Electrohydrodynamics within the electrical double layer in the presence of finite temperature gradients

Blue energy generation by the temperature-dependent properties in funnel-shaped soft nanochannels

Salinity energy generation (SEG) studies have only been done under isothermal conditions at ambient temperature. The production of salinity energy can be improved under non-isothermal conditions, albeit preserving the energy efficiency. In the current study, the effects of gradients of temperature and concentration on the salinity energy generation process were examined simultaneously. Based on the temperature-dependent properties resulting from both temperature and concentration gradients, a numerical study was carried out to determine the maximum efficiency of salinity energy generation in funnel-shaped soft nanochannels. It was presumed that a dense layer of negative charge, called a polyelectrolyte layer (PEL), is coated on the walls of the nanochannels. Co-current and counter-current modes were used to obtain temperature and concentration gradients. Under steady-state conditions, the Poisson-Nernst-Planck, Stokes-Brinkman, and energy equations were numerically solved using equivalent approaches. The results revealed that by increasing the temperature and concentration ratios in both co-current and counter-current modes of operation, the salinity energy generation increased appreciably. The salinity energy generation increased from 30 to 80 pW upon increasing the temperature ratio from 1 to 8 at a constant concentration ratio of 1000 in counter-current mode. As verified from this analysis, low-grade heat sources (<100 °C) provide considerable energy conversion in PEL grafted nanofluidic confinement when placed between electrolyte solutions of different temperatures.

Charge Regulation and pH Effects on Thermo-Osmotic Conversion

Thermo-osmotic energy conversion using waste heat is one of the approaches to harvesting sustainable energy and reducing associated environmental impacts simultaneously. In principle, ions transport through a charged nanopore membrane under the effect of a thermal gradient, inducing a different voltage between two sides of the membrane. Recent publications mainly reported novel materials for enhancing the thermoelectric voltage in response to temperature difference, the so-called Seebeck coefficient. However, the effect of the surface charge distribution along nanopores on thermo-osmotic conversion has not been discussed yet. In this paper, a numerical simulation based on the Nernst-Planck-Poisson equations, Navier-Stokes equations, and heat transfer equations is carried out to consider the effect of surface charge-regulation density and pH of KCl solutions on the Seebeck coefficient. The results show that the highest ionic Seebeck coefficient of -0.64 mV/K is obtained at 10^-4 M KCl solution and pH 9. The pH level and pore structure also reveal a strong effect on the thermo-osmotic performance. Moreover, the pH level at one reservoir is varied from 5 to 9, while the pH of 5 is fixed at the other reservoir to investigate the pH effect on the thermos-osmosis ion transport. The results confirm the feasibility that using the pH can enhance the thermo-osmotic conversion for harvesting osmotic power from low-grade heat energy.

Simultaneous thermoosmotic and thermoelectric responses in nanoconfined electrolyte solutions: Effects of nanopore structures and membrane properties

HYPOTHESIS

Nanofluidic systems provide an emerging and efficient platform for thermoelectric conversion and fluid pumping with low-grade heat energy. As a basis of their performance enhancement, the effects of the structures and properties of the nanofluidic systems on the thermoelectric response (TER) and the thermoosmotic response (TOR) are yet to be explored.

METHODS

The simultaneous TER and TOR of electrolyte solutions in nanofluidic membrane pores on which an axial temperature gradient is exerted are investigated numerically and semi-analytically. A semi-analytical model is developed with the consideration of finite membrane thermal conductivity and the reservoir/entrance effect.

FINDINGS

The increase in the access resistance due to the nanopore-reservoir interfaces accounts for the decrease of short circuit current at the low concentration regime. The decrease in the thermal conductivity ratio can enhance the TER and TOR. The maximum power density occurring at the nanopore radius twice the Debye length ranges from several to dozens of mW K^-2 m^-2 and is an order of magnitude higher than typical thermo-supercapacitors. The surface charge polarity can heavily affect the sign and magnitude of the short-circuit current, the Seebeck coefficient and the open-circuit thermoosmotic coefficient, but has less effect on the short-circuit thermoosmotic coefficient. Furthermore, the membrane thickness makes different impacts on TER and TOR for zero and finite membrane thermal conductivity.

Streaming-potential-mediated pressure-driven transport of Phan-Thien-Tanner fluids in a microchannel

Streaming potential mediated pressure driven electrokinetic transport of Phan-Thien-Tanner fluids in a slit type parallel plate microchannel is studied analytically and semianalytically. Without adopting the traditional considerations of Debye-Hückel linearization approximation for low surface potentials, exact analytical solutions are obtained for the electrostatic potential distribution, velocity, and volumetric flow rates taking into account the full Poisson-Boltzmann equation. The influences of interfacial electrokinetics and viscoelasticity on the streaming potential development, polymeric stress components, shear viscosity, and the hydroelectric energy conversion efficiency are incorporated concurrently. Major findings indicate that the magnitude of the induced streaming potential, volumetric flow rates, and the energy conversion efficiency increases up to a threshold limit of zeta potential of ζ≤6, however, it follows an asymptotic reduction at the other end of higher zeta potentials 6<ζ≤10. The polymeric stress components and shear viscosity follow a similar trend in the regime of 1≤ζ≤10, which is primarily governed by the streaming potential field. In contrast, the transverse averaged shear viscosity in the range 1≤ζ≤10 obeys an opposite trend by yielding an inverted parabolic shape. Amplification in the Stern layer conductivity yields a progressive reduction in the streaming potential magnitude and the hydroelectric energy conversion efficiency. The effect of the fluid viscoelasticity designated by the Weissenberg number exhibits a linear enhancement in streaming potential, flow rates, and the energy conversion efficiency. Moreover, we show that with the optimal combinations of surface charging and fluid viscoelasticity, it is possible to accomplish a giant augmentation in the hydroelectric energy conversion efficiency and flow rates. The analytical and semianalytical results presented in this investigation are believed to be worthy not only to cater deeper understanding in micro- and nanofluidic transport characteristics but also will act as functional design instrument for the future generation of energy efficient narrow fluidic devices.

Non-isothermal flow of an electrolyte in a charged nanochannel

Electrokinetic flows are generally analyzed, assuming isothermal conditions even though such situations are hard to be achieved in practice. In this paper, the flow of a symmetric electrolyte in a charged nanochannel subjected to an axial temperature gradient is investigated using molecular dynamics simulations. We analyze the relative contribution of the Soret effect, the thermoelectric effect, and the double layer potential in the electrical double layer for various surface charges and temperature gradients. We find the flow driven by thermal gradient is analogous to electroosmotic flow. The thermophoretic motion of the electrolyte is significant for negative surface charge than the positive surface charge. The vibrational spectrum of graphene is calculated to delineate the effect of the surface charge polarity on the observed thermophoretic motion of the electrolyte. A unique structure of interfacial water layer is observed for the positive and negative surface charges. We attribute the presence of these structures to the differences in water-carbon interactions existing for various surface charge polarity. For an applied thermal gradient in the range 2.6 K nm-1 to 8 K nm-1, we observe a continuous net flow with average velocities reaching up to 9.4 m s-1 inside the channel for a negative surface charge of -0.101 C m-2. The results indicate that in a charged graphene-based nanochannel, temperature gradients can be employed to induce streaming current, depending on the relative influence of the Soret effect and the double layer potential.

Thermal-Driven Ion Transport in Porous Materials for Thermoelectricity Applications

Transport of thermal-driven ions in porous materials has not been clearly explained yet, while this transport has great application potential in co-generation of vapor and electricity for a bi-layer seawater desalination system. In this work, by taking into account the actually structure of a porous material, we theoretically modeled the thermal-driven ion transport in a porous material and also the resultant current and potential produced by such a transport. With models solved by the finite element method, it turns out that a porous material with a cross section of 30 × 10 mm² could give a thermal current of about 27.2 mA, a thermal potential of about 63.7 mV, and a thermal power of about 433.2 μW, which are large enough to drive commercial electronic devices. This work provides a possibility of a vapor electricity co-generation in a bi-layer desalination system.

Self-thermoelectrophoresis at low salinity

A locally heated Janus colloid can achieve motion in an electrolyte by an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte using the finite-element method and analytic theory. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we employ Teubner's integral formalism to arrive at expressions for the speed, which agree semi-quantitatively with our numerical results for conducting swimmers. This lends credibility to the remarkably high swim speed at very low ionic strength, which we numerically obtain for a fully insulating swimmer. We also report on hot swimmers with a mixed electrostatic boundary conditions. Our results should benefit the realization and analysis of further experiments on thermo(di)electrophoretic swimmers.

Patterned surface charges coupled with thermal gradients may create giant augmentations of solute dispersion in electro-osmosis of viscoelastic fluids

Augmenting the dispersion of a solute species and fluidic mixing remains a challenging proposition in electrically actuated microfluidic devices, primarily due to an inherent plug-like nature of the velocity profile under uniform surface charge conditions. While a judicious patterning of surface charges may obviate some of the concerning challenges, the consequent improvement in solute dispersion may turn out to be marginal. Here, we show that by exploiting a unique coupling of patterned surface charges with intrinsically induced thermal gradients, it may be possible to realize giant augmentations in solute dispersion in electro-osmotic flows. This is effectively mediated by the phenomena of Joule heating and surface heat dissipation, so as to induce local variations in electrical properties. Combined with the rheological premises of a viscoelastic fluid that are typically reminiscent of common biofluids handled in lab-on-a-chip-based micro-devices, our results demonstrate that the consequent electro-hydrodynamic forcing may open up favourable windows for augmented hydrodynamic dispersion, which has not yet been unveiled.

Interfacial Electric Effects on a Non-Isothermal Electroosmotic Flow in a Microcapillary Tube Filled by Two Immiscible Fluids

In this work, a non-isothermal electroosmotic flow of two immiscible fluids within a uniform microcapillary is theoretically studied. It is considered that there is an annular layer of a non-Newtonian liquid, whose behavior follows the power-law model, adjacent to the inside wall of the capillary, which in turn surrounds an inner flow of a second conducting liquid that is driven by electroosmosis. The inner fluid flow exerts an interfacial force, dragging the annular fluid due to shear and Maxwell stresses at the interface between the two fluids. Because the Joule heating effect may be present in electroosmotic flow (EOF), temperature gradients can appear along the microcapillary, making the viscosity coefficients of both fluids and the electrical conductivity of the inner fluid temperature dependent. The above makes the variables of the flow field in both fluids, velocity, pressure, temperature and electric fields, coupled. An additional complexity of the mathematical model that describes the electroosmotic flow is the nonlinear character due to the rheological behavior of the surrounding fluid. Therefore, based on the lubrication theory approximation, the governing equations are nondimensionalized and simplified, and an asymptotic solution is determined using a regular perturbation technique by considering that the perturbation parameter is associated with changes in the viscosity by temperature effects. The principal results showed that the parameters that notably influence the flow field are the power-law index, an electrokinetic parameter (the ratio between the radius of the microchannel and the Debye length) and the competition between the consistency index of the non-Newtonian fluid and the viscosity of the conducting fluid. Additionally, the heat that is dissipated trough the external surface of the microchannel and the sensitivity of the viscosity to temperature changes play important roles, which modify the flow field.

Temperature effects on the electrohydrodynamic and electrokinetic behaviour of ion-selective nanochannels

A non-isothermal formulation of the Poisson-Nernst-Planck with Navier-Stokes equations is used to study the influence of heating effects in the form of Joule heating and viscous dissipation and imposed temperature gradients on a microchannel/nanochannel system. The system is solved numerically under various cases in order to determine the influence of temperature-related effects on ion-selectivity, flux and fluid flow profiles, as well as coupling between these phenomena. It is demonstrated that for a larger reservoir system, the effects of Joule heating and viscous dissipation only become relevant for higher salt concentrations and electric field strengths than are compatible with ion-selectivity due to Debye layer overlap. More interestingly, it is shown that using different temperature reservoirs can have a strong influence on ion-selectivity, as well as the induced electrohydrodynamic flows.

Effect of thermodiffusion on pH-regulated surface charge properties of nanoparticle

Surface properties of nanoparticle are of high importance in the field of biotechnology, drug delivery and micro/nanofabrication. In this article, we developed a comprehensive theoretical model and subsequently solved that numerically to study the effect of thermodiffusion of ions on surface charge properties of nanoparticle. The theoretical study has been done considering silica nanoparticle for two aqueous solutions NaCl and KCl. The effect of solution pH in conjunction with nanoparticle temperature on surface charge density has been obtained for different salt concentrations (1, 10 and 100 mM) and nanoparticle size (diameter of 2 and 100 nm). It is observed from the results that with increasing temperature of the nanoparticle, the negative surface charge density gets higher due to increasing thermodiffusion effect. It is also found out that the magnitude of surface charge density is higher for KCl solution than NaCl solution under same condition which is attributed mostly due to less thermodiffusion of counterions for KCl than NaCl. Present study also shows that magnitude of surface charge density decreases with increasing nanoparticle size until it reaches a limiting value (called critical size) above which the effect of nanoparticle size on surface charge density is insignificant.