Mean Concentration Gradient Research Articles

Effective diffusivity of sulfuric acid in Antarctic ice cores

Abstract. Deposition of sulfuric acid in ice cores is important both for understanding past volcanic activity and for synchronizing ice core timescales. Sulfuric acid has a low eutectic point, so it can potentially exist in liquid at grain boundaries and veins, accelerating chemical diffusion. A high effective diffusivity would allow post-depositional diffusion to obscure the climate history and the peak matching among older portions of ice cores. Here, we use records of sulfate from the European Project of Ice Coring in Antarctica (EPICA) Dome C (EDC) ice core to estimate the effective diffusivity of sulfuric acid in ice. We focus on EDC because multiple glacial–interglacial cycles are preserved, allowing analysis for long timescales and deposition in similar climates. We calculate the mean concentration gradient and the width of prominent volcanic events, and analyze the evolution of each with depth and age. We find the effective diffusivities for interglacial and glacial maximums to be 5±3×10-9 m2 a−1, an order of magnitude lower than a previous estimate derived from the Holocene portion of EDC (Barnes et al., 2003). The effective diffusivity may be even smaller if the bias from artificial smoothing from the sampling is accounted for. Effective diffusivity is not obviously affected by the ice temperature until about −10 ∘C, 3000 m depth, which is also where anomalous sulfate peaks begin to be observed (Traversi et al., 2009). Low effective diffusivity suggests that sulfuric acid is not readily diffusing in liquid-like veins in the upper portions of the Antarctic Ice Sheet and that records may be preserved in deep, old ice if the ice temperature remains well below the pressure melting point.

Solute Front Shear and Coalescence Control Concentration Gradient Dynamics in Porous Micromodel

AbstractIn subsurface environments, incomplete mixing at the pore scale limits reaction rates, rendering their prediction by Darcy‐scale models challenging. Such pore scale concentration gradients are enhanced by the deformation of solute fronts and decay under the action of molecular diffusion and solute filament merging. It is currently unclear how these processes govern concentration gradient dynamics under different flow rates. We measure experimentally pore scale concentrations in solute fronts transported in a two‐dimensional porous micromodel over an extensive range of flow rates. We demonstrate that pore‐scale shear flow increases concentration gradients up to a time predicted by the lamellar mixing theory in shear flow. However, the flow rate‐dependency of the mean concentration gradient at this so‐called mixing time is weaker than predicted theoretically, a discrepancy which we explain quantitatively by accounting for lamellae aggregation. These findings shed new light on the pore‐scale mechanisms driving mixing dynamics in porous media.

Dispersion in an array of buildings in stable and convective atmospheric conditions

Wind tunnel experiments were conducted to study the impact of atmospheric stratification on flow and dispersion within and over a regular array of rectangular buildings. Three stable and two convective incoming boundary layers were tested with a Richardson number ranging from −1.5 to 0.29. Dispersion measurements were carried using a fast response flame ionisation detector. The results show that the stratification effect on the plume width is significantly lower than the effect on the vertical profiles. Stable stratification did not affect the plume central axis inside the canopy, but in the unstable case the axis appeared to deviate from the neutral case direction. Above the canopy both stratification types caused an increase in the plume deflection angle compared to the neutral case. Measured mean concentrations in stable stratification were up to two times larger in the canopy compared to the neutral case, while in convective conditions they were to three times smaller. The proportionality between the vertical turbulent fluxes and the vertical mean concentration gradient was also confirmed in the stratified cases. The high-quality experimental data produced during this work may help developing new mathematical models and parametrisation for non-neutral stratified conditions, as well as validating existing and future numerical simulations.

Statistical theory of turbulent mass transfer in electrochemical systems

The paper presents an overview of the statistical theory of turbulent mass transfer in electrochemical systems and some new results which generalize the previously obtained relations for the flows of complex geometry. The developed theory does not use traditional semi-empirical hypotheses and analogies, but directly addresses to the solving of the critical for turbulent transfer the closure problem. The mathematical procedure for solving of the closure problem makes use of new equations for the correlations between concentration and velocity fluctuations in different space points and at different time moments; the dumping of turbulent pulsations in the viscous sublayer allows to neglect high order moments and obtain a closed equation for the turbulent mass flux. In general, the relation between the turbulent mass flux and the mean concentration gradient is non-local. Using available experimental information, the non-local equation for the turbulent mass flux is reduced to the traditional local one and the functional form of the turbulent diffusion coefficient is obtained. It is demonstrated that Reynolds analogy cannot been used for the prediction of the turbulent diffusivity. Applications of the developed theory to chemical engineering and to electrochemical flow diagnostics (prediction of flow characteristics using limiting diffusion current measurements) are discussed.

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.

0618 一定平均濃度勾配下の振動格子乱流中での濃度分布のウェーブレット解析(OS6-4 噴流,後流およびはく離流れ現象の探求と先端的応用,OS6 噴流,後流およびはく離流れ現象の探求と先端的応用)

0618 一定平均濃度勾配下の振動格子乱流中での濃度分布のウェーブレット解析(OS6-4 噴流,後流およびはく離流れ現象の探求と先端的応用,OS6 噴流,後流およびはく離流れ現象の探求と先端的応用)

Air Pollution Steady-State Advection-Diffusion Equation: The General Three-Dimensional Solution

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation as- suming turbulence parameterization for realistic physical scenarios. We present the general steady three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.

Electrodiffusiophoresis: Particle motion in electrolytes under direct current

Colloidal particles in electrolytes move in response to electric fields (electrophoresis) and salt concentration gradients (diffusiophoresis), and related flows also occur at fixed surfaces (electro-osmosis and diffusio-osmosis, respectively). In isolation, these electrokinetic phenomena are well understood, e.g., electrophoresis without far-field concentration gradients and diffusiophoresis without applied electric fields. When the electrolyte passes direct current, however, concentration gradients accompany the bulk electric field (concentration polarization) and the resulting particle motion, called “electrodiffusiophoresis,” involves a nonlinear combination of electrophoresis and diffusiophoresis, depending on ion transference numbers and particle properties. In this work, we analyze the electrodiffusiophoresis of spherical particles in the limit of thin double layers, neglecting surface conduction (Du⪡1) and convection (Pe⪡1), considering both nonpolarizable (fixed charge) and ideally polarizable (induced-charge) surfaces. Via asymptotic approximations and numerical solutions, we develop a physical picture to guide potential applications in electrochemical cells, such as analyte focusing, electrophoretic deposition, and microfluidic mixing near membranes or electrodes. By controlling the mean salt concentration, particle size, current, and concentration gradient, significant motion of particles (or fluid) is possible toward either electrode and toward high or low concentration.

Investigation of passive scalar mixing in a confined rectangular wake using simultaneous PIV and PLIF

A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system was employed to investigate the turbulent mixing in a confined liquid-phase rectangular-wake flow with a Reynolds number based on hydraulic diameter of 37,500 and a Schmidt number of 1250. The simultaneous velocity and concentration field data were analyzed for flow statistics such as turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schimdt number. The streamwise and transverse turbulent fluxes were found to be of the same magnitude. The turbulent flux vector was not aligned with the mean concentration gradient. The turbulent Schimdt number was about 0.8. The spatial correlations of turbulent fluxes and concentration fluctuations were evaluated. In the R u ′ ϕ ′ correlation field, there were a positive and a negative vertically oriented elliptical correlation region, which were symmetric around the basis point. The R v ′ ϕ ′ correlation region was a horizontally oriented ellipse with negative values of the correlation coefficient. The correlation field of R ϕ ′ ϕ ′ was also an ellipse with a horizontal major axis. The behavior of large-scale structures in both the velocity and concentration field was studied using linear stochastic estimation with a defined event of concentration fluctuation. Vortex streets were observed in the estimated velocity fields. The streamwise growth of the structure size increased linearly initially but then grew more slowly.

A semi-analytical solution for the three-dimensional advection–diffusion equation considering non-local turbulence closure

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection–diffusion equation. Moreover, large eddies are able to mix scalar quantities in a manner that is counter to the local gradient. In this work we present a semi-analytical solution for the three-dimensional steady-state advection–diffusion equation, considering non-local turbulence closure using the Generalized Integral Advection Diffusion Multilayer Technique (GIADMT). We report some examples of applications of the new solution for two different datasets and for a water tank experiment.

The flow across a street canyon of variable width—Part 2:: Scalar dispersion from a street level line source

As described in Part 1 [Simoëns et al., 2007. The flow across a street canyon of variable width—Part 1: kinematic description. Atmospheric Environment 41, 9002–9017] measurements have been made of the velocity field around and within the canyon formed by two obstacles placed on the wall of a turbulent boundary layer. Here in Part 2 measurements of the scalar dispersion of smoke released from a two-dimensional slot in the wall perpendicular to the mean flow and located parallel to and midway between these two square obstacles are presented. The Reynolds number of the boundary layer at the slot location without the obstacles in place was R θ ≈ 980 . Statistical properties of the concentration field and the scalar fluxes in the streamwise plane are reported here for canyon openings that have been chosen based on characteristics of the kinematic description. These opening widths, expressed as multiples of the obstacle height, are 1 h, 4 h and 8 h. The mean concentration field revealed that the much of the scalar is trapped on the leeward side of the upstream obstacle before some of it escapes the canyon and is entrained on the roof of the upstream obstacle. It then is spread downstream by the turbulence in the wake of this obstacle. Surprisingly, the root mean square (rms) concentration field reveals that high concentration fluctuations exist in a zone where velocity field turbulence is very low. Measured streamwise scalar fluxes were found to be negative above the obstacles, whereas they are mainly positive between the obstacles. The measured wall normal scalar fluxes have an inverse behavior. Within the canyon, the scalar fluxes are greatest in the region between the large primary vortex, evident in the kinematic field, and the secondary vortex located in the corner of the leeward side of the upstream obstacle. In the flow above the obstacle roofs the wake of the upstream obstacle seems to dominate the scalar transport. Between the obstacles in and above the canyon, the existence of intermittent and intense events appear to prevent the modelling of these fluxes with a simple mean concentration gradient model.

Multipoint correlations of concentration fluctuations in a turbulent passive scalar field

This study experimentally analyzes a turbulent passive scalar field using two-point and three-point correlation functions of the concentration fluctuations. The scalar field was created by the iso-kinetic release of a high Schmidt number dye into a fully developed turbulent boundary layer of an open channel flow. Concentration data at spatially separated measurement points were collected via the planar laser induced fluorescence (PLIF) technique. The current study complements previous research efforts by examining three-point correlations for several configurations in a turbulent shear flow. In the case of two streamwise-aligned points combined with one transversely separated point, contours of the three-point correlation function exhibit the symmetric properties reported in an earlier study of non-shear flow. In a second set of three-point configurations consisting of isosceles and collinear geometries, the influence of the orientation angle between the three-point configuration and the mean concentration gradient varies depending on the specified three-point geometry. The results also suggest that the scaling exponent in the inertial-convective regime is dependent on the injection length scale with weak dependence on the Reynolds number.

Effective macroscopic transport parameters between parallel plates with constant concentration boundaries

A macroscopic transport model is developed, following the Taylor shear dispersion analysis procedure, for a 2D laminar shear flow between parallel plates possessing a constant specified concentration. This idealized geometry models flow with contaminant dissolution at pore-scale in a contaminant source zone and flow in a rock fracture with dissolving walls. We upscale a macroscopic transient transport model with effective transport coefficients of mean velocity, macroscopic dispersion, and first-order mass transfer rate. To validate the macroscopic model the mean concentration, covariance, and wall concentration gradient are compared to the results of numerical simulations of the advection–diffusion equation and the Graetz solution. Results indicate that in the presence of local-scale variations and constant concentration boundaries, the upscaled mean velocity and macrodispersion coefficient differ from those of the Taylor–Aris dispersion, and the mass transfer flux described by the first-order mass transfer model is larger than the diffusive mass flux from the constant wall. In addition, the upscaled first-order mass transfer coefficient in the macroscopic model depends only on the plate gap and diffusion coefficient. Therefore, the upscaled first-order mass transfer coefficient is independent of the mean velocity and travel distance, leading to a constant pore-scale Sherwood number of 12. By contrast, the effective Sherwood number determined by the diffusive mass flux is a function of the Peclet number for small Peclet number, and approaches a constant of 10.3 for large Peclet number.

Simultaneous velocity and concentration field measurements of passive-scalar mixing in a confined rectangular jet

Simultaneous velocity and concentration fields in a confined liquid-phase rectangular jet with a Reynolds number based on the hydraulic diameter of 50,000 (or 10,000 based on the velocity difference between streams and the jet exit dimension) and a Schmidt number of 1,250 were obtained by means of a combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system. Data were collected at the jet exit and six further downstream locations. The velocity and concentration field data were analyzed for flow statistics such as turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schmidt number (Sc T ). The streamwise turbulent flux was found to be larger than the transverse turbulent flux, and the mean concentration gradient was not aligned with the turbulent flux vector. The average Sc T was found to vary both in streamwise and in cross stream directions and had a mean value around 0.8, a value consistent with the literature. Spatial correlation fields of turbulent fluxes and concentration were then determined. The R u′ϕ′ correlation was elliptical in shape with a major axis tilted downward with respect to the streamwise axis, whereas the R v′ϕ′ correlation was an ellipse with a major axis aligned with the cross-stream direction. Negative regions of R u′ϕ′ were observed in the outer streams, and these negatively correlated regions decayed with downstream distance and finally disappeared altogether. The R ϕ′ϕ′ correlation field was found to be an ellipse with the major axis inclined at about 45° with respect to the streamwise direction. Linear stochastic estimation was used to interpret spatial correlation data and to determine conditional flow structures. It is believed that a vortex street formed near the splitter plate is responsible for the negatively correlated region observed in the R u′ϕ′ spatial correlations of turbulent fluxes. A positive concentration fluctuation event was observed to correspond to a finger of nearly uniform concentration fluid reaching out into the outer stream, whereas a negative event corresponds to a pocket of nearly uniform fluid being entrained from the outer stream into the center jet region. Large-scale vortical structures were observed in the conditional velocity fields with an elliptical shape and a streamwise major axis. The growth of the structure size increased linearly initially but then grew more slowly as the flow transitioned toward channel flow.

An analytical solution of the advection-diffusion equation considering non-local turbulence closure

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Moreover, large eddies are able to mix scalar quantities in a manner that is counter to the local gradient. We present a general solution of a two-dimension steady state advection-diffusion equation, considering non-local turbulence closure using the General Integral Laplace Transform Technique. We show some examples of applications of the new solution with different vertical diffusion parameterisations.

On the small-scale statistics of turbulent mixing in electrochemical systems

Using the electrochemical method, measurements were made in a plane channel liquid flow, for which the Reynolds number (Re ≡ U ∗ a/ν, U is the mean velocity and a is the hydraulic diameter) is variable between 3000 and 40,000. The Schmidt number of the salt (here, ferri-ferrocyanide) diffusing in water is typically about 1400, consequently the diffusion layer is located inside the viscous sublayer (y+ < 0.5, where superscripts + denote quantities dimensionless with respect to wall variables). The scalar field fluctuations are maintained by a mean concentration gradient, imbedded in a strongly sheared velocity field. The skewness and flatness factors were used to investigate the concentration field in the near-vicinity of the wall (in terms of anisotropy and internal intermittency). Thus, the concentration PDFs are very nearly Gaussian, with a slight dissymmetry that diminishes with increasing Reynolds numbers. On the direction x parallel to the wall, the skewness factor of ∂c∂x is about 1, independently on the Reynolds number. This property is very similar to that of a Pr ∼ 1 passive scalar mixing in a sheared flow, already studied in the literature.

Comparação entre coeficientes de difusão derivados do espectro de energia turbulenta e coeficientes de difusão que dependem da razão entre os fluxos de entranhamento e os de superfície

Uma grande parte das pesquisas em dispersão turbulenta de contaminantes na Camada Limite Planetária (CLP) é relacionada com a especificação dos fluxos turbulentos de concentração. A aproximação para estes termos desconhecidos permite resolver a equação de difusão-advecção. O processo de especificação da parametrização dos fluxos turbulentos de concentração é conhecido como o problema de fechamento do transporte turbulento. O esquema matemático mais comum que conduz à uma solução da equação de difusão-advecção emprega coeficientes de difusão que relacionam os fluxos turbulentos de concentração ao gradiente da concentração média. Neste estudo, empregando-se um modelo Euleriano de dispersão e dados de concentração, coeficientes de difusão derivados do espectro de energia turbulenta e aqueles que dependem da razão entre o fluxo de entranhamento e o de superfície, serão usados na simulação do campo de concentração superficial.

Mixing of a passive scalar near a free surface

We study numerically and analytically the mixing of a passive scalar in turbulent shear flow with a free surface. The Navier–Stokes and scalar mixing equations are solved by direct numerical simulation. We find that the mean concentration of the scalar exhibits a two-layer structure near the free surface: an outer layer, characterized by a fast reduction in the value of the turbulent diffusivity of the scalar, and a much thinner inner layer characterized by a fast reduction of the mean concentration gradient. We develop a similarity theory for the variation of the mean concentration, which agrees very well with the numerical results and provides us with scaling relations for the thickness of each layer.

TURBULENT TRANSPORT OF A PASSIVE SCALAR FIELD

Several statistical theories of the transport of a passive scalar quantity make use of a Green's function and statistical properties of the fluid velocity field. The theories are applied to the problems of mean gradient transport in a turbulent fluid and of turbulent transport to a wall or a fluid interface. For the case of mass transfer by a uniform mean concentration gradient in homogeneous turbulence, a weak mixing hypothesis leads to results similar to those of Kraichnan's direct interaction approximation (D1A). Further use of a smoothing hypothesis leads to an algebraic expression for the eddy diffusivity which compares well with the DIA and with laboratory experiments.

Experimental analysis of pore-scale flow and transport in porous media

A novel, non-intrusive fluorescence imaging technique has been used to quantitatively measure the pore geometry, fluid velocity, and solute concentration within a saturated, three-dimensional porous medium. Discrete numerical averages of these quantities have been made over a representative volume of the medium and used to estimate macroscopic quantities that appear in conventional continuum models of flow and transport. The approach is meant to illustrate how microscopic information can be measured, averaged, and used to characterize medium-scale processes that are typically approximated constitutively. The experimental system consisted of a clear, cylindrical column packed with clear spherical beads and a refractive index-matched fluid seeded with fluorescent tracer particles and solute dye. By illuminating the fluid within the column with a scanning planar laser beam, details of flow and concentration within the pore spaces can be quantitatively observed, allowing for three-dimensional, dimensional, time dependent information to be obtained at good resolution. In time dependent information to be obtained at good resolution. In the current experiment, volumetrically averaged velocities and void-to-volume ratios are first compared with bulk measurements of fluid flux and medium porosity. Microscopic measurements of concentration are then used to construct cross-sectionally averaged profiles, mean breakthrough curves, and direct measurements of the dispersive flux, velocity variance, and concentration variance. In turn, the dispersive flux measurements are compared with mean concentration gradients to provide a basis for confirming the Fickian dispersion model and estimating dispersion coefficients for the medium. Coefficients determined in this manner are compared with others based upon traditional length-scale arguments, mean breakthrough analyses, and curve fits with numerical simulations.