Ion Steric Effect Induces Giant Enhancement of Thermoelectric Conversion in Electrolyte-Filled Nanochannels.

Ionic thermoelectricity in nanochannels has received increasing attention because of its advantages, such as high Seebeck coefficient and low cost. However, most studies have focused on dilute simple electrolytes that neglect the effects of finite ion sizes and short-range electrostatic correlation. Here, we reveal a new thermoelectric mechanism arising from the coupling of the ion steric effect due to finite ion sizes and ion thermodiffusion in electric double layers, using both theoretical and numerical methods. We show that this mechanism can significantly enhance the thermoelectric response in nanoconfined electrolytes depending on the properties of electrolytes and nanochannels. Compared to the previously known mechanisms, the new mechanism can increase the Seebeck coefficient by 100% or even 1 order of magnitude enhancement under optimal conditions. Moreover, we demonstrate that the short-range electrostatic correlation can help preserve the Seebeck coefficient enhancement in a weaker confinement or in more concentrated electrolytes.

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions.

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.

Effects of fluid slippage on pressure-driven electrokinetic energy conversion in conical nanochannels.

The effects of fluid slippage on the pressure-driven electrokinetic energy conversion in conical nanochannels are systematically investigated in this paper. We present a multiphysical model that couples the Planck-Nernst-Poisson equations and the Navier-Stokes equation with a Navier slip condition to fulfill this purpose. We systematically look into the variation of various performance indicators of electrokinetic energy conversion, for example, streaming current, streaming potential, generation power, energy conversion efficiency, regulation parameter, and enchantment ratio, with the conicity of nanochannels and the slip length for two pressure differences of the same magnitude but opposite directions. Particularly, enhancement ratios related to streaming current, streaming potential, generation power, and energy conversion efficiency are defined to comprehensively measure the enhancement of the performance of electrokinetic energy conversion due to the slip length. The results demonstrate that a combination of large slip length and small conicity enhances the electrokinetic energy conversion performance significantly. Furthermore, the fluid slippage-induced enhancement of the electrokinetic energy conversion in the backward pressure difference mode is stronger than that in the forward pressure difference mode. Our results provide design and operation guidelines for pressure-driven electrokinetic energy conversion devices.

Structural features and electrostatic energy storage of electric double layers in confined polyelectrolyte solutions under low-salt conditions.

An electric double layer (EDL) in a polyelectrolyte solution plays a crucial role in diverse fields ranging from physical and life sciences to modern technologies. Due to the nonnegligible excluded volume effects, chain connectivity and complex intermolecular interactions, the EDLs in (confined) polyelectrolyte solutions display distinct features compared to those in simple electrolyte solutions. Here, we conducted a systematic study on the characteristics of EDLs in confined polyelectrolyte solutions for salt-free and low salt concentration systems using self-consistent field theory. Results suggest that the characteristic length scales measuring the EDL structures are different for positively and negatively charged surfaces. The former is the same as in the electrolyte solutions, while the latter is smaller due to the accumulation of oppositely charged polyelectrolytes near the surface. Furthermore, for low surface charge densities, a scaling law for the electrostatic energy stored in polyelectrolyte EDLs (in units of mJ m-2) was found to be U ∝ |σ|ν with ν ∼ 2-2.7, which differs from the electrolyte EDLs with ν ∼ 2; however, such a scaling law breaks down for high surface charge densities.

Radial basis function interpolation supplemented lattice Boltzmann method for electroosmotic flows in microchannel.

Large gradients of physical variables near the channel walls are characteristic of EOF. The previous numerical simulations of EOFs with the lattice Boltzmann method (LBM) utilize uniform lattice and are not efficient, especially when the electric double layer (EDL) thickness is significantly smaller than the channel height. The efficient LBM simulation of EOF in microchannel calls for a nonuniform mesh which is dense in the EDL region and sparse in the bulk region. In this article, we formulate a radial basis function (RBF)-based interpolation supplemented LBM (ISLBM) to solve the governing equations of EOF, that is, the Poisson, Nernst-Planck, and Navier-Stokes equations, in a nonuniform mesh system. Unlike the conventional ISLBM, the RBF-ISLBM determines the prestreaming distribution functions by using the local RBF-based interpolation over circular supporting regions and is particularly suitable for nonuniform meshes. The RBF-ISLBM is validated by the EOFs in infinitely long and finitely long microchannels. The results show that the RBF-ISLBM possesses excellent robustness and accuracy. Finally, we use the RBF-ISLBM to simulate the EOFs with the hitherto highest electrokinetic parameter, κa, defined by the ratio of channel height a to EDL thickness κ-1 , in LBM simulations of EOF.

Numerical investigation of the solute dispersion in finite-length microchannels with the interphase transport.

This paper utilizes a combined approach of the convection-diffusion theory and the moment analysis to conduct a comprehensive investigation of the solute dispersion under the influence of the interphase transport in finitely long inner coated microchannels. The present work has threefold novel contributions: (1) The 2D solute concentration contours in the stationary phase are calculated for the first time to facilitate the understanding the role of the interphase transport in the solute dispersion in the mobile phase. (2) The skewness of the elution curves is investigated to guide the control of solute band shape at the channel outlet. (3) The 2D diffusion-convection theory and zero-dimensional (0D) moment analysis complement each other to present a characterization of the solute dispersion behaviors more comprehensive than that by either of the two methods alone. Parametric studies are performed to clarify the effects of four major parameters related to the interphase transport (i.e., stationary phase Péclet number, interphase transport rate, partition coefficient, and stationary phase thickness) on the solute dispersion characteristics. The results from this study provide a straightforward understanding of the effects of interphase transport on the solute dispersion in finitely long microchannels and are of potential relevance to the design and operation of the microfluidics-based analytical devices.

A numerical study on ion concentration polarization and electric circuit performance of an electrokinetic battery.

Ion concentration polarization (ICP) imposes remarkable adverse effects on the energy conversion performance of the pressure-driven electrokinetic (EK) flows through a capillary system that can be equivalently treated as a battery. An optimized dimensionless numerical method is proposed in this study to investigate the causes and the effects of the ICP. Results show that remarkable ICP phenomena are induced under certain conditions such as high applied pressure, high surface charge density, and small inversed Debye length at dimensionless values of 6000, -10, and 0.5. Meanwhile, different factors influence the ICP and the corresponding electric properties in different ways. Particularly for the overall electric resistance, the applied pressure and the surface charge density mainly affect the variation amplitude and the level of the overall electric resistance when varying the output electric potential, respectively. Differently, the Debye length affects the overall electric resistance in both aspects. Ultimately, the induced ICP leads to significant nonlinear current-potential curves.

Electrokinetic power generation in conical nanochannels: regulation effects due to conicity.

Electrokinetic power generation is a promising clean energy production technology, which utilizes the electric double layer in a nanochannel to convert the hydrodynamic energy to electrical power. Previous research largely focused on electrokinetic power generation in nanochannels with a uniform cross-section. In this work, we perform a systematic investigation of electrokinetic power generation in a conical nanochannel. For this purpose, a multiphysical model consisting of the Planck-Nernst-Poisson equations and the Navier-Stokes equation is formulated and solved numerically. In particular, we discover various regulation effects in electrokinetic power generation in conical nanochannels, which manifest as the difference in the power generation characteristics (streaming potential, streaming current and current-voltage relationship) between two opposite pressure differences of the same magnitude. These regulation effects are found to originate from the conicity of the nanochannel. Furthermore, the regulation parameters are defined to quantify the observed regulation effects. Various regulation parameters can be up to severals tens of percent under extreme conditions (e.g., large pressure difference, high surface charge density or large conicity), indicating the substantial significance of the regulation effects in electrokinetic power generation. The conclusions from this work can serve as an important reference for the design and operation of nanofluidic electrokinetic power generation devices.

Continuous-flow trapping and localized enrichment of micro- and nano-particles using induced-charge electrokinetics.

In this work, we report an effective microfluidic technique for continuous-flow trapping and localized enrichment of micro- and nano-particles by using induced-charge electrokinetic (ICEK) phenomena. The proposed technique utilizes a simple microfluidic device that consists of a straight microchannel and a conducting strip attached to the bottom wall of the microchannel. Upon application of the electric field along the microchannel, the conducting strip becomes polarized to introduce two types of ICEK phenomena, the ICEK flow vortex and particle dielectrophoresis, and they are identified by a theoretical model formulated in this study to be jointly responsible for the trapping of particles over the edge of the conducting strip. Our experiments showed that successful trapping requires an AC/DC combined electric field: the DC component is mainly to induce electroosmotic flow for transporting particles to the trapping location; the AC component induces ICEK phenomena over the edge of the conducting strip for particle trapping. The performance of the technique is examined with respect to the applied electric voltage, AC frequency and the particle size. We observed that the trapped particles form a narrow band (nearly a straight line) defined by the edge of the conducting strip, thereby allowing localized particle enrichment. For instance, we found that under certain conditions a high particle enrichment ratio of 200 was achieved within 30 seconds. We also demonstrated that the proposed technique was able to trap particles from several microns down to several tens of nanometer. We believe that the proposed ICEK trapping would have great flexibility that the trapping location can be readily varied by controlling the location of the patterned conducting strip and multiple-location trapping can be expected with the use of multiple conducting strips.

Enhancement of electrophoretic mobility of microparticles near a solid wall--experimental verification.

Although the existing theories have predicted enhancement of electrophoretic mobility of microparticles near a solid wall, the relevant experimental studies are rare. This is mainly due to difficulties in experimentally controlling and measuring particle-wall separations under dynamic electrophoretic conditions. This paper reports an experimental verification of the enhancement of electrophoretic mobility of a microparticle moving near the wall of a microchannel. This is achieved by balancing dielectrophoretic and lift forces against gravitational force acting on the microparticle so as to control the gap of particle-wall separation. A simple experimental setup is configured and a fabrication method is developed to measure such separation gap. The experiments are conducted for various particle sizes under different electric field strengths. Our experimental results are compared against the available theoretical predictions in the literature.

Amplitude modulation atomic force microscopy, is acoustic driving in liquid quantitatively reliable?

Measuring quantitative tip-sample interaction forces in dynamic atomic force microscopy in fluids is challenging because of the strong damping of the ambient viscous medium and the fluid-mediated driving forces. This holds in particular for the commonly used acoustic excitation of the cantilever oscillation. Here we present measurements of tip-sample interactions due to conservative DLVO and hydration forces and viscous dissipation forces in aqueous electrolytes using tips with radii varying from typical 20 nm for the DLVO and hydration forces, to 1 µm for the viscous dissipation. The measurements are analyzed using a simple harmonic oscillator model, continuous beam theory with fluid-mediated excitation and thermal noise spectroscopy (TNS). In all cases consistent conservative forces, deviating less than 40% from each other, are obtained for all three approaches. The DLVO forces are even within 5% of the theoretical expectations for all approaches. Accurate measurements of dissipative forces within 15% of the predictions of macroscopic fluid dynamics require the use of TNS or continuous beam theory including fluid-mediated driving. Taking this into account, acoustic driving in liquid is quantitatively reliable.

Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel.

EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field.

Electro-osmotic flows in a microchannel with patterned hydrodynamic slip walls.

We present an analysis of the electro-osmotic flow of electrolytic solutions in a microchannel with patterned hydrodynamic slippage on channel walls. A set of governing equations is formulated to account for the effects of small variations in hydrodynamic slippage over the microchannel walls on the electro-osmotic flow. These equations are then solved analytically by using the perturbation method. Two frequently encountered surface patterns, (i) cosine wave variation and (ii) square wave variation in slip length, are considered in our analyses. The results show that patterned slippage over microchannel walls can induce complex flow patterns (such as vortical flows) in otherwise plug-like electro-osmotic flows, which suggests potential applications of such flows in microfluidic mixers.

Trampolining of Droplets on Hydrophobic Surfaces Using Electrowetting.

Droplet detachment from solid surfaces is an essential part of many industrial processes. Electrowetting is a versatile tool for handling droplets in digital microfluidics, not only on plain surface but also in 3-D manner. Here, we report for the first time droplet trampolining using electrowetting. With the information collected by the real-time capacitor sensing system, we are able to synchronize the actuation signal with the spreading of the droplet upon impacting. Since electrowetting is applied each time the droplet impacts the substrate and switched off during recoiling of the droplet, the droplet gains additional momentum upon each impact and is able to jump higher during successive detachment. We have modelled the droplet trampolining behavior with a periodically driven harmonic oscillator, and the experiments showed sound agreement with theoretical predictions. The findings from this study will offer valuable insights to applications that demands vertical transportation of the droplets between chips arranged in parallel, or detachment of droplets from solid surfaces.

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.

AC field induced-charge electroosmosis over leaky dielectric blocks embedded in a microchannel.

An effective electrical boundary condition is formulated to describe AC field-driven induced-charge electrokinetic (ICEK) phenomena at the interface between a liquid and a leaky dielectric solid. Since most materials in reality possess finite dielectric and conductive properties, i.e. leaky dielectric, the present boundary condition can be used to describe the induced zeta potential on a leaky dielectric surface with consideration of both bond charges (due to polarization) and free charges (due to conduction). Two well-known limiting cases, i.e. the perfectly dielectric and the perfectly conducting wall boundary conditions can be recovered from the present formulation. Utilizing the derived boundary condition, we obtain analytical solutions in closed form for the AC field-driven induced-charge electroosmosis (ICEO) over two symmetric leaky dielectric blocks embedded in the walls of an infinitely long microchannel. Two important factors for the induced zeta potential are identified to respectively account for the polarization charges and the free charges, and their effects on AC field-driven ICEO oscillating flow patterns are analyzed. It is found that the flow patterns exhibit two counter-rotating vortices, which can be deformed, relocated, eliminated and even reverse their rotating directions. It is very promising that such temporary evolution of flow patterns can possibly induce chaotic advection which can enhance microfluidic mixing.

Nonlinear Smoluchowski velocity for electroosmosis of Power-law fluids over a surface with arbitrary zeta potentials.

Electroosmotic flow of Power-law fluids over a surface with arbitrary zeta potentials is analyzed. The governing equations including the nonlinear Poisson-Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek exact solutions for the electroosmotic velocity, shear stress, and dynamic viscosity distributions inside the electric double layer. Specifically, an expression for the general Smoluchowski velocity is obtained for electroosmosis of Power-law fluids in a fashion similar to the classic Smoluchowski velocity for Newtonian fluids. The existing Smoluchowski slip velocities under two special cases, (i) for Newtonian fluids with arbitrary zeta potentials and (ii) for Power-law fluids with small zeta potentials, can be recovered from our derived formula. It is interesting to note that the general Smoluchowski velocity for non-Newtonian Power-law fluids is a nonlinear function of the electric field strength and surface zeta potentials; this is due to the coupling electrostatics and non-Newtonian fluid behavior, which is different from its counterpart for Newtonian fluids. This general Smoluchowski velocity is of practical significance in determining the flow rates in microfluidic devices involving non-Newtonian Power-law fluids.

Electrokinetically driven continuous-flow enrichment of colloidal particles by Joule heating induced temperature gradient focusing in a convergent-divergent microfluidic structure.

Enrichment of colloidal particles in continuous flow has not only numerous applications but also poses a great challenge in controlling physical forces that are required for achieving particle enrichment. Here, we for the first time experimentally demonstrate the electrokinetically-driven continuous-flow enrichment of colloidal particles with Joule heating induced temperature gradient focusing (TGF) in a microfluidic convergent-divergent structure. We consider four mechanisms of particle transport, i.e., advection due to electroosmosis, electrophoresis, dielectrophoresis and, and further clarify their roles in the particle enrichment. It is experimentally determined and numerically verified that the particle thermophoresis plays dominant roles in enrichment of all particle sizes considered in this study and the combined effect of electroosmosis-induced advection and electrophoresis is mainly to transport particles to the zone of enrichment. Specifically, the enrichment of particles is achieved with combined DC and AC voltages rather than a sole DC or AC voltage. A numerical model is formulated with consideration of the abovementioned four mechanisms, and the model can rationalize the experimental observations. Particularly, our analysis of numerical and experimental results indicates that thermophoresis which is usually an overlooked mechanism of material transport is crucial for the successful electrokinetic enrichment of particles with Joule heating induced TGF.

Design of a hybrid advective-diffusive microfluidic system with ellipsometric detection for studying adsorption.

Establishing and maintaining concentration gradients that are stable in space and time is critical for applications that require screening the adsorption behavior of organic or inorganic species onto solid surfaces for wide ranges of fluid compositions. In this work, we present a design of a simple and compact microfluidic device based on steady-state diffusion of the analyte, between two control channels where liquid is pumped through. The device generates a near-linear distribution of concentrations. We demonstrate this via experiments with dye solutions and comparison to finite-element numerical simulations. In a subsequent step, the device is combined with total internal reflection ellipsometry to study the adsorption of (cat)ions on silica surfaces from CsCl solutions at variable pH. Such a combined setup permits a fast determination of an adsorption isotherm. The measured optical thickness is compared to calculations from a triple layer model for the ion distribution, where surface complexation reactions of the silica are taken into account. Our results show a clear enhancement of the ion adsorption with increasing pH, which can be well described with reasonable values for the equilibrium constants of the surface reactions.

Extracting local surface charges and charge regulation behavior from atomic force microscopy measurements at heterogeneous solid-electrolyte interfaces.

We present a method to determine the local surface charge of solid-liquid interfaces from Atomic Force Microscopy (AFM) measurements that takes into account shifts of the adsorption/desorption equilibria of protons and ions as the cantilever tip approaches the sample. We recorded AFM force distance curves in dynamic mode with sharp tips on heterogeneous silica surfaces partially covered by gibbsite nano-particles immersed in an aqueous electrolyte with variable concentrations of dissolved NaCl and KCl at pH 5.8. Forces are analyzed in the framework of Derjaguin-Landau-Verwey-Overbeek (DLVO) theory in combination with a charge regulation boundary that describes adsorption and desorption reactions of protons and ions. A systematic method to extract the equilibrium constants of these reactions by simultaneous least-squared fitting to experimental data for various salt concentrations is developed and is shown to yield highly consistent results for silica-electrolyte interfaces. For gibbsite-electrolyte interfaces, the surface charge can be determined, yet, an unambiguous identification of the relevant surface speciation reactions is not possible, presumably due to a combination of intrinsic chemical complexity and heterogeneity of the nano-particle surfaces.