Session Q16: Electrokinetic Flows III

Impact of Faradaic Reactions on the Charging Dynamics of the Electrical Double Layers

Electrical double layers (EDLs) and faradaic reactions are commonly observed in electrochemical systems such as batteries, fuel cells and hybrid capacitors. However, the impact of faradaic reactions on the structure of EDLs is typically neglected, making it harder to accurately predict the concentration, charge, and current profiles. Here, we propose a time-dependent perturbation expansion model in the thin EDL limit that accounts for a constant faradaic flux at the Stern layer/diffuse layer boundary. Our analysis yields two main conclusions: (i) Faradaic reactions impact the definition of the Boltzmann distribution, and thus the widely utilized Gouy-Chapman-Stern model needs to be appropriately modified; (ii) The current due to double layer charging dominates at shorter time scales whereas the current from the faradaic reaction dominates at longer timescales. We validate our perturbation expansion model through direct numerical simulations of the Poisson-Nernst-Planck equations. Overall, our analysis enables us to connect the micro-scale transport problem near the electrical double layer with the macro-scale bulk transport problem and allows us to qualitatively predict the current evolution for electrochemical systems.   

Numerical Simulation of Pattern Accelerated Electroconvection

Electroconvection is an emerging topic of interest for engineers due to its great potential in industrial applications such as separation, desalination, fuel cells and, more recently by nanofluidic channels. Research has shown that Electroconvection can enhance ion transport at polarized surfaces and thereby shorten the plateau region of limiting current. The patterned surfaces with alternating permeable and impermeable regions can increase the ion transport and Electroconvection process. In this work, numerical simulation has been used to investigate and optimized patterned accelerated Electroconvection. An iterative algorithm is used for the robust treatment of the coupling of concentration and momentum. Linearization of electromigration fluxes helps in decreasing the complexity and faster convergence. The effect of patterned and homogeneous boundary on mean ion transport and current density will be discussed. Finally, we will discuss how to improve ion transport by having time-dependent Boundary conditions that regularize large-scale flow circulation cells.   

Modeling and simulation of multi-layered electrochemical cells

Numerous studies have demonstrated the usefulness of multi-layered electrochemical cells for a wide variety of chemical processing applications. An example of such multi-layered structures is bi-polar membranes, in which an anion exchange membrane and cation exchange membrane (or appropriate poly-electrolytes) are layered adjacently, producing a built-in voltage and facilitating transport of species to/from the junction. Modeling and numerical simulation of such electrochemical cells allows for rapid design iteration and testing of hypotheses, particularly with regard to device geometry, layer physical properties, chemical compositions, reaction mechanisms, and catalyst application. In this work, we demonstrate the key features of a simulation suite that solves the extended Poisson-Nernst-Planck equations on a user-specified, multi-layered domain with user-specified physical/chemical properties in each layer. Solver implementation details are briefly discussed, validation cases are shown, and novel examples of multi-layered systems involving involving diffusion, electromigration, and chemical reactions are presented.   

Numerical study of electric-charge diffusion in wall-bounded flows of dielectric liquids

Flow electrification during transport of dielectric liquids constitutes a major safety hazard.  This is particularly the case in petrochemical and process industries, in which several accidents have occurred in the past due to the dielectric properties of liquid hydrocarbons.  For this reason, it has been the subject of various research efforts over the years.

Typically, flow electrification occurs via diffusion of electric-charge carriers (ions) from the electrical double layer, which is inevitably formed between a liquid-solid interface, to the bulk of the flow. This phenomenon is currently not well understood but it is generally accepted that flow turbulence plays a major role and can dramatically increase the electrification rate.  More specifically, at sufficiently high Reynolds numbers, and for low-conductivity fluids such as liquid hydrocarbons, the thickness of the hydrodynamic boundary layer becomes comparable to that of the electrical double layer. In turn, this leads to increased transport of charges away from the wall region and towards the bulk of the flow.  However, quantitative information on the underpinning mechanisms of this phenomenon is still lacking.

In the first part of this presentation, we outline our numerical method for the simulation of the problem for interest In the second part, we present results from direct numerical simulations of turbulent flow electrification for bulk Reynolds numbers ranging from 4600 to 6700.  Our study focuses on the rate of accumulation of charge in the bulk and on the statistical properties of the charge density distribution.   

Influence of Relative Debye Length on Electric-Double-Layer Charging Inside a Nanopore

The operating principle of energy storage devices, such as supercapacitors and hybrid capacitors, is the accumulation of charge onto double layers inside their porous electrodes. Typically, the relative Debye length, i.e., the ratio of Debye length to pore diameter, varies by orders of magnitude inside a porous electrode. However, theoretical models in the literature assume either thin or overlapping double layers. Here, we develop a perturbation expansion theory for arbitrary relative Debye lengths to solve the Poisson-Nernst-Planck (PNP) equations in the limit of small potentials. We derive analytical expressions for the charge distribution, potential profile and total current, and show that our analytical results compare favorably with direct numerical simulations of the PNP equations. We show that an arbitrary relative Debye length results in a jump discontinuity in the electric potential at the pore mouth, and also modifies the nanopore charging timescale. Finally, we derive an expression for effective capacitance that is able to qualitatively explain the pore-size dependence of nanopore capacitance results reported in the literature.   

Revisiting the electroacoustic phenomenon in the presence of surface acoustic waves

Recently, one observes abundant studies on the application of surface acoustic waves (SAWs) in solid substrates for manipulating liquids and particulates in micron to nanometer thick films and channels and in porous media. At these length scales, contributions of SAWs to the electrical double layer (EDL) of ions and of the latter to particulates and flow may become appreciable. However, the nature of interplay between SAWs and EDLs is unknown. Inert solids support a mechanical wave which translates to acoustic flow in the nearby liquid. Piezoelectric solids, common for generating SAW, further support a voltage signal which travels along the mechanical SAW in the solid. We demonstrate the near equilibrium distortion of the electrical and ion concentration field in the EDL near inert and piezoelectric substrates under SAW excitation. We concentrate on the resulting escape of transient and steady electrical fields from a charged solid surface through the near equilibrium EDL and to the bulk of liquid. The electrical fields far from the solid may be interpreted by different models of EDL to give information about its dynamics and statics and about the zeta potential or properties of the Stern layer and of the intrinsic surface electrical potential at the solid surface.   

An integral analysis in tensorial notation for streaming-potential phenomena

In microfluidic applications, induced-charge electroosmosis can be used to drive fluids. Moreover, the same electrohydrodynamic effects play an essential role in the behavior of particles and bio surfaces at the microscale. Nonlinear electrohydrodynamic effects induce strong gradients in the thin geometry of the Debye layer. Thus, an integral description of the layer that illustrates those effects in a simplified form is valuable for their understanding and computation. 

Therefore, we present jump conditions for integral parameters, such as stress, mass flux, and ion fluxes. Our approach relies on previous asymptotic solutions to streaming-potential phenomena within Debye layers. We expand this model to curved surfaces by solving the contravariant form of the set of differential equations for the flow, electric potential, and charge distributions. These integral jump conditions suggest multiple definitions for the Debye layer thickness, all considering the zeta-potential, and conservation of various properties can be derived.

References:

[1] Marthaler & Class (2021) PAMM 20. 

[2] Yariv et al. (2011) J. Fluid Mech. 685.

[3] Class et al. (2003) J. Fluid Mech. 491.   

Bipolar nanochannels: a systematic approach to asymmetric problems

Nanofluidic diodes are capable of rectifying the electrical current by orders of magnitude. In the current state of affairs, determining the rectification factor is not possible as it depends on many system parameters. In this talk, we will show how an interplay of geometric and surface charge effects can vary the current−voltage response between the two extreme behaviors of unipolar and bipolar responses. To this end, we account for the diode and its adjacent microchannels whereby we vary both the geometry and the surface charge to any desired configuration. Instead of the classical signature of concentration polarization, such as ionic depletion and enrichment, our system exhibits a more complicated behavior as such the formation of two depletion layers. The system can be characterized by various steady-state parameters such as the transport numbers and rectification factor, but we also show that these “steady-state” parameters exhibit spatial and temporal dependencies. The findings of our work [1] can be used to elucidate the complicated behavior of ion transport in nanofluidic diodes and to rationalize experimental results. The insights of this work can be used to improve the design of nanofluidic diodes.

[1] Abu-Rjal and Green, ACS Appl. Mater. Interfaces 13, 27622 (2021).   

Electric field-driven accumulation and separation of proteins at liquid-liquid interfaces in aqueous two-phase systems

Liquid-liquid interfaces in aqueous two-phase systems (ATPS) represent a transport resistance to charged molecules driven by an electric field. As a result, depending on the applied electric field strength, the composition of the phases and the molecular properties, molecules accumulate at the interface. In this work, the interaction of two types of proteins with the interface of an ATPS is examined using a microfluidic device and confocal as well as epifluorescence microscopy. Both proteins are initially dissolved in the same phase of the ATPS and transported by an electric field normal to the interface. The temporal development of the fluorescence intensity at the interface and in the extraction phase indicates that one protein mainly accumulates at the interface while the other already crosses over, suggesting that the transport resistance differs for both types of proteins. A mathematical model based on the assumption that this transport resistance results from adsorption in a potential well at the interface supports the experimental results. Hence, the liquid-liquid interface of an ATPS can be utilized to separate different types of proteins.   

Enhanced sample preconcentration through fast capillary-driven flow in microfluidic paper-based analytical devices.

Microfluidic paper-based analytic devices (µPADs) for early diagnosis have gained significant attentions in the last decade. Due to low sensitivity of µPADs, several preconcentration mechanisms for high enrichment factor have been developed, but still have critical nuisances such as complex fabrication and long process times. While conventional µPADs based ion concentration polarization (ICP) preconcentrator has used only passive capillary imbibition, in this work, we introduced air gap between the stacked paper layers for fast flow generation to demonstrate fast and enhanced preconcentration by ICP in µPADs. First, we developed air-gap forming doubly stacked µPADs and demonstrated an enhanced preconcentration factor of up to 135-folds in 10 minutes. Second, we analyzed theoretically why the fast flow can be formed and the preconcentration time can be shortened in the air-gap forming doubly stacked µPADs. Thus, this air-gap forming doubly stacked µPADs with reduced sample loading time and increased sample volume would be utilized as point-of-care testing devices to detect low abundant targets in shorter operation time.