The stable, time-periodic flow between a porous injector disk and an impermeable substrate disk is explored for the case where fluid is injected into the gap region with a spatially uniform time-periodic velocity V(τ)=V0(1+α cos(στ)), where V0 is the mean injection velocity, α is the flow modulation amplitude, and σ is the flow modulation frequency. Fourier series expansions in time (τ) are combined with regular perturbation expansions of the Fourier coefficients in powers of α to describe the linear and nonlinear frequency dispersion in the system when 0<α<1. Generalized analytical expressions are obtained for the quasisteady response, and the method of matched asymptotic expansions is used to analyze the high frequency linear response of the system. Finite difference methods are used to calculate the frequency dispersion of the system for a wide range of modulation frequencies (σ) and Reynolds numbers. Oscillating harmonics are shown to interact destructively (via nonlinear inertial terms), resulting in the nullification of certain Fourier modes in the flow field. The Reynolds number and frequency dependence of harmonic nullification events are explored and their implications for creating multilayered alloys are briefly discussed.

We report on the dynamic response of limiting current when the uniform injection cell is subjected to large amplitude sinusoidal modulation of the electrolyte injection velocity. A general formalism for analyzing the linear and nonlinear system dynamics is used as the cornerstone of the theoretical and experimental work. Experimental measurements of the mean, linear, and lowest order nonlinear contributions to the modulated limiting current are found to agree reasonably well with theoretical predictions over the limited dynamic range achievable by the experimental apparatus. Theoretical results show that complicated nonlinear behavior arises from interactions between oscillating harmonics in the flow and concentration fields. For example, certain combinations of oscillation frequency, Reynolds number, and Schmidt number can create conditions where nonlinear harmonic interactions generate resonant or nullified response in specific nonlinear contributions to the limiting current. InfroductionRecently the steady-state characteristics and perfor-* Electrochemical Society Student Member.

The effect of the presence of an impurity species on the trapped particle turbulence is studied using the gyro-bounce kinetic code TERESA, which allows the study of Trapped Electron Modes and Trapped Ion Modes. The impurity species is treated self-consistently and its influence on the nature of the turbulence, ion driven or electron driven, is investigated. It is found that the presence of heavy impurities with a flat density profile tends to stabilize the both electron and ion modes, whereas a peaked or hollow impurity density profile can change the turbulence from an electron driven turbulence to an ion driven turbulence. The effect of the turbulence regime on impurity transport is studied.

In gyrokinetic simulations of turbulent impurity transport, trace impurity species are often treated as passive species, in the sense that they are not included in Maxwell equations. This is consistent with the assumption that impurities with low enough concentrations are impacted by turbulence generated by electrons and main ions, but do not impact it significantly in return. In this work, we relax this assumption, and investigate the active impacts of impurity on impurity transport as a function of its concentration, in the presence of trapped-particle-driven turbulence. We focus on W 40+ tungsten, which is relevant for modern tokamaks, and adopt a reduced gyrokinetic bounce-averaged model for trapped particles in a simplified tokamak geometry. The impacts depend on the relationship between equilibrium density gradient and temperature gradient. When these gradients are equal, we observe that tungsten can be treated as a passive species for concentrations below 2 × 10 −4. Above this concentration, the impurity significantly impacts both density and heat transport, essentially quenching them for concentrations above 10 −3. This quenching occurs as electric potential fluctuations become in phase with impurity density fluctuations.

The diffusive impurity transport as a function of the charge and mass numbers is investigated in an ion driven or an electron driven turbulence, in the limit of zero impurity temperature gradient. It is found that the impurity transport decreases slightly with increasing mass number, and depends much strongly on the charge number. Moreover, this transport depends on the nature of the instability that drives turbulence. The impurity flux due to Trapped Electron Mode (TEM) turbulence increases with the charge number Z. In contrast, it is found to decrease with Z in the Trapped Ion Mode (TIM) dominated. In order to explain these observations, the quasilinear flux is derived and is compared with results obtained from the nonlinear simulations. Quasi-linear theory qualitatively reproduces the gyro-kinetic numerical observations.

Presented is the theoretical characterization of an electrochemical cell that is uniformly accessible to mass transfer and exhibits a nearly uniform primary current distribution over most of the electrode. Conceptually, the cell consists of two parallel, coaxial disks of radius R with a gap between the disks of length L . One disk forms the working electrode, and the other disk is a porous surface through which electrolyte is assumed to be injected with a uniform axial velocity V . The aspect ratio of the gap between the disks false(L/2Rfalse) is small compared to unity. Analytic expressions analogous to the Levich equation are derived for the mass‐transfer‐limited current density as a function of the physical properties of the electrolyte, the injection velocity V , and the gap length L . The approximate analytic results are compared to numerical computations and are found to agree within 2% for typical operating conditions. The effect of gap aspect ratio on the primary current distribution is also explored. Numerical solutions show that the primary current distribution is flat over most of the electrode when the gap aspect ratio is much less than unity, but, because of the cell geometry, the local current density always becomes infinite at the electrode/insulator boundary.

In the context of temperature gradient-driven, collisionless trapped-ion modes in magnetic confinement fusion, we perform and analyse numerical simulations to explore the turbulent transport of density and heat, with a focus on the velocity dimension (without compromising the details in the real space). We adopt the bounce-averaged gyrokinetic code TERESA, which focuses on trapped particles dynamics and allows one to study low frequency phenomena at a reduced computational cost. We focus on a time in the simulation where the trapped-ion modes have just saturated in amplitude. We present the structure in velocity space of the fluxes. Both density and heat fluxes present a narrow (temperature-normalized energy width DE/T % 0.15) resonance peak with an amplitude high enough for resonant particles to contribute for 90% of the heat flux. We then compare these results obtained from a nonlinear simulation to the prediction from the quasi-linear theory and we find a qualitative agreement throughout the whole energy dimension: from thermal particles to high-energy particles. Quasi-linear theory over-predicts the fluxes by about 15%; however, this reasonable agreement is the result of a compensation between two larger errors of about 50%, both at the resonant energy and at the thermal energy.

The design and experimental characterization of a laboratory‐scale uniform injection cell (UIC) are presented. The experimental cell contains a disk electrode of radius R=0.5 normalcm embedded in the center of an insulating shroud. Parallel and coaxial with the disk electrode is an electrolyte injector consisting of a porous disk of radius R=0.5 normalcm that is also embedded in an insulating shroud. The counterelectrode is placed upstream of the porous disk injector. The thin gap between the parallel disks has a length L between 0.01 and 0.15 cm. Electrolyte is injected with a (nominally) uniform velocity Vfalse(0.03 normalcm/normals≤V≤7.2 normalcm/normalsfalse) into the gap between the disks. Convective mass transport in the UIC was investigated for Reynolds numbers false(normalRe=VL/vfalse) between 0.03 and 108 and was compared to theoretical predictions. Experimental results for low and intermediate flow rates agree with theory, but the highest‐flow‐rate data deviate somewhat. Measurements of the collection efficiency for a ring‐disk electrode placed in the UIC also agree with theory at low and intermediate flow rates, but deviate as the injection velocity exceeds 1.7 normalcm/normals . We suggest that the high‐flow‐rate deviations between theory and experiments may be due to nonuniform electrolyte injection.