Resolving Anomalies in Predicting Electrokinetic Energy Conversion Efficiencies of Nanofluidic Devices

Energy harvesting from water streaming at charged surface

Water flowing at a charged surface may produce electricity, known as streaming current/potentials, which may be traced back to the 19th century. However, due to the low gained power and efficiencies, the energy conversion from streaming current was far from usable. The emergence of micro/nanofluidic technology and nanomaterials significantly increases the power (density) and energy conversion efficiency. In this review, we conclude the fundamentals and recent progress in electrical double layers at the charged surface. We estimate the generated power by hydrodynamic energy dissipation in multi-scaling flows considering the viscous systems with slipping boundary and inertia systems. Then, we review the coupling of volume flow and current flow by the Onsager relation, as well as the figure of merits and efficiency. We summarize the state-of-the-art of electrokinetic energy conversions, including critical performance metrics such as efficiencies, power densities, and generated voltages in various systems. We discuss the advantages and possible constraints by the figure of merits, including single-phase flow and flying droplets.

A hybrid theoretical method for predicting electrokinetic energy conversion in nanochannels

The traditional methods to predict electrokinetic energy conversion (EKEC) in nanochannels are mostly based on the Navier-Stokes (NS) equation for ionic flow and the Poisson-Boltzmann (PB) equation for charge distributions, which is questionable for ion transport through highly charged nanochannels. In this work, the classical density functional theory (cDFT) is used together with molecular dynamics (MD) simulation and the Navier-Stokes (NS) equation to predict the electrical current and the thermodynamic efficiency of electrokinetic energy conversion in nanochannels. By introducing numerical results for the slip length calculated from MD simulation, a significant increase of the electrokinetic current is predicted in comparison to that obtained from the traditional electrokinetic equations with the non-slip boundary condition, leading to the theoretical predictions of the thermodynamic efficiency for electrokinetic energy conversion in nanochannels in good agreement with recent experiments. The hybrid method predicts that maximum electrokinetic efficiency can be achieved by tuning the channel height and solution conditions including electrolyte concentrations, ion valences, and surface energies. The theoretical results provide new insights into pressure-driven electrical energy generation processes and helpful guidelines for engineering design and optimization of electrokinetic energy conversion.

The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates

Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed for strongly overlapped electrical double layers (EDL), accounting for the steric effect of ions and their expulsion from EDL edges into the surrounding solution. As a generalization of a study by Philipse et al. which does not account for these effects, an analytical expression is derived for the repulsion pressure in the limit of infinitely long plates with a zero-field assumption, which agrees closely with the corresponding numerical solution at low inter-plate separations. Our results show an augmented repulsive pressure for finite-sized ions at strong EDL overlaps. For plates with a finite lateral size, we demonstrate a further extended domain of low inter-plate gaps where the repulsion pressure increases with ion size due to a strong interplay between the steric interaction of ions and the EDL overspill phenomenon, considered earlier in a study by Ghosal & Sherwood limited to the linear Debye-Hückel regime (which cannot account for the steric effect of ions). This investigation on a simple model should enhance our understanding of the interaction between charged particles in electrophoresis, nanoscale self-assembly, active particles, and various other electrokinetic systems.

Microfluidic Schottky-junction photovoltaics with superior efficiency stimulated by plasmonic nanoparticles and streaming potential

A droplet energy harvester (DEH) composed of aqueous salt solution could generate electrical energy from light when placed on a metal-semiconductor Schottky-junction emulating the principles of electrochemical photovoltaics (ECPV). The maximum potential difference generated was ∼95 mV under sun, which was enhanced by ∼1.5 times after the addition of gold nanoparticles (AuNPs) in the droplet because of the generation of additional charge carriers from the localized surface plasmon resonance (LSPR). Focusing the solar illumination through a bi-convex lens on five such droplets increased the voltage to ∼320 mV with a power density of ∼0.25 mW cm^-2. When the DEH was converted to a microfluidic energy harvester (MEH) by flowing the AuNP laden salt solution through a microchannel integrated with an array of Schottky-junction electrodes, at an optimal flow rate, another two-fold increase in the power density was observed. In the MEH, because the ECPV aided by the LSPR converted the solar energy into electrical energy, the streaming potential (SP) generated across the electrodes because of the fluid flow converted the mechanical energy into electrical energy. Increase in the number of electrode pairs improved the voltage generation, which suggested that the MEH had potential for microscale-very-large-scale-integration (μ-VLSI). The combined effects of ECPV, LSPR, and SP in the MEH could show an efficiency ∼2.5%, which was one of the highest ones reported, for Schottky-junction energy harvesters. This study shows some simple and efficient pathways to harvest high-density electrical power using microchannels and droplets from the naturally abundant solar or hydroelectric (hydel) energy resources.

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.

Efficient electrochemomechanical energy conversion in nanochannels grafted with end-charged polyelectrolyte brushes at medium and high salt concentration

We develop a theory to study the generation of the streaming potential and the resulting electrochemomechanical energy conversion (ECMEC) in the presence of pressure-driven transport in nanochannels grafted with end-charged polyelectrolyte (PE) brushes. Our theory gives a thermodynamically self-consistent coupled description of the PE-brush and the electrostatics of the electric double layer (EDL) induced by the PE charges. The end-charged brushes localize the maximum EDL charge density away from the wall, thereby enabling a larger magnitude of pressure-driven transport to stream the ions downstream. This effect is retarded by the drag force imparted by the brushes as well as by the enhanced electroosmotic transport in a direction opposite to the pressure-driven transport. An interplay of these three issues leads to highly non-trivial electrohydrodynamic transport that eventually allows us to converge on appropriate properties of the brushes (e.g., grafting density and the number of monomers) that lead to the generation of a significantly larger streaming potential and a much improved efficiency of the ECMEC as compared to the brush-free nanochannels particularly at medium and high salt concentrations.

Theory of diffusioosmosis in a charged nanochannel

We probe the diffusioosmotic transport in a charged nanofluidic channel in the presence of an applied tangential salt concentration gradient. Ionic salt gradient driven diffusioosmosis or ionic diffusioosmosis (IDO) is characterized by the generation of an induced tangential electric field and a diffusioosmotic velocity (DOSV) that is a combination of an electroosmotic velocity (EOSV) triggered by this electric field and a chemiosmotic velocity (COSV) triggered by an induced tangential pressure gradient. We explain that unlike the existing theories on IDO, it is more appropriate to apply the zero net current conditions (formulation F2) and not more restrictive zero net local flux conditions (formulation F1) particularly for the case where one considers a nanochannel connected to two reservoirs. We pinpoint limitations in the existing literature in correctly predicting the diffusioosmotic behavior even for the case where formulation F1 is used. We address these limitations and establish that (a) the induced electric field is an interplay of the differences in ionic diffusivity, the EDL-induced imbalance in ion concentrations, and the advection effects, (b) formulation F1 may overpredict or underpredict the electric field and the EOSV leading to an overprediction/underprediction of the DOSV and (c) formulation F2 demonstrates remarkable fluid physics of localized backflows owing to a dominant local influence of the COSV, which is missed by formulation F1. We anticipate that our theory will provide the first rigorous understanding of nanofluidic IDO with applications in multiple areas of low Reynolds number transport such as biofluidics, microfluidic separation, and colloidal transport.

What Controls Thermo-osmosis? Molecular Simulations Show the Critical Role of Interfacial Hydrodynamics

Thermo-osmotic and related thermophoretic phenomena can be found in many situations from biology to colloid science, but the underlying molecular mechanisms remain largely unexplored. Using molecular dynamics simulations, we measure the thermo-osmosis coefficient by both mechanocaloric and thermo-osmotic routes, for different solid-liquid interfacial energies. The simulations reveal, in particular, the crucial role of nanoscale interfacial hydrodynamics. For nonwetting surfaces, thermo-osmotic transport is largely amplified by hydrodynamic slip at the interface. For wetting surfaces, the position of the hydrodynamic shear plane plays a key role in determining the amplitude and sign of the thermo-osmosis coefficient. Finally, we measure a giant thermo-osmotic response of the water-graphene interface, which we relate to the very low interfacial friction displayed by this system. These results open new perspectives for the design of efficient functional interfaces for, e.g., waste-heat harvesting.

Electro-osmosis of nematic liquid crystals under weak anchoring and second-order surface effects

Advent of nematic liquid crystal flows has attracted renewed attention in view of microfluidic transport phenomena. Among various transport processes, electro-osmosis stands as one of the efficient flow actuation mechanisms through narrow confinements. In the present study, we explore the electrically actuated flow of an ordered nematic fluid with ionic inclusions, taking into account the influences from surface-induced elasticity and electrical double layer (EDL) phenomena. Toward this, we devise the coupled flow governing equations from fundamental free-energy analysis, considering the contributions from first- and second-order elastic, dielectric, flexoelectric, charged surface polarization, ionic and entropic energies. The present study focuses on the influence of surface charge and elasticity effects in the resulting linear electro-osmosis through a slit-type microchannel whose surfaces are chemically treated to display a homeotropic-type weak anchoring state. An optical periodic stripe configuration of the nematic director has been observed, especially for higher electric fields, wherein the Ericksen number for the dynamic study is restricted to the order of unity. Contrary to the isotropic electrolytes, the EDL potential in this case was found to be dependent on the external field strength. Through a systematic investigation, we brought out the fact that the wavelength of the oscillating patterns is dictated mainly by the external field, while the amplitude depends on most of the physical variables ranging from the anchoring strength and the flexoelectric coefficients to the surface charge density and electrical double layer thickness.

Electro-osmosis at surfactant-laden liquid-gas interfaces: beyond standard models

Electro-osmosis (EO) is a powerful tool to manipulate liquids in micro and nanofluidic systems. While EO has been studied extensively at liquid-solid interfaces, the case of liquid-vapor interfaces, found e.g. in foam films and bubbles, remains to be explored. Here we perform molecular dynamics (MD) simulations of EO in a film of aqueous electrolyte covered with fluid layers of ionic surfactants and surrounded by gas. Following the experimental procedure, we compute the zeta potential from the EO velocity, defined as the velocity difference between the middle of the liquid film and the surrounding gas. We show that the zeta potential can be smaller or larger than existing predictions depending on the surfactant coverage. We explain the failure of previous descriptions by the fact that surfactants and bound ions move as rigid bodies and do not transmit the electric driving force to the liquid locally. Considering the reciprocal streaming current effect, we then develop an extended model, which can be used to predict the experimental zeta potential of surfactant-laden liquid-gas interfaces.

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.

Strong Coupling between Nanofluidic Transport and Interfacial Chemistry: How Defect Reactivity Controls Liquid-Solid Friction through Hydrogen Bonding

Defects are inevitably present in nanofluidic systems, yet the role they play in nanofluidic transport remains poorly understood. Here, we report ab initio molecular dynamics (AIMD) simulations of the friction of liquid water on defective graphene and boron nitride sheets. We show that water dissociates at certain defects and that these "reactive" defects lead to much larger friction than the "nonreactive" defects at which water molecules remain intact. Furthermore, we find that friction is extremely sensitive to the chemical structure of reactive defects and to the number of hydrogen bonds they can partake in with the liquid. Finally, we discuss how the insight obtained from AIMD can be used to quantify the influence of defects on friction in nanofluidic devices for water treatment and sustainable energy harvesting. Overall, we provide new insight into the role of interfacial chemistry on nanofluidic transport in real, defective systems.