arXiv subjects

Martin Z. Bazant

Publications and source records attributed to Martin Z. Bazant.

At least 145 records · Page 8Linked to original sources

arXiv2010

Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor

In a variety of applications, most notably microfluidic design, slip-based boundary conditions have been sought to characterize fluid flow over patterned surfaces. We focus on laminar shear flows over surfaces with periodic height fluctuations and/or fluctuating Navier scalar slip properties. We derive a general formula for the "effective slip", which describes equivalent fluid motion at the mean surface as depicted by the linear velocity profile that arises far from it. We show that the slip and the applied stress are related linearly through a tensorial mobility matrix, and the method of domain perturbation is then used to derive an approximate formula for the mobility law directly in terms of surface properties. The specific accuracy of the approximation is detailed, and the mobility relation is then utilized to address several questions, such as the determination of optimal surface shapes and the effect of random surface fluctuations on fluid slip.

physics.flu-dyn↗

arXiv2009

Effective zero-thickness model for a conductive membrane driven by an electric field

The behavior of a conductive membrane in a static (DC) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Non-equilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.

cond-mat.soft↗

arXiv2009

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions near a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage ($kT/e \approx 25$ mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several Volts $\approx 100 kT/e$ are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the literature, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counter-ions. Using simple continuum models, we predict two general trends, each enhanced by dielectric response: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that ICEO flows are ion-specific. Similar issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.

physics.flu-dyn↗

arXiv2009

Anisotropic electro-osmotic flow over super-hydrophobic surfaces

Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to greatly enhance electrokinetic phenomena. Existing theories assume either homogeneous flat surfaces or patterned surfaces with thin double layers (compared to the texture correlation length) and thus predict simple surface-averaged, isotropic flows (independent of orientation). By analyzing electro-osmotic flows over striped slip-stick surfaces with arbitrary double-layer thickness, we show that surface anisotropy generally leads to a tensorial electro-osmotic mobility and subtle, nonlinear averaging of surface properties. Interestingly, the electro-osmotic mobility tensor is not simply related to the hydrodynamic slip tensor, except in special cases. Our results imply that significantly enhanced electro-osmotic flows over super-hydrophobic surfaces are possible, but only with charged liquid-gas interfaces.

physics.flu-dyn↗

arXiv2009

Strongly nonlinear dynamics of electrolytes in large ac voltages

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.

physics.flu-dyn↗

arXiv2009

Ultrafast High-pressure AC Electro-osmotic Pumps for Portable Biomedical Microfluidics

This paper details the development of an integrated AC electro-osmotic (ACEO) microfluidic pump for dilute electrolytes consisting of a long serpentine microchannel lined with three dimensional (3D) stepped electrode arrays. Using low AC voltage (1 Volt rms, 1 kHz), power (5 mW) and current (3.5 mA) in water, the pump is capable of generating a 1.4 kPa head pressure, a 100-fold increase over prior ACEO pumps, and a 1.37 mm/sec effective slip velocity over the electrodes without flow reversal. The integrated ACEO pump can utilize low ionic strength solutions such as distilled water as the working solution to pump physiological strength (100 mM) biological solutions in separate microfluidic devices, with potential applications in portable or implantable biomedical microfluidic devices. As a proof-of-concept experiment, the use of the ACEO pumps for DNA hybridization in a microfluidic microarray is demonstrated.

physics.flu-dyn↗

arXiv2009

Size-dependent spinodal and miscibility gaps for intercalation in nano-particles

Using a recently-proposed mathematical model for intercalation dynamics in phase-separating materials [Singh, Ceder, Bazant, Electrochimica Acta 53, 7599 (2008)], we show that the spinodal and miscibility gaps generally shrink as the host particle size decreases to the nano-scale. Our work is motivated by recent experiments on the high-rate Li-ion battery material LiFePO4; this serves as the basis for our examples, but our analysis and conclusions apply to any intercalation material. We describe two general mechanisms for the suppression of phase separation in nano-particles: (i) a classical bulk effect, predicted by the Cahn-Hilliard equation, in which the diffuse phase boundary becomes confined by the particle geometry; and (ii) a novel surface effect, predicted by chemical-potential-dependent reaction kinetics, in which insertion/extraction reactions stabilize composition gradients near surfaces in equilibrium with the local environment. Composition-dependent surface energy and (especially) elastic strain can contribute to these effects but are not required to predict decreased spinodal and miscibility gaps at the nano-scale.

cond-mat.mtrl-sci↗

arXiv2009

Topology and shape optimization of induced-charge electro-osmotic micropumps

For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the topology and shape of the dielectric solid. In particular, we extend existing conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial design field. Our results show the importance of the topology and shape of the dielectric solid in ICEO systems and point to new designs of ICEO micropumps with significantly improved performance.

physics.flu-dyn↗

arXiv2008

Effective slip over superhydrophobic surfaces in thin channels

Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work has focused on specific cases, such as striped grooves or arrays of pillars, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g. low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. For isotropic (e.g. chessboard or random) textures, the Hashin-Strikman conditions further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.

physics.flu-dyn↗

arXiv2008

Tensorial hydrodynamic slip

We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as an constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful to extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.

physics.flu-dyn↗

arXiv2008

A design principle for improved 3D AC electro-osmotic pumps

Three-dimensional (3D) AC electro-osmotic (ACEO) pumps have recently been developed that are much faster and more robust than previous planar designs. The basic idea is to create a ``fluid conveyor belt'' by placing opposing ACEO slip velocities at different heights. Current designs involve electrodes with electroplated steps, whose heights have been optimized in simulations and experiments. Here, we consider changing the boundary conditions--rather than the geometry--and predict that flow rates can be further doubled by fabricating 3D features with non-polarizable materials. This amplifies the fluid conveyor belt by removing opposing flows on the vertical surfaces, and it increases the slip velocities which drive the flow.

physics.flu-dyn↗

arXiv2008

Induced-charge Electrophoresis of Metallo-dielectric Particles

The application of AC electric fields in aqueous suspensions of anisotropic particles leads to unbalanced liquid flows and nonlinear, induced-charge electrophoretic (ICEP) motion. We report experimental observations of the motion of "Janus" microparticles with one dielectric and one metal-coated hemisphere induced by uniform fields of frequency 100 Hz - 10 kHz in NaCl solutions. The motion is perpendicular to the field axis and persists after particles are attracted to a glass wall. This phenomenon may find applications in microactuators, microsensors, and microfluidic devices.

physics.flu-dyn↗

arXiv2007

Induced-charge electrophoresis near an insulating wall

Induced-charge electrophoresis (ICEP) has mostly been analyzed for asymmetric particles in an infinite fluid, but channel walls in real systems further break symmetry and lead to dielectrophoresis (DEP) in local field gradients. Zhao and Bau (Langmuir, \textbf{23}, 2007, pp 4053) recently predicted that a metal (ideally polarizable) cylinder is repelled from an insulating wall in a DC field. We revisit this problem with an AC field and show that attraction to the wall sets in at high frequency and leads to an equilibrium distance, where DEP balances ICEP, although, in three dimensions, a metal sphere is repelled from the wall at all frequencies. This conclusion, however, does not apply to asymmetric particles. Consistent with the recent experiments of Gangwal et al. (arXiv:0708.2417), we show that a metal/insulator Janus particle is always attracted to the wall in an AC field. The Janus particle tends to move toward its insulating end, perpendicular to the field, but ICEP torque rotates this end toward the wall. Under some conditions, the theory predicts steady translation along the wall with an equilibrium tilt angle, as seen in experiments, although more detailed modeling of the contact region of overlapping double layers is required.

cond-mat.mtrl-sci↗

arXiv2007

High-frequency flow reversal of AC electro-osmosis due to steric effects

The current theory of alternating-current electro-osmosis (ACEO) is unable to explain the experimentally observed flow reversal of planar ACEO pumps at high frequency (above the peak, typically 10-100 kHz), low salt concentration (1-1000 $μ$M), and moderate voltage (2-6 V), even if taking into account Faradaic surface reactions, nonlinear double-layer capacitance and bulk electrothermal flows. We attribute this failure to the breakdown of the classical Poisson-Boltzmann model of the diffuse double layer, which assumes a dilute solution of point-like ions. In spite of low bulk salt concentration, the large voltage induced across the double layer leads to crowding of the ions and a related decrease in surface capacitance. Using several mean-field models for finite-sized ions, we show that steric effects generally lead to high frequency flow reversal of ACEO pumps, similar to experiments. For quantitative agreement, however, an unrealistically large effective ion size (several nm) must be used, which we attribute to neglected correlation effects.

cond-mat.other↗

arXiv2007

Nonlinear Electrokinetics at large applied voltages

The classical theory of electrokinetic phenomena assumes a dilute solution of point-like ions in chemical equilibrium with a surface whose double-layer voltage is of order the thermal voltage, $k_BT/e = 25$ mV. In nonlinear ``induced-charge'' electrokinetic phenomena, such as AC electro-osmosis, several Volts $\approx 100 k_BT/e$ are applied to the double layer, so the theory breaks down and cannot explain many observed features. We argue that, under such a large voltage, counterions ``condense'' near the surface, even for dilute bulk solutions. Based on simple models, we predict that the double-layer capacitance decreases and the electro-osmotic mobility saturates at large voltages, due to steric repulsion and increased viscosity of the condensed layer, respectively. The former suffices to explain observed high frequency flow reversal in AC electro-osmosis; the latter leads to a salt concentration dependence of induced-charge flows comparable to experiments, although a complete theory is still lacking.

cond-mat.other↗

arXiv2007

Surface Conservation Laws at Microscopically Diffuse Interfaces

In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability in the context of microscopically diffuse is less theoretically well-established. Furthermore, surface conservation laws (and interfacial in general) are often derived phenomenologically rather than systematically. In this article, provide a mathematically rigorous justification for surface conservation laws at diffuse interfaces on an asymptotic analysis of transport processes in the boundary layer and derive general the surface and normal fluxes that appear in surface conservation laws. Next, we use non-thermodynamics to formulate surface conservation laws in terms of chemical potentials a method for systematically deriving the structure of the interfacial layer. Finally, we conservation laws for a few examples from diffusive and electrochemical transport.

physics.chem-ph↗

arXiv2006

Steric effects in the dynamics of electrolytes at large applied voltages: II. Modified Poisson-Nernst-Planck equations

In situations involving large potentials or surface charges, the Poisson Boltzman(PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations", which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these MPNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari(2004} for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I for such problems.

physics.chem-ph↗

arXiv2006

The stochastic flow rule: A multi-scale model for granular plasticity

In spite of many attempts to model dense granular flow, there is still no general theory capable of describing different types of flows, such as gravity-driven drainage in silos and wall-driven shear flows in Couette cells. Here, we summarize our recent proposal of the Stochastic Flow Rule (SFR), which is able to describe these cases in good agreement with experiments, and we focus on testing the theory in more detail against brute-force simulations with the discrete-element method (DEM). The SFR is a general rate-independent constitutive law for plastic flow, based on diffusing spots of fluidization. In the case of quasi-2D granular materials, we assume limit-state stresses from Mohr-Coulomb plasticity and postulate that spots undergo biased random walks along slip-lines, driven by local stress imbalances. We compare analytical predictions of the SFR against DEM simulations for silos and Couette cells, carrying out several parametric studies in the latter case, and find good agreement.

cond-mat.soft↗