Mass Exchange Rate Research Articles

The Role of Discrete Capillary Rings in Mass Transfer From the Surface of a Drying Capillary Porous Medium

The mass exchange between the surface of a model capillary porous medium and the adjacent gas-side boundary layer is studied in the limiting condition of isothermal, slow drying. In order to quantify the role and significance of liquid films in the mass exchange process, three-dimensional pore network Monte Carlo simulations are carried out systematically in the presence and absence of discrete capillary rings. The pore network simulations performed with capillary rings show a noticeable delay in transition from the capillary-supported regime to the diffusion-controlled regime. These simulation results differ significantly from the predictions of classical pore network models without liquid films, and they appear to be more consistent with the experiments conducted with real porous systems. As compared to classical pore network models, the pore network model with rings seems to predict favorably the spatiotemporal evolution of wet and dry patches at the medium surface as well as of their relative contributions to the net mass exchange rate. This is apparent when the analytical solution of the commonly used Schlünder’s model is examined against the numerical simulations conducted using classical and ring pore network models.

Photo-electric capacitive deionization enabled by solar-driven nano-ionics on the edges of plasma-made vertical graphenes

Unimpeded ion traffic in carbon materials with ionic selectivity remains a challenge in electrochemical energy storage and chemical purifications represented by capacitive deionization (CDI) of potable and industrial water. In this work, a new concept of solar nano-ionics is developed to directly feed solar energy into photocarriers and localized electric fields near the edges of graphene nanostructures that enable effective, mobility-based ion transport with high mass exchange rates and selectivity. This concept is applied to demonstrate the new approach for CDI, namely the photo-electric capacitive deionization (PECDI), enabled by the solar-enhanced ionic transport. Materialized by edge-enhanced vertical graphenes (eVG), the photocarriers are localized along the edge nano-antennas of eVG to boost the edge-localized electric fields by two orders of magnitude, as confirmed by near-field photo-induced force microscopy. The localized photo-electric fields control and restructure the nano-ionic flows leading to selective transport of ions with different mobility and dramatically enhanced kinetics, as validated by in situ electrochemical quartz crystal microbalance measurements and molecular dynamics simulations. With the photo-enhanced ionic transport kinetics, an average adsorption capacity of 33 mg g−1 at 200 mg L–1 (165 mg g−1 at 5000 mg L–1), a fast adsorption/desorption response and the impressive efficiency are achieved. This work opens a new avenue for solar-enhanced nano-ionic manipulation, which can be extended for a broad range of chemical engineering, energy, and environmental applications.

Thermosolutal natural convection across an inclined square enclosure partially filled with a porous medium

The present study is a numerical inspection of the natural convection with double diffusion in a tilted square cavity filled with a vertical bi-layered composed porous and an adjacent fluid. Isotropic and homogeneous porous layer is considered in this case study. The porous layer is saturated by an aqueous solution with a Prandtl number Pr = 7. The horizontal walls are considered impermeable and adiabatic, while uniform concentrations and temperatures are set on the vertical walls. The Thomas algorithm is employed to find a solution for the system of the governing equations. The divergence of the non-linear system is avoided by introducing under–relaxation factors. The effects of the various non-dimensional governing parameters namely the thickness of porous layer, Rayleigh number, buoyancy ratio, Lewis number, cavity inclination angle, and the thermal conductivity ratio on the thermo-solutal natural convection and the rate of mass and thermal exchange are highlighted and discussed. The predicted findings are given in terms of flow patterns, thermal fields, and iso-concentration lines. The variation of the velocity field, stream function, Sherwood number, and Nusselt number is also inspected. The numerical results show complex flow structure modifying the local transfer (Nusselt and Sherwood numbers).

Non-Fickian Solute Transport in Rough-Walled Fractures: The Effect of Contact Area

The influence of contact area, caused by normal deformation, on fluid flow and solute transport through three-dimensional (3D) rock fractures is investigated. Fracture surfaces with different Hurst exponents (H) were generated numerically using the modified successive random addition (SRA) method. By applying deformations normal to the fracture surface (Δu), a series of fracture models with different aperture distributions and contact area ratios (c) were simulated. The results show that the contact area between the two fracture surfaces increases and more void spaces are reduced as deformation (Δu) increases. The streamlines in the rough-walled fractures show that the contact areas result in preferential flow paths and fingering type transport. The non-Fickian characteristics of the “early arrival” and “long tail” in all of the breakthrough curves (BTCs) for fractures with different deformation (Δu) and Hurst parameters (H) were determined. The solute concentration distribution index (CDI), which quantifies the uniformity of the concentration distribution within the fracture, decreases exponential as deformation (Δu) and/or contact area ratios (c) increase, indicating that increased contact area can result in a larger delay rate of mass exchange between the immobile zone around the contact areas and the main flow channel, thus, resulting in a longer time for the solute to fill the entire fracture. The BTCs were analyzed using the continuous time random walk (CTRW) inverse model. The inverse modeling results show that the dispersion exponent β decreases from 1.92 to 0.81 as c increases and H decreases, suggesting that the increase in contact area and fracture surfaces enhance the magnitude of the non-Fickian transport.

Influence of strut on cavity at subsonic speeds: Ignition characteristics

In high-speed airflow, the use of cavity and struts in combination can improve fuel distribution and flame-stabilization, but may weaken the ignition performance. Herein, the lean ignition characteristics of several cavity–strut flame holders in a tandem turbine-based combined cycles combustor are experimentally investigated with the flow fields by using particle image velocimetry and high-speed chemiluminescence imaging techniques. Additionally, the effects of the strut structure parameters on the lean ignition performance in the cavity are studied. Experimental results indicate that changes in structural parameters have the opposite effects on the ignition performance and the flame-propagation performance. Reducing the strut inclination angle has a contrary function with the decrease in the cavity–strut space, which also transforms the flame-stabilizing mechanism between strut-stabilizing and cavity-stabilizing, accompanied by the flame morphology behind strut changes from no-flame to intermittent-flame, and finally continuous-flame. The lean ignition limit changes with the structure parameters, mainly due to the inverse change in the mass exchange rate and cavity residence time. Compared with the single cavity, the proper cavity–strut combined structure has a wider lean ignition limit at high subsonic speeds due to the advantage of simultaneously increasing the mass exchange rate and cavity residence time.

The Snowball Stratosphere

AbstractAccording to the Snowball Earth hypothesis, Earth has experienced periods of low‐latitude glaciation in its deep past. Prior studies have used general circulation models (GCMs) to examine the effects such an extreme climate state might have on the structure and dynamics of Earth's troposphere, but the behavior of the stratosphere has not been studied in detail. Understanding the snowball stratosphere is important for developing an accurate account of the Earth's radiative and chemical properties during these episodes. Here we conduct the first analysis of the stratospheric circulation of the Snowball Earth using ECHAM6 general circulation model simulations. In order to understand the factors contributing to the stratospheric circulation, we extend the Statistical Transformed Eulerian Mean framework. We find that the stratosphere during a snowball with prescribed modern ozone levels exhibits a weaker meridional overturning circulation, reduced wave activity, and stronger zonal jets and is extremely cold relative to modern conditions. Notably, the snowball stratosphere displays no sudden stratospheric warmings. Without ozone, the stratosphere displays a complete lack of polar vortex and even colder temperatures. We also explicitly quantify for the first time the cross‐tropopause mass exchange rate and stratospheric mixing efficiency during the snowball and show that our values do not change the constraints on CO2 inferred from geochemical proxies during the Marinoan glaciation (ca. 635 Ma), unless the O2 concentration during the snowball was orders of magnitude less than the CO2 concentration.

Numerical Analysis with Keller-Box Scheme for Stagnation Point Effect on Flow of Micropolar Nanofluid over an Inclined Surface

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor.

Ubiquitous ultra-depleted domains in Earth’s mantle

Partial melting of Earth’s mantle generates oceanic crust and leaves behind a chemically depleted residual mantle. The time-integrated composition of this chemically depleted mantle is generally inferred from basalts produced at mid-ocean ridges. However, isotopic differences between oceanic mantle rocks and mid-ocean ridge basalts suggest that mantle and basalt composition could differ. Here we measure neodymium isotope ratios in olivine-hosted melt inclusions from lavas of the Azores mantle plume. We find neodymium isotope ratios that include the highest values measured in basalts, and suggest that melts from ultra-depleted mantle contribute to the isotopic diversity of the erupted lavas. Ultra-depleted melts have exceedingly low preservation potential during magma extraction and evolution due to progressive mixing with melts that are enriched in incompatible elements. A notable contribution of ultra-depleted melts to the Azores mantle plume therefore implies that variably depleted mantle is the volumetrically dominant component of the Azores plume. We argue that variably depleted mantle, sometimes ranging to ultra-depleted compositions, may be a ubiquitous part of most ocean island and mid-ocean ridge basalt sources. If so, Earth’s mantle may be more depleted than previously thought, which has important implications for the rate of mass exchange between crust and mantle, plume dynamics and compositional stratification of Earth’s mantle. Depleted mantle is a volumetrically dominant component of the Azores plume and possibly of oceanic basalt sources more generally, according to neodymium isotope compositions of olivine-hosted melt inclusions from lavas of the Azores mantle plume.

Flow Structure in the Eclipsing Polar V808 Aur. Results of 3D Numerical Simulations

The structure of the flows in the eclipsing polar V808 Aur is studied. Comparison of computations with observed light curves is used to identify and clarify a number of features in the system, such as the drift of the hot spot—the place where the stream from the inner Lagrange point approaches the surface of the white dwarf, changes in the brightness in the secondary minimum, a dip in the light curve in the high state before entering the eclipse, the asymmetrical eclipse profile in high state, and others. A three-dimensional numerical MHD model based on the approximation of modified magnetic hydrodynamics is used in these studies. Numerical computations were carried out for several mass-exchange rates corresponding to different states of activity of the V808 Aur system. The computations show that, as the mass-exchange rate increases, the length of the ballistic part of the accretion stream increases, leading to changes in the spatial configuration of the flow and an appreciable drift of the region of energy release on the surface of the white dwarf (by up to 30° in longitude). These changes in the flow structure lead to effects in the light curve that are in good agreement with the available observations.

A D-type adsorption kinetic model for single system based on irreversible thermodynamics

The adsorption process is a highly efficient and widely applied fundamental technique in the field of Geo-environmental engineering. Most existing adsorption models are empirical or semi-empirical and lack a consistent and unified scientific theoretical basis. In this work, a new adsorption kinetic model with dispersion-type (D-type) has been proposed within the framework of irreversible thermodynamics for investigating the adsorption behavior of a single ionic species onto a solid adsorbent. Based on Ziegler’s maximal rate of dissipation, an expression for mass exchange rate was determined after a detailed theoretical deviation by defining the thermodynamic force and thermodynamic flow; and by formulating two dispersion-type free energy functions and a dispersion-type dissipation rate density function. The mass exchange rate expression was introduced into the mass balance equation as further validation of the D-type adsorption kinetic model for a single system. Comparing the adsorption process predicted by the presented model with the tested adsorption processes of Pb2+ and Cd2+ onto beidellite and Pb2+ on bentonite, the results reveal good agreement with experimental data. The D-type adsorption kinetic model could provide a correct description of the kinetics of adsorption process for single ionic species onto solid adsorbent.

Influence of struts on cavity at subsonic speeds: Flow characteristics

Cavity–strut combined flame holder is a promising choice for turbine-based combined cycle engines with its excellent fuel distribution and flame stabilization. In this paper, the effects of the strut structure parameters on the flow characteristics in the cavity were investigated by using particle image velocimetry and numerical simulation. Experimental and numerical results show that the struts induce complex three-dimensional flow patterns, which have a significant influence on the cavity transverse vortex. The relative position between the cavity and the strut influences the critical length-to-depth ratio of the open cavity reverting to the closed cavity. The mass exchange rate of the cavity decreases with the increase in the space between the cavity and the struts, while it increases with the strut inclination angle increases. The variation law of mean cavity residence time with the structure parameters is exactly opposite to that of the mass exchange rate. Compared with a single cavity, at a high subsonic speed, the cavity–strut combined structure has the advantage of increasing the mass exchange rate and cavity residence time simultaneously.

Multiscale roughness influence on conservative solute transport in self-affine fractures

In this article, the influence of multiscale roughness on transport of a conservative solute through a self-affine fracture was investigated. The fracture roughness was decomposed into two different scales (i.e., a small-scale stationary secondary roughness superimposed on a large-scale non-stationary primary roughness) by a wavelet analysis technique. The fluid flow in the single fracture was characterized by Forchheimer’s law and exhibited nonlinear flow features such as eddies and tortuous streamlines. The results indicated that the small-scale secondary roughness was primarily responsible for the nonlinear flow features. Numerical simulations of conservative solute transport showed non-Fickian transport characteristics (i.e., early arrivals and long tails) in breakthrough curves (BTCs) and in residence time distributions (RTDs) with and without consideration of the secondary roughness. Analysis of multiscale BTCs and RTDs showed that the small-scale secondary roughness played a significant role in enhancing the non-Fickian transport characteristics. Removing small-scale secondary roughness delayed the arrival time and shortened the tail. The peak concentrations in BTCs decreased as the secondary roughness was removed, implying that the secondary roughness could also enhance the solute dilution. Fitting the one-dimensional (1D) Fickian advection–dispersion equation (ADE) to the numerical BTCs resulted in considerable errors that decreased with the small-scale secondary roughness being removed. The 1D mobile-immobile model (MIM) provided a better fit to the numerical BTCs and inclusion of the small-scale secondary roughness in numerical simulations resulted in a decreasing MIM mobile domain fraction and an increasing mass exchange rate between immobile and mobile domains.

Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere.

Evaporation or condensation in the vicinity of the immobile (pinned) contact line in an atmosphere of some inert (noncondensable) gas is considered here in a partial wetting configuration. Such a problem is relevant to many situations, in particular to a drop or a liquid film drying in open air. The thermal effects are not important and the mass exchange rate is controlled by the vapor dynamics in the gas. By following previous works, we account for the weak coupling between the diffusion in the gas and flow in the liquid through the Kelvin effect. Such a problem is nonlocal because of the diffusion in the gas. For generality, we consider a geometry of a liquid wedge posed on a flat and homogeneous substrate surrounded by a gas phase with a diffusion boundary layer of uniform thickness [Formula: see text]. Similarly to the moving contact line problem, the phase change leads to the hydrodynamic contact line singularity. The asymptotic analysis of this problem is carried out for the liquid wedge of the length [Formula: see text]. Three asymptotic regions are identified: the microscopic one (in which the singularity is relaxed, in the present case with the Kelvin effect) and two intermediate regions. The Kelvin effect alone turns to be sufficient to relax the singularity. The scaling laws for the interface slope and mass evaporation/condensation flux in each region are discussed. It is found that the difference of the apparent contact angle (i.e., interface slope in the second intermediate region) and the equilibrium contact angle is inversely proportional to the square root of [Formula: see text] and square root of the microscopic length, whatever is the singularity relaxation mechanism.

The effect of washover geometry on sediment transport during inundation events

Storm-induced sediment transport across a barrier island can lead to vertical accretion and onshore migration of the barrier island. Many barrier islands either have high dunes that prevent inundation, or are so low-lying that they are inundated several times a year. The Wadden Islands in the Netherlands, Germany and Denmark typically have alongshore-varying topography, where high dunes alternate with low-lying washover openings. The effects of the geometry of the washover openings on hydrodynamics and sediment transport are still unknown and are the main focus of this research. First, we present data on width and for some cases also vertical elevation of bed level for all washover openings along the Wadden Islands. The mean width is 200 m but the actual width ranges from 35 to 1100 m, and the elevation is between 1.5 and 2.1 m above MSL. Further, we present results of an XBeach model study to investigate how the washover opening geometry affects sediment transport during storm-induced inundation. We identify two important effects of washover width: firstly, for narrow openings flow contraction is important, causing relatively larger sediment exchange rates per unit width; secondly, in a wider opening sediment is transported over a larger width, resulting in larger sediment mass exchange rates. Furthermore, the elevation of the washover opening is of high importance: washover openings that are 30 cm higher than the reference case significantly decrease currents and sediment transport across the island. Divergence of sediment transport occurs in the washover opening, which leads to erosional patterns. Landward from the opening, sediment transport converges which leads to depositional patterns. The pressure gradient between North Sea and Wadden Sea across the Wadden Islands is an important forcing parameter: higher water levels in the back-barrier reduce onshore-directed currents and sediment transport.

On the Thermal Explosion Theory of a Heterogeneous Liquid–Liquid System

In this paper, the regularities of a thermal explosion of a heterogeneous system consisting of two immiscible liquids have been studied. Each phase is a solution of A and B reagents. Reagent B is extracted into a solution of reagent A, where the bimolecular exothermic reaction A + B → Products takes place. It has been shown that an exothermic reaction (combustion regime) continues to proceed in the system at high mass-exchange rates between phases after a thermal explosion. As a result, the maximal temperature may significantly exceed the temperature of the thermal explosion. The critical value of the Semenov parameter decreases with an increase in the mass-exchange rate between phases. In the limited range of values of the distribution coefficient of reagent B between phases, the increase of this coefficient is also accompanied by a decrease in the critical value of the Semenov parameter. The concentration of reagent B in the initial phase decreases monotonically due to its extraction into another phase. However, the equilibrium of the extraction of reagent B can shift, due to the temperature dependence of the distribution coefficient during the reaction. Thus, the time dependence of the concentration of reagent B on may be more complex and can pass through a minimum.

Pore-scale insights into transport and mixing in steady-state two-phase flow in porous media

Hydrodynamic dispersion and mixing under two-phase flow can be found in many natural, industrial, and engineering processes such as the modified salinity water flooding (MSWF). In MSWF the injected water displaces the formation brine and will interact with the crude oil and rock to improve the oil recovery. We show throughout numerical simulations that access of the injection water to the available pore space is not homogeneous, even in homogeneous porous media, and it is controlled by the saturation topology and pore-scale velocity field.Under the steady-state two-phase flow in a homogeneous porous medium, the velocity field has a bimodal distribution. The bimodal distribution of pore-scale velocity dictates two different transport time scales spatially distributed over the stagnant and flowing regions at a given saturation topology. These distinctly different transport time scales lead to a non-Fickian transport, which cannot be captured using the conventional advection-dispersion equation.Using the volume-of-fluid method implemented in the OpenFOAM (ver. 4.0), we simulated pore-scale two-phase flow and the hydrodynamic transport at different saturations. We have investigated the impact of stagnant saturation and the tortuosity of flow pathways on the dispersion coefficient and the mass exchange rate - as the two major parameters controlling transport and mixing - under steady-state two-phase flow. At the Darcy scale, different theories such as the mobile-immobile (MIM) theory have been proposed to capture the non-Fickian transport and mixing in two-phase flow through porous media. Based on the simulation results, we assess the validity of the assumptions employed in MIM to define the stagnant saturation and mass exchange rate coefficient. The results of this research provide fresh insights into the potential impact of saturation topology on mixing between the modified salinity water and the formation brine under steady-state flow conditions, which has not been investigated and reported in the literature.

Comparison of Time Nonlocal Transport Models for Characterizing Non-Fickian Transport: From Mathematical Interpretation to Laboratory Application

Non-Fickian diffusion has been increasingly documented in hydrology and modeled by promising time nonlocal transport models. While previous studies showed that most of the time nonlocal models are identical with correlated parameters, fundamental challenges remain in real-world applications regarding model selection and parameter definition. This study compared three popular time nonlocal transport models, including the multi-rate mass transfer (MRMT) model, the continuous time random walk (CTRW) framework, and the tempered time fractional advection–dispersion equation (tt-fADE), by focusing on their physical interpretation and feasibility in capturing non-Fickian transport. Mathematical comparison showed that these models have both related parameters defining the memory function and other basic-transport parameters (i.e., velocity v and dispersion coefficient D) with different hydrogeologic interpretations. Laboratory column transport experiments and field tracer tests were then conducted, providing data for model applicability evaluation. Laboratory and field experiments exhibited breakthrough curves with non-Fickian characteristics, which were better represented by the tt-fADE and CTRW models than the traditional advection–dispersion equation. The best-fit velocity and dispersion coefficient, however, differ significantly between the tt-fADE and CTRW. Fitting exercises further revealed that the observed late-time breakthrough curves were heavier than the MRMT solutions with no more than two mass-exchange rates and lighter than the MRMT solutions with power-law distributed mass-exchange rates. Therefore, the time nonlocal models, where some parameters are correlated and exchangeable and the others have different values, differ mainly in their quantification of pre-asymptotic transport dynamics. In all models tested above, the tt-fADE model is attractive, considering its small fitting error and the reasonable velocity close to the measured flow rate.

On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension

We consider a sharp interface approach for the inviscid isothermal dynamics of compressible two-phase flow that accounts for phase transition and surface tension effects. Kinetic relations are frequently used to fix the mass exchange and entropy dissipation rate across the interface. The complete unidirectional dynamics can then be understood by solving generalized two-phase Riemann problems. We present new well-posedness theorems for the Riemann problem and corresponding computable Riemann solvers that cover quite general equations of state, metastable input data and curvature effects. The new Riemann solver is used to validate different kinetic relations on physically relevant problems including a comparison with experimental data. Riemann solvers are building blocks for many numerical schemes that are used to track interfaces in two-phase flow. It is shown that the new Riemann solver enables reliable and efficient computations for physical situations that could not be treated before.

Characterization of land surface energy fluxes in a tropical lowland rice paddy

A field experiment was conducted in 2015 to study the land surface energy fluxes from tropical lowland rice paddy in eastern India with an objective to determine the mass, momentum, and energy exchange rates between rice paddies and the atmosphere. All the land surface energy fluxes were measured by eddy covariance (EC) system (make Campbell Scientific) in dry season (DS, 1–125 Julian days), dry fallow (DF, 126–181 Julian days), wet season (WS, 182–324 Julian days), and wet fallow (WF, 325–365 Julian days). The rice was cultivated in dry season (January–May) and wet season (July–November) in low wet lands and the ground is kept fallow during the remainder of the year. Results showed that albedo varied from 0.09 to 0.24 and showed positive value from morning 6:00 h until evening 18:00 h. Mean soil temperature (Tg) was highest in DF, while the skin temperature (Ts) was highest in WS. Average Bowen ratio (B) ranged from 0.21 to 0.64 and large variation in B was observed during the fallow periods as compared to the cropping seasons. The magnitude of aerodynamic, canopy, and climatological resistances increased with the progress of cropping season and their magnitudes decreased during the end of both cropping seasons and found minimum during the fallow periods. At a constant vapor pressure deficit (VPD) at 0.16, 0.18, 0.15, and 0.43 kPa, latent heat flux (LE) initially increased, but later it tended to level off with an increase in VPD. The actual evapotranspiration (ETa) during both the cropping seasons was higher than the fallow period. This study can be used as a source of default values for many land surface energy fluxes which are required in various meteorological or air-quality models for rice paddies. A larger imbalance of energy was observed during the wet season as the energy is stored and perhaps advected in the fresh water.

Direct methods to calculate the mass exchange between solutes inside and outside aggregates in macroscopic model for solute transport in aggregated soil

Macroscopic modeling of solute transport in aggregated soil is often based on the dual-domain approach assuming that water flow occurs mainly in the inter-aggregates pores while the water inside the aggregates is stagnant; the solutes in the two waters can exchange driven by molecular diffusion. Since such a mass exchange is not measurable, practical modeling often uses pre-defined empirical memory functions to describe it with the parameters in the functions calculated by calibration against experimental measurement. It is hence difficult to verify that the calibrated memory functions correctly describe the mass exchange process or just to bridge the model and the measurements in that a shift from the experimental conditions could invalidate the model. Furthermore, most researches on such mass exchanges are for inert tracers, while most solutes in soil are reactive. How to link the mass exchange rates for inter tracer and reactive solutes is poorly studied. The purpose of this paper is to present direct methods to calculate the mass exchange rates for inert tracer and reactive solute using x-ray tomography and pore-scale simulations. Sample of an aggregated soil is scanned using x-ray micro-tomography by assuming, judged by visual observation in imaging the soil, that the sizes of the inter-aggregate pores are larger than 40 μm and using 40 μm as the resolution can separate the inter-aggregate pores from the aggregates. The aggregates are assumed to be permeable and their ability to conduct solute is described by an effective diffusion coefficient. We then numerically simulate the movement of both inert tracer and reactive solute from the inter-aggregate pores into the aggregates using pore-scale modeling. The simulated solute concentration in all voxels is sampled and then volumetrically averaged to calculate the average mass exchange rates between solute inside and outside the aggregates in the soil image. For reactive solute, we take nitrate as an example and analytically link its mass exchange rate to that for the inert tracer assuming that the nitrate reduction is a first-order kinetics. We also analytically establish the relationship between the mass exchange rates of solutes with different molecular diffusion coefficients, and verify this relationship against the results directly calculated from the pore-scale simulations. We additionally examine the accuracy of the commonly used empirical memory functions against those directly calculated from pore-scale simulations, finding that none of these functions can accurately describe the mass exchange process. To verify these directly- calculated mass exchange rates, we apply them to model the leaching of the inert tracer and the reactive nitrate in an aggregated soil column.