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At least 37 records · Page 2

Search for nonvirialized axions with 3.3 − 4.2 μ ⁢eV mass at selected resolving powers

The Axion Dark Matter eXperiment is sensitive to narrow axion flows, given axions compose a fraction of the dark matter with a non-negligible local density. Detecting these low-velocity dispersion flows requires a high spectral resolution and careful attention to the expected signal modulation due to Earth’s motion. Here, we report an exclusion on the local axion dark matter density in narrow flows of ρ a ≳ 0.03 GeV/cm 3 and ρ a ≳ 0.004 GeV/cm 3 for Dine-Fischler-Srednicki-Zhitnitski and Kim-Shifman-Vainshtein-Zakharov axion-photon couplings, respectively, over the mass range 3.3−4.2 μeV. Measurements were made at selected resolving powers to allow for a range of possible velocity dispersions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for non-virialized axions with 3.3-4.2 $\mu$eV mass at selected resolving powers

The Axion Dark Matter eXperiment is sensitive to narrow axion flows, given axions compose a fraction of the dark matter with a non-negligible local density. Detecting these low-velocity dispersion flows requires a high spectral resolution and careful attention to the expected signal modulation due to Earth's motion. We report an exclusion on the local axion dark matter density in narrow flows of $\rho_a \gtrsim 0.03\,\mathrm{GeV/cm^3}$ and $\rho_a \gtrsim 0.004\,\mathrm{GeV/cm^3}$ for Dine-Fischler-Srednicki-Zhitnitski and Kim-Shifman-Vainshtein-Zakharov axion-photon couplings, respectively, over the mass range $3.3-4.2\,\mu\text{eV}$. Measurements were made at selected resolving powers to allow for a range of possible velocity dispersions.

79 ASTRONOMY AND ASTROPHYSICS↗

Investigation of carbon incorporation in laser-assisted MOCVD of GaN

Background carbon (C) impurity incorporation in metalorganic chemical vapor deposition (MOCVD) grown gallium nitride (GaN) represents one of the major issues in further improving GaN vertical power device performance. This work presents a laser-assisted MOCVD (LA-MOCVD) technique to address the high-C issue in MOCVD homoepitaxial GaN under different growth rate (Rg) regimes and studies the correlations between [C] and Rg. [C] in LA-MOCVD GaN is reduced by 50%–90% as compared to the conventional MOCVD GaN for a wide growth rate range between 1 and 16 μm/h. A mass-transport based model is developed to understand the C incorporation at different Rg regimes. The results obtained from the developed model are in good agreement with experimental data. The model further reveals that LA-MOCVD effectively suppresses C incorporation by reducing the active C species in the gas phase. Moreover, high step velocity in step flow growth mode can facilitate C incorporation at fast Rg, exhibiting steeper C increase. The theoretical model indicates that [C] can be suppressed below 1016 cm−3 with a fast growth rate (Rg) of 10 μm/h by utilizing higher power LA-MOCVD and freestanding GaN substrates with larger off-cut angles.

Physics↗

Critical analysis of velocimetry methods for particulate flows from synthetic data

Particle tracking methods that extract high-fidelity particle velocity data from high speed video of particle laden flows is a common experimental technique applied to chemical processes. These measurements are used to better understand the motion of particles and fluids in complex systems and create data against which computational models are validated. However, the methods, codes, and experimental setups all have limitations. It is imperative that practitioners verify the methods and their implementation as well as understand the limitations of experimental setups. This work focuses on quantifying the visible depth of field in a high particle concentration fluidized bed. Following a precedent set by the particle imaging velocimetry community, a particle velocity field is manufactured using a computational fluid dynamics and discrete element method simulation. Photo realistic high-speed videos are rendered based on the simulated data using the three-dimensional creation software Blender. Particle velocities are extracted from the synthetic high-speed videos using three variants of Particle Tracking Velocimetry and Optical Flow Velocimetry methodologies. Here, the tracked results are then compared to the known solution, quantifying the error associated with the assumed visible depth. The results indicate that at depth of one particle diameter, all three particle tracking codes give accurate measurements, largely within 5%. However, the error increases when the full bed video measurements are compared to the known solution at one particle diameter, i.e., mimicking a validation study. Finally, for some statistics the constant depth assumption only increases the error slightly, for others significantly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The effects of in-situ emulsion formation and superficial velocity on foam performance in high-permeability porous media

Foam has been considered as a mobility control agent for Enhanced Oil Recovery (EOR) applications in heterogeneous and fractured reservoirs. Foam enhances sweep efficiency by enabling the injected gas to flow from high-permeability to low-permeability regions. The foam injection velocity is an essential factor affecting foam mobility control and flow behavior. Furthermore, the presence of remaining oil adversely impacts foam generation leading to a failure in governing mobility control. In this study, foam performance in establishing mobility control effect and favorable apparent viscosity was experimentally investigated under a range of total superficial velocities in the presence and absence of crude oil during foam propagation in high permeability sand packs representing a propped fracture network. In the absence of oil, a pronounced effect of total superficial velocity on the mobility control performance was observed at the transition foam quality regime. Co-injection of oil and foam led to noticeable foam destabilization, as expected. However, a further increase in oil fractional flow resulted in larger overall flow resistance. We found that the formation of in-situ surfactant/oil emulsion contributed to the high apparent viscosity exhibited at the steady-state condition. These findings suggest that the steady-state flow resistance established during foam flooding at high oil saturations should be interpreted as the mobility control effect resulting from emulsion formation rather than the development of strong foam.

02 PETROLEUM↗

High-speed characterization of two-phase flow and bubble dynamics in titanium felt porous media for hydrogen production

Bubble dynamics and two-phase flow phenomena are closely related to the performance of proton exchange membrane electrolyzer cells (PEMECs). This paper reports an in-situ study of the oxygen bubble behavior and associated multiphase evolutions in the anode side of PEMECs with titanium (Ti) felt liquid gas diffusion layers (LGDLs) by a high-speed visualization system. The micro oxygen bubble dynamics was captured and analyzed at different locations and virous operating conditions. The results show that the bubble detachment frequency and detachment diameter greatly increase with the operating current density. Additionally, they are significantly impacted by the local pore structure and morphology of Ti felt LGDLs. In the flow channels, there exist only several discrete micro bubbles at a low current density (0.04 A/cm 2 ) and a large flow velocity (133 mm/s). At a current density (0.2 A/cm 2 ) and a flow velocity (67 mm/s), a number of gas slugs are formed in the follow channels, in addition to discrete micro bubbles. At a high current density (1 A/cm 2 ) and a flow velocity (67 mm/s), more bubbles appear in the channel, and the flow field is dominated by slug or annular flows. These investigations can help to better understand the two-phase flow and bubble detachment mechanism, and provide a foundation for electrochemical reaction, multiphase flow studies and optimize the design of gas diffusion layers and flow fields for PEMECs in the future.

08 HYDROGEN↗

Development of Microwave Resonant Cavity Transducer Recalibration Procedures

We are investigating a microwave resonant cavity transducer for flow sensing in the vessel of a high temperature fluid advanced reactor (AR), such as a molten salt cooled reactor (MSCR) or a sodium fast reactor (SFR). This transducer is a hollow metallic cylindrical cavity, with one of the flat walls of the cylinder flexible enough to undergo microscopic deflection due to dynamic fluid pressure. Membrane deflection leads to a shift in the microwave resonant frequency, which can be detected with a spectrum analyzer. We have performed a preliminary proof-of-principle test of flow sensing in high temperature liquid sodium in environment. The liquid sodium setup consists of a cylindrical vessel with a center feed line, where a transducer inserted through the top cap of the vessel measures velocity of the impinging liquid jet. For this test, we have developed a cylindrical resonator, which was machined from stainless steel 316 and electroplated with silver on the interior surfaces. Inner diameter of the cylindrical cavity is 22.2 mm, and the thin wall is approximately 200µm thick. The cavity was excited through a WR-42 waveguide through a subwavelength hole on the side of the wall of the cylinder in the TE 011 mode with resonant frequency f ≈ 17.8GHz. Sodium flow rate sensing study was performed in a liquid sodium vessel at 340°C temperature and ambient pressure. The flow rate was changed by varying sodium pump power, and a frequency shift of several hundred KHz was observed. From the measurements, we observed significant scatter in high temperature liquid sodium at low flow velocity values. Our hypothesis is that this is caused by temperature drift in the liquid, which results in thermal expansion of the cavity and a drift in the resonator frequency. In this report, we investigate temperature dependence of the resonant frequency through development of analytic models and preliminary analysis of experimental data. In addition, we develop a procedure for compensation for temperature drift during flow sensing.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Fiber Sorbents – A Versatile Platform for Sorption-Based Gas Separations

Increasing demand for high-purity fine chemicals and a drive for process intensification of large-scale separations have driven significant work on the development of highly engineered porous materials with promise for sorption-based separations. While sorptive separations in porous materials offer energy-efficient alternatives to longstanding thermal-based methods, the particulate nature of many of these sorbents has sometimes limited their large-scale deployment in high-throughput applications such as gas separations, for which the necessary high feed flow rates and gas velocities accrue prohibitive operational costs. These processability limitations have been historically addressed through powder shaping methods aimed at the fabrication of structured sorbent contactors based on pellets, beads or monoliths, commonly obtained as extrudates. These structures overcome limitations such as elevated pressure drops commonly recorded across powder adsorption beds but often accrue thermal limitations arising from elevated particle density and aggregation, which ultimately cap their maximum separation performance. Furthermore, the harsh mechanical strain to which powder particles are subjected during contactor fabrication, in the form of extrusion/compression forces, can result in partial pore occlusion and framework degradation, further limiting their performance. Here, we present the development of porous fiber sorbents as an alternative sorbent contactor design capable of addressing sorbent processability limitations while enabling an array of performance-maximizing heat integration capabilities. This new sorbent form factor leverages pre-existing know-how from hollow fiber spinning to produce fiber-shaped sorbent contactors through the phase inversion of known polymers in a process known as dry-jet/wet quenching. The process of phase inversion allows microporous sorbent particles to be latched onto a macroporous polymer matrix under mild processing conditions, thus making it compatible with soft porous materials prone to amorphization under traditional pelletization conditions. Sorbent fibers can be created with different geometries through control of the spinning apparatus and process, offering the possibility to produce monolithic and hollow fibers alike, the latter of which can be integrated with thermalization fluid flows. In this Account, we summarize our progress in the field of fiber sorbents from both design and application standpoints. We further guide the reader through the evolution of this field from the early inceptive work on zeolite hollow fibers to recent developments on MOF fibers. We highlight the versatile nature of fiber sorbents, both from the composition, fabrication and structure points of view, and further demonstrate how fiber sorbents offer alternative paths in tackling new and challenging chemical separation challenges like direct air capture (DAC), with a final perspective on the future of the field.

36 MATERIALS SCIENCE↗

Particle velocity measurement within a free-falling particle curtain using microscopic shadow velocimetry

We report an optical method for particle velocity measurement that is suitable for the measurement of particle velocities within dense particle-laden flows with high spatial resolution. The technique is based on particle shadow velocimetry with the use of a long-distance microscopic lens for images collection. The narrow depth of field of the lens allows particles within the focal plane to have much higher pattern intensities than those outside it on the collected images. Data processing was then employed to remove particles from outside the focal plane based on the gradient of the signal and a threshold. Following this, particle velocity was calculated from two successive images in the usual way. The technique was successfully demonstrated in a free-falling particle curtain with volume fractions in the four-way coupling regime of near-spherical micro-particles falling under gravity. The method was successfully employed to measure the transverse velocity profile through the curtain, which is the first time that such a measurement has been performed. Other highly-fidelity experimental data, which is also well suited to model development and validation, include the particle mass flow rate, curtain thickness and opacity.

Han, Shipu (ORCID:0000000278545882)↗

High-Fidelity Velocity and Concentration Measurements of Turbulent Buoyant Jets

Accurate models of turbulent buoyant flows are essential for the design of the cooling circuit of nuclear reactors and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We analyze experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous particle image velocimetry and laser-induced fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The refractive index matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy-driven flows (e.g. natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in a uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as a basis for the development of a new model that captures turbulent mixing.

laser induced fluorescence↗

System efficiency of packed bed TES with radial flow vs. axial flow – Influence of aspect ratio

Here, this paper compares the net system efficiency, including thermal efficiency and pressure drop effects, of radial versus axial flow packed beds for thermal energy storage. The traditional packed bed system is a cylindrical geometry where fluid flows axially from one end to another. However, issues of thermal stratification and high-pressure drop have led to recent studies on radial flow systems. One potential benefit is the reduced pressure drop in a radial flow system. This paper compares the performance of radial flow and axial flow systems at a range of aspect ratios (AR = H/D bed ) from 0.21 to 1.92 using a numerical model where the storage volume is held constant in all cases. When the radial flow bed is at a low aspect ratio (short/wide), the thermal front is improved but the pressure drop is high. At a high aspect ratio, the velocity is reduced in radial flow, leading to decreased pressure drop but an increased spreads in the thermal front that lowers thermal efficiency. The opposite trends are noted in axial flow. Thermal efficiencies of 83–91 % were noted for radial flow, while they ranged from 85 to 94 % in axial flow. Net efficiencies including pressure drop ranged from 74 to 82 % for radial flow and 80–87 % for axial flow. In both systems, a peak net efficiency was noted between the highest and lowest aspect ratio. While some aspect ratios with radial flow outperform axial flow from a net efficiency perspective, the results show that the highest net efficiency from axial flow is higher than that from radial flow. Overall, this paper highlights the importance of innovative TES designs and their potential to improve energy efficiency.

25 ENERGY STORAGE↗

Beyond Taylor’s hypothesis: a novel volumetric reconstruction of velocity and density fields for variable‑density and shear flows

Abstract This work presents a novel numerical procedure for reconstructing volumetric density and velocity fields from planar laser-induced fluorescence (PLIF) and stereoscopic particle image velocimetry (SPIV) data. This new method is theoretically and practically demonstrated to provide more accurate 3D vortical structures and density fields in high shear flows than reconstruction methods based on the mean convective velocity. While Taylor’s hypothesis of frozen turbulence is commonly applied by using the local mean streamwise velocity, the proposed algorithm uses the measured local instantaneous velocity for data convection. It consists of a step-by-step reconstruction based on a mixed Lagrangian–Eulerian solver that includes the 3D interpolation of scattered flow data and that relaxes the Taylor’s hypothesis by iterative enforcement of the incompressibility constraint on the velocity field. This methodology provides 3D fields with temporal resolution, spatial resolution, and accuracy comparable to that of real 3D snapshots, thus providing a practical alternative to tomographic measurements. The procedure is validated using numerical data of the constant-density channel flow available on the Johns Hopkins University Turbulence Database (JHTDB), showing the accurate reconstruction of the 3D velocity field. The algorithm is applied to an experimental dataset of PLIF and SPIV measurements of a variable-density jet flow, demonstrating its capability to provide 3D velocity and density fields that are more consistent with the Navier–Stokes equations compared to the mean flow convective method. Graphic abstract

42 ENGINEERING↗

Droplet-Gas Interactions in Nanoelectrospray Multiphase Flow

Electrospray (ES) is production of a charged droplet plume that transits from an electrically biased supply capillary to a counter electrode under the influence of an electric field. Drag interactions with the surrounding gas decelerate the droplets while transferring the momentum from droplets to accelerate the surrounding gas, resulting in an induced gas flow. This work seeks to characterize the structure of the resulting gas jet and identify the key mechanisms defining the flow structure. The phenomenon of gas jets produced by momentum transfer from nano-electrospray (nES) plumes is explored with schlieren visualization, thermal anemometry, and numerical simulations. Schlieren visualization experiments provide information on the flow structure in support of simulation predictions, and the hot thermistor anemometry measurements of gas velocities outside the spray demonstrate quantitatively validated simulation results. The study reveals the formation of a moderately high velocity coaxial gas jet within the nES plume and provides insight into the overall flow structure of the induced flow. The multiphase electrohydrodynamic simulations enable numerical experimentation to explore the fundamental physics of coupled droplet-gas transport and the resulting flow structure. The simulations, confirmed by the experiments, reveal gas jetting induced by nES with a narrow (sub hundred micrometers in diameter) core originating from the nES liquid-jet breakup region and a surrounding larger-in-extent zone (several hundred micrometers in diameter) of lower velocity gas flow within the electrospray plume. This behavior is due to nES ejecting a stream of droplets from the tip of a narrow liquid cone-jet, where the combined effect of many small droplets transferring momentum to a confined region of gas yields a narrow but high-velocity gas stream. Furthermore, the micro-jets produced by nES have practical utility for mass spectrometry, 3D printing and fabrication, and thermal management.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Understanding the relative importance of vertical and horizontal flow in ice-wedge polygons

Abstract. Ice-wedge polygons are common Arctic landforms. The future of these landforms in a warming climate depends on the bidirectional feedback between the rate of ice-wedge degradation and changes in hydrological characteristics. This work aims to better understand the relative roles of vertical and horizontal water fluxes in the subsurface of polygonal landscapes, providing new insights and data to test and calibrate hydrological models. Field-scale investigations were conducted at an intensively instrumented location on the Barrow Environmental Observatory (BEO) near Utqiaġvik, AK, USA. Using a conservative tracer, we examined controls of microtopography and the frost table on subsurface flow and transport within a low-centered and a high-centered polygon. Bromide tracer was applied at both polygons in July 2015 and transport was monitored through two thaw seasons. Sampler arrays placed in polygon centers, rims, and troughs were used to monitor tracer concentrations. In both polygons, the tracer first infiltrated vertically until encountering the frost table and was then transported horizontally. Horizontal flow occurred in more locations and at higher velocities in the low-centered polygon than in the high-centered polygon. Preferential flow, influenced by frost table topography, was significant between polygon centers and troughs. Estimates of horizontal hydraulic conductivity were within the range of previous estimates of vertical conductivity, highlighting the importance of horizontal flow in these systems. This work forms a basis for understanding complexity of flow in polygonal landscapes.

54 ENVIRONMENTAL SCIENCES↗

River Dynamics Control Transit Time Distributions and Biogeochemical Reactions in a Dam-Regulated River Corridor

Residence Time Distributions (RTDs) exert an important control on biogeochemical translation in the hydrological systems. Previous tracer studies have revealed that RTDs often followed time-invariant exponential, lognormal, or heavy-tailed RTDs that have power-law behavior for long tails in headwater or low-order streams. However, there is a recognition that RTDs can be more complicated and time-variable in response to dynamic hydrological forcing. Here, we use particle tracking to estimate RTDs along the Hanford Reach of the Columbia River and to quantify the influences of river stage fluctuations. Particle tracking is conducted using the velocity field from high-resolution 3D groundwater flow simulations. The effects of hydrological forcing on the residence time distribution were evaluated by varying river flow boundary conditions and releasing particles in different time windows. Our results revealed that dynamic stage fluctuations created rapidly changing losing-gaining conditions in the river and led to highly transient RTDs, which contributes to multiple modes of RTDs. Dam-induced high-frequency (sub-daily) flow variation contributes to the short-time (sub-daily) component of the RTDs. Deviation of the reactant consumption under the single-mode assumption compared to the multimodal RTDs is relatively small (~5%) and appears when the Damköhler number was close to one.More specifically, high-frequency (daily) dam-induced stage variations have higher impacts on biogeochemical reactions with faster reaction rate, and can potentially increase the reactant consumption by 26.68%. Based on these findings, we suggest that current river basin models could be improved by including bank storage and more complex RTDs influenced by both short and long term river stage fluctuations.

54 ENVIRONMENTAL SCIENCES↗

3D Simulations Capture the Persistent Low-Mode Asymmetries Evident in Laser-Direct-Drive Implosions on OMEGA

Spherical implosions in Inertial Confinement Fusion (ICF) are inherently sensitive to perturbations that may arise from experimental constraints and errors. Control and mitigation of low-mode (long wavelengths) perturbations is a key milestone to improving implosion performances. Here, we present the first 3-D radiation-hydrodynamic simulations of directly driven ICF implosions with an inline package for polarized Crossed-Beam Energy Transfer (CBET). Simulations match bang times, yields (separately accounting for laser-induced high modes and fuel age), hot spot flow velocities and direction, for which polarized CBET contributes to the systematic flow orientation evident in the OMEGA implosion database. Current levels of beam mispointing, imbalance, target offset and asymmetry from polarized CBET degrade yields by more than 40%. The effectiveness of two mitigation strategies for low-modes is explored.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Uniform momentum and temperature zones in unstably stratified turbulent flows

Wall-bounded turbulent flows exhibit a zonal arrangement, in which streamwise velocity organizes into uniform momentum zones (UMZs), separated by thin layers of elevated interfacial shear. While significant research efforts have focused on these structural features in neutrally stratified flows, the effects of unstable thermal stratification on UMZs and on analogous uniform temperature zones (UTZs) have not been considered previously. In this article, statistical properties of UMZs and UTZs are investigated using a suite of large eddy simulations of unstably stratified turbulent channel flow spanning weakly to highly convective conditions. When normalized by the friction velocity and stability-dependent mixing length, the mean velocity gradient based on UMZ interfacial velocity jumps and the vorticity thickness exhibits good collapse for all stabilities, establishing a link between UMZ properties and scaling predictions from Monin–Obukhov similarity theory. A similar relationship is found between UTZ properties and surface-layer scaling of the mean temperature gradient. In the mixed layer, mean UMZ depth is quasi-constant with wall-normal distance, while the deepest UTZs are found in the centre of the boundary layer. These instantaneous structures are found to be linked to the well-mixed velocity and temperature profiles in the convective mixed layer. Conditional averaging indicates that both UMZ and UTZ interfaces are associated with ejections of momentum and warm updrafts below the interface and sweeps of momentum and cool downdrafts above the interface. These results demonstrate a tangible connection between instantaneous structural features, mean properties and scaling laws in unstably stratified flows.

Mechanics↗

Electro-osmo-dialysis through nanoporous layers physically conjugated to micro-perforated ion-exchange membranes: Highly selective accumulation of trace coions

This study explores theoretically and numerically the phenomenon of counter-flow accumulation of trace coions during electro-osmo-dialysis through composite membranes containing nanoporous and perforated ion-exchange layers. The combination of charged nanopores and perforations allows electroosmosis, and ion concentration polarization appears near the ion-exchange layer. Accumulation of trace coions occurs because their advective and electromigration flow velocity components have opposite signs and are locally compensating in depletion regions where electric fields are high. This local compensation of flow components can give rise to high accumulation factors (>1000 in some cases) for trace coions at some distance from the interface between the nanoporous and ion-exchange layers. Moreover, the extent of this accumulation depends on the trace-coion diffusion coefficient. The resulting selectivity between different coions might serve as a basis for environmentally friendly separation of ionic species such as synthetic peptides or rare-earth elements. For example, a periodic process might include accumulation followed by species release into smaller volumes of solution. For both rare-earth ions and peptide-like species, the accumulation selectivity between ions with small differences in mobilities depends on system parameters such as nanoporous-layer thickness, distance between the perforations, and the zeta potential of the nanopore surface. Here, the use of optimal values of these membrane parameters may enable tuning of the electro-osmo-dialysis system for separation of specific ions. Modelling reveals that despite inhomogeneous patterns of fluid and ion flows close to the nanoporous/perforated ion-exchange interface, at relatively short distances from this interface (less than half the distance between the perforations) all the flows become practically one-dimensional (1D). Similarly, the concentration profiles of trace coions also become 1D. The flow one-dimensionality at short distances from the current-polarized interface enables a simple 1D approximation that is useful for an approximate analysis of trends in this multi-parameter system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗