Novel electroosmotic micromixer configuration based on ion-selective microsphere.

In this paper, a micromixer of a new configuration is presented, consisting of a spherical chamber in the center of which an ion-selective microsphere is placed. Stratified liquid is introduced through the chamber via inlet and outlet holes under an external pressure gradient and an external electric field is directed in such a way that the resulting electroosmotic flow is directed against the pressure-driven flow, resulting in mixing. The investigation is carried out by direct numerical simulation on a super-computer. Optimal values of the applied electric field are determined to yield strong mixing. Above this optimal mixing regime, a number of instabilities and bifurcations are realized, which qualitatively coincide with those occurring during electrophoresis of an ion-selective microgranule. As shown by our calculation, these instabilities do not lead to an enhanced mixing. The resulting electroconvective vortices remain confined near the surface of the microgranule, and do not sufficiently perturb the stratified fluid flow further from the granule. On the other hand, another type of instability caused by the salt concentration gradient can generate sufficiently strong oscillations to enhance mixing. However, this only occurs when the external electric field is sufficiently high that the electroosmotic flow is comparable to the pressure-driven flow. This ultimately leads to creation of reverse flows of the liquid and cessation of the device operation. Thus, it was shown that the best mixing occurs in the absence of electrokinetic instability. Based on the data obtained, it is possible to select the necessary geometric characteristics of the micromixer to achieve the optimal mixing mode for a given set of liquids, which may be ten times more effective than passive mixers at the same flow rates. A comparison with the experimental data of the other authors confirms the effectiveness of this device and its other capabilities. Furthermore, the basic device design can be operated in other modes, for example, an electrohydrodynamic pump, a streaming current generator, or even a micro-reactor, depending on the system parameters and choice of an ion-selective granule.

Ballistic Brownian motion of supercavitating nanoparticles.

We show that the Brownian motion of a nanoparticle (NP) can reach a ballistic limit when intensely heated to form supercavitation. As the NP temperature increases, its Brownian motion displays a sharp transition from normal to ballistic diffusion upon the formation of a vapor bubble to encapsulate the NP. Intense heating allows the NP to instantaneously extend the bubble boundary via evaporation, so the NP moves in a low-friction gaseous environment. We find the dynamics of the supercavitating NP is largely determined by the near field effect, i.e., highly localized vapor phase property in the vicinity of the NP.

Transitions and Instabilities in Imperfect Ion-Selective Membranes.

Numerical investigation of the underlimiting, limiting, and overlimiting current modes and their transitions in imperfect ion-selective membranes with fluid flow through permitted through the membrane is presented. The system is treated as a three layer composite system of electrolyte-porous membrane-electrolyte where the Nernst-Planck-Poisson-Stokes system of equations is used in the electrolyte, and the Darcy-Brinkman approach is employed in the nanoporous membrane. In order to resolve thin Debye and Darcy layers, quasi-spectral methods are applied using Chebyshev polynomials for their accumulation of zeros and, hence, best resolution in the layers. The boundary between underlimiting and overlimiting current regimes is subject of linear stability analysis, where the transition to overlimiting current is assumed due to the electrokinetic instability of the one-dimensional quiescent state. However, the well-developed overlimiting current is inherently a problem of nonlinear stability and is subject of the direct numerical simulation of the full system of equations. Both high and low fixed charge density membranes (low- and high concentration electrolyte solutions), acting respectively as (nearly) perfect or imperfect membranes, are considered. The perfect membrane is adequately described by a one-layer model while the imperfect membrane has a more sophisticated response. In particular, the direct transition from underlimiting to overlimiting currents, bypassing the limiting currents, is found to be possible for imperfect membranes (high-concentration electrolyte). The transition to the overlimiting currents for the low-concentration electrolyte solutions is monotonic, while for the high-concentration solutions it is oscillatory. Despite the fact that velocities in the porous membrane are much smaller than in the electrolyte region, it is further demonstrated that they can dramatically influence the nature and transition to the overlimiting regimes. A map of the bifurcations, transitions, and regimes is constructed in coordinates of the fixed membrane charge and the Darcy number.

Light-Guided Surface Plasmonic Bubble Movement via Contact Line De-Pinning by In-Situ Deposited Plasmonic Nanoparticle Heating.

Precise spatiotemporal control of surface bubble movement can benefit a wide range of applications like high-throughput drug screening, combinatorial material development, microfluidic logic, colloidal and molecular assembly, and so forth. In this work, we demonstrate that surface bubbles on a solid surface are directed by a laser to move at high speeds (>1.8 mm/s), and we elucidate the mechanism to be the depinning of the three-phase contact line (TPCL) by rapid plasmonic heating of nanoparticles (NPs) deposited in situ during bubble movement. On the basis of our observations, we deduce a stick-slip mechanism based on asymmetric fore-aft plasmonic heating: local evaporation at the front TPCL due to plasmonic heating depins and extends the front TPCL, followed by the advancement of the trailing TPCL to resume a spherical bubble shape to minimize surface energy. The continuous TPCL drying during bubble movement also enables well-defined contact line deposition of NP clusters along the moving path. Our finding is beneficial to various microfluidics and pattern writing applications.

Transient response of nonideal ion-selective microchannel-nanochannel devices.

We report evidence of variation in ion selectivity of a fabricated microchannel-nanochannel device resulting in the appearance of a distinct local maximum in the overlimiting chronopotentiometric response. In this system consisting of shallow microchannels joined by a nanochannel, viscous shear at the microchannel walls suppresses the electro-osmotic instability and prevents any associated contribution to the nonmonotonic response. Thus, this response is primarily electrodiffusive. Numerical simulations indicate that concentration polarization develops not only within the microchannel but also within the nanochannel itself, with a local voltage maximum in the chronopotentiometric response correlated with interfacial depletion and having the classic i^{-2} Sands time dependence. Furthermore, the occurrence of the local maxima is correlated with the change in selectivity due to internal concentration polarization. Understanding the transient nonideal permselective response is essential for obtaining fundamental insight and for optimizing efficient operation of practical fabricated nanofluidic and membrane devices.

Liquid phase stabilization versus bubble formation at a nanoscale curved interface.

We investigate the nature of vapor bubble formation near a nanoscale-curved convex liquid-solid interface using two models: an equilibrium Gibbs model for homogenous nucleation, and a nonequilibrium dynamic van der Waals-diffuse-interface model for phase change in an initially cool liquid. Vapor bubble formation is shown to occur for sufficiently large radius of curvature and is suppressed for smaller radii. Solid-fluid interactions are accounted for and it is shown that liquid-vapor interfacial energy, and hence Laplace pressure, has limited influence over bubble formation. The dominant factor is the energetic cost of creating the solid-vapor interface from the existing solid-liquid interface, as demonstrated via both equilibrium and nonequilibrium arguments.

Overlimiting current due to electro-diffusive amplification of the second Wien effect at a cation-anion bipolar membrane junction.

Numerical simulations are presented for the transient and steady-state response of a model electrodiffusive cell with a bipolar ion-selective membrane under electric current. The model uses a continuum Poisson-Nernst-Planck theory including source terms to account for the catalytic second Wien effect between ionogenic groups in the membranes and resolves the Debye layers at interfaces. The resulting electric field at the membrane junction is increased by as much as four orders of magnitude in comparison to the field external to the membrane. This leads to a significant amplification of the second Wien effect, creating an increased ionic flux due to the catalytic decomposition of water. The effect also induces an exaltation effect wherein the salt ion flux undergoes a concomitant increase as well. The interplay of effects results in a unique over-limiting current mechanism due to concentration polarization internal, rather than external, to the membranes. In addition to the case of two equal but oppositely charged membranes under the standard simplifying assumption of equal ionic diffusivities, two variations on this model are studied. Asymmetric diffusivities, representative of the actual mobility difference in dissociated water ions, and the effect of the membrane charge density ratio were also considered. The latter elucidates an overlimiting current shift mechanism for DNA adsorption on anion-selective membranes proposed by Slouka et al. [Langmuir 29, 8275 (2013)]. The former provides more realistic picture of multi-ion transport and demonstrates a surprising steady-state effect due to the asymmetry in the diffusivity of hydroxide and hydronium.

Effect of cooling on droplet size in supersaturation-induced emulsions.

In this work, the droplet size in a water-in-oil emulsion obtained by supersaturation is studied. The emulsion is obtained by cooling down a saturated water/oil solution by a certain temperature difference. The effects of the cooling rate and temperature difference on the produced droplet size are experimentally investigated. The average size of water droplets in the emulsion is found to be proportional to the square root of the cooling rate. By analyzing the time scales of three different steps, including nucleation, droplet growth due to diffusion and coarsening, involved in the emulsification process, it is found that the time scales of nucleation and droplet growth due to mass diffusion are much smaller than the cooling time constant, which is much shorter than the coarsening time scale. A mechanism that links the cooling rate and supersaturation temperature to droplet size is proposed: the cooling rate influences the nucleation and thus droplet density, while the temperature difference, which is linearly proportional to the total volume of precipitated water from the saturated water-in-oil solution, determines the size of each droplet. The droplet size data were found to support this proposed mechanism well. The results obtained from this work may provide useful guidance on controlling the droplet size in the supersaturation-based emulsification process, which has a lot of practical relevance to many applications.

Functionalized Graphene Enables Highly Efficient Solar Thermal Steam Generation.

The ability to efficiently utilize solar thermal energy to enable liquid-to-vapor phase transition has great technological implications for a wide variety of applications, such as water treatment and chemical fractionation. Here, we demonstrate that functionalizing graphene using hydrophilic groups can greatly enhance the solar thermal steam generation efficiency. Our results show that specially functionalized graphene can improve the overall solar-to-vapor efficiency from 38% to 48% at one sun conditions compared to chemically reduced graphene oxide. Our experiments show that such an improvement is a surface effect mainly attributed to the more hydrophilic feature of functionalized graphene, which influences the water meniscus profile at the vapor-liquid interface due to capillary effect. This will lead to thinner water films close to the three-phase contact line, where the water surface temperature is higher since the resistance of thinner water film is smaller, leading to more efficient evaporation. This strategy of functionalizing graphene to make it more hydrophilic can be potentially integrated with the existing macroscopic heat isolation strategies to further improve the overall solar-to-vapor conversion efficiency.

Diffusion layer formation drives zone migration in travelling wave electrophoresis.

COMSOL finite element modeling software is used to simulate 2D traveling-wave electrophoresis for microfluidic separations and sample concentration. A four-phase AC potential is applied to a periodic interdigitated four-electrode array to produce a longitudinal electric wave that travels through the channel. Charged particles are carried along with the electric wave or left behind, depending on their mobilities. A simplified model of asymmetric electrode reactions resolves the issue of electric double layer shielding at the electrodes. Selective reactions allow for the formation of diffusion layers of charged particles which follow the traveling electric wave. These diffusion layers determine the transport of charged species through the system. Our model reproduces experimental separations of charged species based on mobility. With easy control over the frequency and direction, one may employ this method for concentrating and/or separating charged particles.

Confinement effects on electroconvective instability.

We present an analysis of hydrodynamic effects in systems involving ion transport from an aqueous electrolyte to an ion-selective surface. These systems are described by the Poisson-Nernst-Planck and Navier-Stokes equations. Historically, such systems were modeled by one-dimensional geometries with spatial coordinate in the direction of transport and normal to the ion-selective surface. Rubinstein and Zaltzman [JFM 579, 173-226 (2007)] showed that when such systems are unbounded in the transverse directions, a hydrodynamic instability can occur. This instability, referred to as electroconvective instability, leads to advective mixing, which results in overlimiting transport rates significantly beyond what is predicted from one-dimensional models. In this study, we present an analysis of electroconvection in confined systems, considering a broad range of applications including microfluidic systems and porous media. Our analysis reveals that full confinement in the transverse directions significantly suppresses electroconvection and overlimiting current. However, when at least one transverse direction allows for flow escape, such as in thin but wide channels or in porous media, the onset of instability is only weakly affected by confinement. We will also present a review of relevant literature and discuss how the present study resolves the contradictory contrasts between the results of recent work on this topic.

Effect of electric field non-uniformity on droplets coalescence.

Electric field assisted coalescence is one of the most efficient methods for water-in-oil emulsion separation. In this paper, we experimentally study water droplet evolution in an oil phase under different electric field configurations. We determine that non-uniform fields can enhance the performance of electrocoalescence compared to uniform fields. The analysis indicates that the enhanced coalescence is due to the combined effects of dipole-dipole interaction between droplets and dielectrophoresis between individual droplets and the applied non-uniform field. The present study shows that a non-uniform electric field and the induced dielectrophoretic effect can accelerate the coalescence and phase separation of micro-emulsions. These results may provide useful guidance in designing an optimum electrode configuration for efficient electrocoalescence.

Robust ion current oscillations under a steady electric field: An ion channel analog.

We demonstrate a nonlinear, nonequilibrium field-driven ion flux phenomenon, which unlike Teorell's nonlinear multiple field theory, requires only the application of one field: robust autonomous current-mass flux oscillations across a porous monolith coupled to a capillary with a long air bubble, which mimics a hydrophobic protein in an ion channel. The oscillations are driven by the hysteretic wetting dynamics of the meniscus when electro-osmotic flow and pressure driven backflow, due to bubble expansion, compete to approach zero mass flux within the monolith. Delayed rupture of the film around the advancing bubble cuts off the electric field and switches the monolith mass flow from the former to the latter. The meniscus then recedes and repairs the rupture to sustain an oscillation for a range of applied fields. This generic mechanism shares many analogs with current oscillations in cell membrane ion channel. At sufficiently high voltage, the system undergoes a state transition characterized by appearance of the ubiquitous 1/f power spectrum.

Effect of field-focusing and ion selectivity on the extended space charge developed at the microchannel-nanochannel interface.

We present results demonstrating the effect of varying microchannel depth and bulk conductivity on the space charge-mediated transition between classical, diffusion-limited current and over-limiting current in microchannel-nanochannel devices. The extended space charge layer develops at the depleted microchannel-nanochannel entrance when the limiting current is exceeded and is correlated with a distinctive maximum in the dc resistance. This maximum is shown to be affected by the microchannel depth, via field-focusing, and solution conductivity. In particular, we observe that upon their increase, the maximum becomes flatter and shifts to higher voltages.

Universal low-frequency asymptotes of dynamic conic nanopore rectification: An ionic nanofluidic inductor.

We report the first nanofluidic inductor (L) to complement the known nanofluidic capacitors (C), resistors (R), and diodes for ion currents. Under negative bias, the nanopore behaves like a parallel RC circuit at low frequencies; however, under positive bias, the asymptotic dynamics is that of a serial RL circuit. This new ionic circuit element can lead to nanofluidic RLC or diode-inductor oscillator circuits and new intrapore biosensing/rapid sequencing strategies. A universal theory, with explicit estimates for the capacitance and inductance at opposite biases, is derived to collapse the rectified dynamics of all conic nanopores to facilitate design of this new nanofluidic circuit.

Ion current rectification in funnel-shaped nanochannels: Hysteresis and inversion effects.

Ion current rectification inversion is observed in a funnel-shaped nanochannel above a threshold voltage roughly corresponding to the under-limiting to over-limiting current transition. Previous experimental studies have examined rectification at either low-voltages (under-limiting current region) for conical nanopores/funnel-shaped nanochannels or at high-voltages (over-limiting region) for straight nanochannels with asymmetric entrances or asymmetric interfacing microchannels. The observed rectification inversion occurs because the system resistance is shifted, beyond a threshold voltage, from being controlled by intra-channel ion concentration-polarization to that controlled by external concentration-polarization. Additionally, strong hysteresis effects, due to residual concentration-polarization, manifest themselves through the dependence of the transient current rectification on voltage scan rate.

Probing space charge and resolving overlimiting current mechanisms at the microchannel-nanochannel interface.

We present results demonstrating the space charge-mediated transition between classical, diffusion-limited current and surface-conduction dominant over-limiting current in a shallow microchannel-nanochannel device. The extended space charge layer develops at the depleted microchannel-nanochannel entrance at high current and is correlated with a distinctive maximum in the dc resistance. Experimental results for a shallow surface-conduction dominated system are compared with theoretical models, allowing estimates of the effective surface charge at high voltage to be obtained. In comparison to an equilibrium estimate of the surface charge obtained from electrochemical impedance spectroscopy, it is further observed that the effective surface charge appears to change under applied voltage.

Extended space charge near nonideally selective membranes and nanochannels.

We demonstrate the role of selectivity variation in the structure of the nonequilibrium extended space charge using one-dimensional analytic and two-dimensional numerical Poisson-Nernst-Planck models for the electro-diffusive transport of a symmetric electrolyte. This provides a deeper understanding of the underlying mechanism behind a previously observed maximum in the resistance-voltage curve for a shallow micro-nanochannel interface device [Schiffbauer, Liel, Leibowitz, Park, and Yossifon, arXiv:1409.4548, Phys. Rev. E (to be published)]. The current study helps to establish a connection between parameters such as the geometry and nanochannel surface charge and the control of selectivity and resistance in the overlimiting current regime.

Influence of electric-double-layer structure on the transient response of nanochannels.

A fundamental Poisson-Nernst-Planck-Stokes model is presented for the impedance response of a long nanochannel under zero bias, capturing the effects of surface conduction and the coupling between transverse momentum and axial ion distribution in a manner reminiscent of Taylor dispersion. This is shown to result in a shift of the impedance frequency spectrum with bulk concentration similar to previous experimental observation [Schiffbauer, Liel, and Yossifon, Phys. Rev. E 89, 033017 (2014)]. It further predicts an additional downward shift in frequency with increasing viscosity. Finally, the introduction of a phenomenological model for the impedance response of a dynamic Stern layer in parallel with the diffuse layer transport model is shown to yield good agreement between theory and experiment. As a result, we are able to obtain an equivalent circuit model based on the fundamental model and proposed corrections.

Concentration dependence of nanochannel impedance and the determination of surface charge.

In this paper, we demonstrate the variation of nanochannel impedance with bulk (reservoir) electrolyte concentration. The impedance of a nanochannel is shown to correspond to a characteristic deformed semicircular arc. The degree of deformation decreases with increasing concentration, and at a sufficiently low concentration the complex impedance saturates, becoming essentially independent of the reservoir concentration. This behavior is indicative of a surface-conduction dominant regime. Here we demonstrate that this effect extends beyond dc conductance and affects the ac response of the system as well, including both phase relationship and magnitude. The nanochannel resistance, obtained from low-voltage ac measurements, is then used to extract the nanochannel surface charge density. This is found to increase in magnitude with increasing electrolyte concentration.