Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel.

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries1 and electrocatalysts2. Experimental characterizations of such materials by operando microscopy produce rich image datasets3-6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

Learning the Physics of Pattern Formation from Images.

Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.

Clusters of circulating tumor cells traverse capillary-sized vessels.

Multicellular aggregates of circulating tumor cells (CTC clusters) are potent initiators of distant organ metastasis. However, it is currently assumed that CTC clusters are too large to pass through narrow vessels to reach these organs. Here, we present evidence that challenges this assumption through the use of microfluidic devices designed to mimic human capillary constrictions and CTC clusters obtained from patient and cancer cell origins. Over 90% of clusters containing up to 20 cells successfully traversed 5- to 10-µm constrictions even in whole blood. Clusters rapidly and reversibly reorganized into single-file chain-like geometries that substantially reduced their hydrodynamic resistances. Xenotransplantation of human CTC clusters into zebrafish showed similar reorganization and transit through capillary-sized vessels in vivo. Preliminary experiments demonstrated that clusters could be disrupted during transit using drugs that affected cellular interaction energies. These findings suggest that CTC clusters may contribute a greater role to tumor dissemination than previously believed and may point to strategies for combating CTC cluster-initiated metastasis.

Oscillations and Multiple Equilibria in Microvascular Blood Flow.

We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through a combination of analytic and numeric techniques, we predict in a series of two-parameter bifurcation diagrams a range of dynamical behaviors, including multiple equilibria flow configurations, simple oscillations in volumetric flow rate, and multiple coexistent limit cycles at physically realizable parameters. We show that complexity in network topology is not necessary for complex behaviors to arise and that nonlinear rheology, in particular the plasma skimming effect, is sufficient to support oscillatory dynamics similar to those observed in vivo.

In-Situ Characterization of Cathode Catalyst Degradation in PEM Fuel Cells.

The composition and morphology of the cathode catalyst layer (CCL) have a significant impact on the performance and stability of polymer electrolyte membrane fuel cells (PEMFC). Understanding the primary degradation mechanism of the CCL and its influencing factors is crucial for optimizing PEMFC performance and durability. Within this work, we present comprehensive in-situ characterization data focused on cathode catalyst degradation. The dataset consists of 36 unique durability tests with over 4000 testing hours, including variations in the cathode ionomer to carbon ratio, platinum on carbon ratio, ionomer equivalent weight, and carbon support type. The applied accelerated stress tests were conducted with different upper potential limits and relative humidities. Characterization techniques including IV-curves, limiting current measurements, electrochemical impedance spectroscopy, and cyclic voltammetry were employed to analyse changes in performance, charge and mass transfer, and electrochemically active surface area of the catalyst. The aim of the dataset is to improve the understanding of catalyst degradation by allowing comparisons across material variations and provide practical information for other researchers in the field.

Double layer in ionic liquids: overscreening versus crowding.

We develop a simple Landau-Ginzburg-type continuum theory of solvent-free ionic liquids and use it to predict the structure of the electrical double layer. The model captures overscreening from short-range correlations, dominant at small voltages, and steric constraints of finite ion sizes, which prevail at large voltages. Increasing the voltage gradually suppresses overscreening in favor of the crowding of counterions in a condensed inner layer near the electrode. This prediction, the ion profiles, and the capacitance-voltage dependence are consistent with recent computer simulations and experiments on room-temperature ionic liquids, using a correlation length of order the ion size.

Instability of electro-osmotic channel flow with streamwise conductivity gradients.

This work considers the stability of an electro-osmotic microchannel flow with streamwise electrical conductivity gradients, a configuration common in microfluidic applications such as field amplified sample stacking. Previous work on such flows has focused on how streamwise conductivity gradients set a nonuniform electro-osmotic velocity which results in dispersion of the conductivity field. However, it has been known for many years that electric fields can couple with conductivity gradients to generate unstable flows. This work demonstrates that at high electric fields such an electrohydrodynamic instability arises in this configuration and the basic mechanisms are explored through numerical simulations. The instability is unique in that the nonuniform electro-osmotic flow sets the shape of the underlying conductivity field in a way that makes it susceptible to instability. While nonuniform electro-osmotic flow sets the stage, the instability is ultimately the result of electric body forces due to slight departure from electroneutrality in the fluid bulk. A simple stability map is created where two dimensionless numbers can predict system stability reasonably well, even though the system formally depends on six dimensionless groups.

Steric effects on ac electro-osmosis in dilute electrolytes.

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 microM) , and moderate voltage (2-6 V), even 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 pointlike 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 nanometers) must be used, which we attribute to neglected correlation effects.

Electrohydrodynamic instabilities in microchannels with time periodic forcing.

In microfluidic applications it has been observed that flows with spatial gradients in electrical conductivity are unstable under the application of sufficiently strong electric fields. These electrohydrodynamic instabilities can drive a nonlinear flow despite the low Reynolds number. Such flows hold promise as a simple mechanism for mixing fluids. In this work, the effect of a time periodic electric field on the instability is explored. The case where an electric field is applied across a diffuse interface of two fluids with varying electrical conductivity is considered. Frequency-dependent behavior is found only in the regime where the instability growth rates are very slow and cannot outpace mixing by molecular diffusion. Improving mixing by modulation of the electric body force is not a viable strategy in this geometry.

Bulk electroconvective instability at high Péclet numbers.

Bulk electroconvection pertains to flow induced by the action of a mean electric field upon the residual space charge in the macroscopic regions of a locally quasielectroneutral strong electrolyte. For a long time, controversy has existed in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge-selective solid, such as a metal electrode or ion exchange membrane, is stable with respect to bulk electroconvection. While it was recently claimed that bulk electroconvective instability could not occur, this claim pertained to an aqueous, low-molecular-weight electrolyte characterized by an order-unity electroconvection Péclet number. In this paper, we show that the bulk electroconvection model transforms into the leaky dielectric model in the limit of infinitely large Péclet number. For the leaky dielectric model, conduction of the above-mentioned type is unstable, and so it is in the bulk electroconvection model for sufficiently large Péclet numbers. Such instability is sensitive to the ratio of the diffusivity of the cations to the anions. For infinite Péclet number, the case with equal ionic diffusivities is a bifurcation point separating stable and unstable regimes at the low-current limit. Further, for a cation-selective solid, when the Péclet number is finite and the anions are much more diffusive than the cations, an unreported bulk electroconvective instability is possible at low current. At higher currents and large Péclet numbers, we found that the system is unstable for all cation-to-anion diffusivity ratios, but passes from a monotonic instability to an oscillatory one as this ratio passes through unity.

Observations of spontaneous oscillations in simple two-fluid networks.

We investigate the laminar flow of two-fluid mixtures inside a simple network of interconnected tubes. The fluid system is composed of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct phases. Downstream of a diverging network junction the two fluids do not necessarily split in equal fraction and thus heterogeneity is introduced into network. We find that in the simplest network, a single loop with one inlet and one outlet, under steady inlet conditions, the flow rates and distribution of the two fluids within the network loop can undergo persistent spontaneous oscillations. We develop a simple model which highlights the basic mechanism of the instability and we demonstrate that the model can predict the region of parameter space where oscillations exist. The model predictions are in good agreement with experimental observations.

Effects of electrostatic correlations on electrokinetic phenomena.

The classical theory of electrokinetic phenomena is based on the mean-field approximation that the electric field acting on an individual ion is self-consistently determined by the local mean charge density. This paper considers situations, such as concentrated electrolytes, multivalent electrolytes, or solvent-free ionic liquids, where the mean-field approximation breaks down. A fourth-order modified Poisson equation is developed that captures the essential features in a simple continuum framework. The model is derived as a gradient approximation for nonlocal electrostatics of interacting effective charges, where the permittivity becomes a differential operator, scaled by a correlation length. The theory is able to capture subtle aspects of molecular simulations and allows for simple calculations of electrokinetic flows in correlated ionic fluids. Charge-density oscillations tend to reduce electro-osmotic flow and streaming current, and overscreening of surface charge can lead to flow reversal. These effects also help to explain the suppression of induced-charge electrokinetic phenomena at high salt concentrations.

Bistability in a simple fluid network due to viscosity contrast.

We study the existence of multiple equilibrium states in a simple fluid network using Newtonian fluids and laminar flow. We demonstrate theoretically the presence of hysteresis and bistability, and we confirm these predictions in an experiment using two miscible fluids of different viscosity-sucrose solution and water. Possible applications include blood flow, microfluidics, and other network flows governed by similar principles.

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 in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 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 V approximately 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 experimental and theoretical literatures, 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 counterions. Using simple continuum models, we predict two general trends at large voltages: (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; each trend is enhanced by dielectric saturation. 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 several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical 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.

Argon rectification and the cause of light emission in single-bubble sonoluminescence.

In single-bubble sonoluminescence, repeated brief flashes of light are produced in a gas bubble strongly driven by a periodic acoustic field. A startling hypothesis has been made by Lohse and co-workers [Phys. Rev. Lett. 78, 1359 (1997)] that the non-noble gases in an air bubble undergo chemical reaction into soluble products, leaving only argon. In the present work, this dissociation hypothesis is supported by simulations, although the associated temperatures of about 7000 K seem too low for bremsstrahlung, which has been proposed as the dominant light emission mechanism. This suggests that emission from water vapor and its reaction products, heretofore not included, may play an important role.