral method under the framework of boundary layer analysis. The wall of the microtube is considered to be consisting of series of straight parallel cylindrical pores with charged inner surface. The solute transport through the pores is considered to be composed of diffusive, convective and electric potential gradient governed by Nernst-Planck equation. Transport in the microtube and pores is coupled through the osmotic pressure model for the solvent and Donnan equilibrium distribution for the solute. The simulated results agree remarkably well with the experimental data conducted by in-house experimental set up. The charge density of the porous wall is estimated through the minimization of errors involved between the experimental and simulated data for different operating conditions.

Heat Transport of Electrokinetic Flow in Slit Soft Nanochannels

Soft nanochannels are defined as nanochannels with a polyelectrolyte layer (PEL) on the rigid walls. In the present study, the thermal transport properties of the fluids through slit soft nanochannels are investigated under the combined influences of pressure-driven and streaming potential. Based on the analytical solutions of electric potential and velocity distributions, a dimensionless temperature of electrolyte solution in soft nanochannels is obtained by resolving the energy equation. Then, a finite difference method is used to compute the energy equation and test the validity of the analytical solution. Results show that the temperature increases with the decrease of dimensionless velocity and the heat transfer rate for rigid nanochannel are higher than that for the soft one. Moreover, we find the total entropy generation decreases with the increases of the ratio K_λ of the electrical double layer (EDL) thickness in PEL to the EDL thickness on the solid wall.

Softness Induced Enhancement in Net Throughput of Non-Linear Bio-Fluids in Nanofluidic Channel under EDL Phenomenon

In this article, we describe the electro-hydrodynamics of non-Newtonian fluid in narrow fluidic channel with solvent permeable and ion-penetrable polyelectrolyte layer (PEL) grafted on channel surface with an interaction of non-overlapping electric double layer (EDL) phenomenon. In this analysis, we integrate power-law model in the momentum equation for describing the non-Newtonian rheology. The complex interplay between the non-Newtonian rheology and interfacial electrochemistry in presence of PEL on the walls leads to non-intuitive variations in the underlying flow dynamics in the channels. As such, we bring out the variations in flow dynamics and their implications on the net throughput in the channel in terms of different parameters like power-law index (n), drag parameter (α), PEL thickness (d) and Debye length ratio (κ/κ_PEL) are discussed. We show, in this analysis, a relative enhancement in the net throughput through a soft nanofluidic channel for both the shear-thinning and shear-thickening fluids, attributed to the stronger electrical body forces stemming from ionic interactions between polyelectrolyte layer and electrolyte layer. Also, we illustrate that higher apparent viscosity inherent with the class of shear-thickening fluid weakens the softness induced enhancement in the volumetric flow rate for the shear-thickening fluids, since the viscous drag offered to the f low f ield becomes higher for the transport of shear-thickening fluid.

Macroion adsorption-electrokinetic and optical methods

Recent studies on macroion adsorption at solid/liquid interfaces evaluated by electrokinetic and optical methods are reviewed. In the first section a description of electrokinetic phenomena at a solid surface is briefly outlined. Various methods for determining both static and dynamic properties of the electrical double layer, such as the appropriate location of the slip plane, are presented. Theoretical approaches are discussed concerning quantitative interpretation of streaming potential/current measurements of homogeneous macroscopic interfaces. Experimental results are presented, involving electrokinetic characteristics of bare surfaces, such as mica, silicon, glass etc. obtained from various types of electrokinetic cells. The surface conductivity effect on zeta potential is underlined. In the next section, various theoretical approaches, proposed to determine a distribution of electrostatic potential and flow distribution within macroion layers, are presented. Accordingly, the influence of the uniform as well as non-uniform distribution of charges within macroion layer, the dissociation degree, and the surface conductance on electrokinetic parameters are discussed. The principles, the advantages and limits of optical techniques as well as AFM are briefly outlined in Section 4. The last section is devoted to the discussion of experimental data obtained by streaming potential/current measurements and optical methods, such as reflectometry, ellipsometry, surface plasmon resonance (SPR), optical waveguide lightmode spectroscopy (OWLS), colloid enhancement, and fluorescence technique, for mono- and multilayers of macroions. Results of polycations (PEI, PAMAM dendrimers, PAH, PDADMAC) and polyanions (PAA, PSS) adsorption on mica, silicon, gold, and PTFE are quantitatively interpreted in terms of theoretical approaches postulating the three dimensional charge distribution or the random sequential adsorption model (RSA). Macroion bilayer formation, experimentally examined by streaming current measurements, and theoretically interpreted in terms of the comprehensive formalism is also reviewed. The utility of electrokinetic measurements, combined with optical methods, for a precise, in situ characteristics of macroion mono- and multilayer formation at solid/liquid interfaces is pointed out.

Transient alternating current electroosmotic flow of a Jeffrey fluid through a polyelectrolyte-grafted nanochannel

Comparison of the velocity amplitude for Newtonian, Maxwell and Jeffrey fluids in PE-grafted and rigid nanochannels.

Electrokinetics in polyelectrolyte grafted nanofluidic channels modulated by the ion partitioning effect

The effects of ion partitioning on the electrokinetics in a polyelectrolyte grafted nanochannel, which is the representative of a soft nanochannel, are analyzed. Earlier studies in this regard have considered low polyelectrolyte layer (PEL) grafting density at the rigid nanochannel wall and, hence, an equal permittivity inside and outside the grafted layer. In order to overcome this shortcoming, the concept of Born energy is revisited. The coupled system of the modified Poisson-Boltzmann and Navier-Stokes equation is solved numerically, going beyond the widely employed Debye-Hückel linearization and low PEL densities. The complex interplay between the hydrodynamics and charge distribution, modulated by the ion partitioning effect, along with their consequent effects on the streaming potential and electrokinetic energy conversion efficiency (EKEC) have been systemically investigated. It has been observed that the ion partitioning effect reduces the EKEC in comparison to the case with equal permittivity up to a certain electrical double layer thickness after which it increases the EKEC. For a high concentration of mobile charges within the PEL, the net gain in the maximum EKEC due to the ion partitioning effect is about 10 fold that of the case when the ion partitioning effect is not considered. We delve into the various scaling regimes in the streaming potential and intriguingly point out the exact location of peaks in efficiency. The present study also reveals the possibility of improvement in streaming potential mediated energy conversion by the use of polyelectrolyte materials, which possess substantially lower dielectric permittivity than the bulk electrolyte.