Dimensionless Mass Transfer Coefficient Research Articles

Mass transfer from a sheared spherical rigid capsule

Solute mass transfer from a spherical fluid-filled rigid capsule subjected to shear flow is studied numerically, while considering unsteady, continuous, and nonuniform boundary conditions on its surface. Here, the capsule acts as a reservoir with its initially encapsulated solute concentration decaying over time. This scenario differs from the classical case study of either constant concentration or constant mass flux at the surface of the particle. The flow and the concentration field are computed using fully three-dimensional lattice Boltzmann simulations, where the fluid-structure two-way coupling is achieved by the immersed boundary method. The effects of the flow and the boundary conditions on mass transfer efficacy are quantified by the Sherwood number (the dimensionless mass transfer coefficient), which is found to increase due to the combined effects of forced convection and the rotation of the capsule. Having continuity of both the concentration and the mass flux on the capsule significantly decreases the Sherwood number as compared to the case with constant and uniform boundary condition. All the obtained results can be applied to heat transfer in the case of cooling an initially hot spherical particle, for which the concentration must be replaced by the temperature and the Sherwood number by the Nusselt number.

Unsteady mass transfer from a core-shell cylinder in crossflow

Mass transfer from a composite cylinder - made of an inner core and an outer enveloping semipermeable shell - under channel crossflow is studied numerically using two-dimensional lattice-Boltzmann simulations. The core is initially loaded with a solute that diffuses passively through the shell towards the fluid. The cylinder internal structure and the initial condition considered in this study differ and thus complement the classical studies dealing with homogeneous uncoated cylinders whose surfaces are sustained at either constant concentration or constant mass flux. Here, the cylinder acts as a reservoir endowed with a shell that controls the leakage rate of the encapsulated solute. The transition from steady to unsteady laminar flow regime, around the cylinder, alters the released solute spatial distribution and the mass transfer efficiency, which is characterized by the Sherwood number (the dimensionless mass transfer coefficient). Moreover, the reservoir involves unsteady and continuous boundary conditions, which lead to unsteady and nonuniform distribution of both the concentration and the mass flux at the cylinder surface. The effect of adding a coating shell is highlighted, for a given ratio of the cylinder diameter to the channel width, by extracting a correlation from the computed data set. This new correlation shows explicit dependency of the Sherwood number upon the shell solute permeability (the shell mass transfer coefficient).

Numerical simulations and modelling of mass transfer through random assemblies of catalyst particles: From dilute to dense reactive particulate regime

We study mass transfer through random assemblies of fixed spherical catalyst particles experiencing an external convective-diffusive fluid stream. Chemical species are transported through the array and are diffused from fluid to solid phase through particles surface. An internal first order irreversible chemical reaction takes place within the porous catalyst particles. We address the determination of mass transfer coefficient by performing direct numerical simulations with fully internal-external coupling using concentration and flux continuity boundary conditions at the solid-fluid interface. We derive a theoretical prediction of the profiles of cup-mixing concentration, average of mean surface and average of mean volume concentration of the particles along the height of the domain. The model for the dimensionless mass transfer coefficient (‘reactive’ Sherwood number) is accounting for the five dimensionless parameters that control the physics of the system: the Reynolds number Re, the Schmidt number Sc, the Damköhler number Da, the internal-to-external diffusion coefficient ratio γ and the solid volume fraction αs. We use a coupled Sharp Interface/ Discrete Lagrange Multiplier-Fictitious Domain Method (SIM-DLM/FD), thoroughly validated in our previous study (Sulaiman et al., 2019) to test the accuracy of the model over a wide range of dimensionless parameters and solid volume faction (from dilute αs=0.1 to dense regime αs=0.5). We show and discuss the limitations of the proposed model.

An experimental study of density-driven convection of fluid pairs with viscosity contrast in porous media

CO2 dissolution in saline water during aquifer sequestration causes natural convection because of the density difference between CO2-saturated brine and native brine. In this study, the convective fingers behavior during convection in porous media was visualized by magnetic resonance imaging (MRI). Four kinds of miscible fluid pairs were used as the equivalents of CO2-saturated brine and native brine. Images of finger development were obtained. There are two types of convective fingers that form vertically symmetrical shapes: downward fingers of the dense fluid and upward fingers of the light fluid. The typical stages of natural convection, finger appearance, finger propagation, new finger generation, and finger coalescence were observed in this study. We analyzed the effects of viscosity contrast variation on convective onset. It was found that the viscosity contrast affects not only the convection time but also the finger growth velocity. The dimensionless mass transfer coefficient is characterized by the Sherwood number. The Sherwood number has a power law relationship with the Rayleigh number, with the exponent being larger than 1 for fluid pairs with apparent viscosity contrast. Experimental results showed that a higher viscosity contrast of the fluid pair causes a viscosity increase in the transition zone, resulting in lower mobility of the fluids and retarding convective mixing. For fluid pairs with similar densities, a high viscosity contrast is not conducive to efficient mass transfer in the density-driven convection process.

Experimental and numerical study on the leaching of pesticides into the groundwater through a porous medium: Effects of transport parameters

Abstract This study aims to investigate, experimentally and numerically, the pesticide transport through the soil in unsaturated zone. The movement of pesticide is described with one dimensional model. The transport equation incorporates terms accounting for diffusion –convection, adsorption and reaction. The first objective of this work was to identifies the effects of the parameters transport such us; the dimensions first order degradation coefficient ( μ ), the peclet number ( ρ e ) and the dimensionless mass transfer coefficient (w). The evolution of pesticide concentration in function of depth and time was found by using the non-equilibrium transport model. The data obtained show the importance of the adsorbed concentration. The second objective is to find the relation between the concentration and the transport parameters because there is a difficulty of the analytical solution. The solution of the problem was carried out by a numerical approach by using the finite difference method and a Fortran program.

An experimental and theoretical investigation of pure carbon dioxide absorption in aqueous sodium hydroxide in glass millichannels

In this work, chemisorption experiments of pure CO2 (99% (v/v)) in different concentrations of sodium hydroxide solutions were carried out in a T-junction glass circular milli-channel in the slug flow regime. The absorption of the gas from the slug results in a shrinking of the slug as it moves along the channel. The rate of decrease of slug size and slug velocity are used to quantify the mass transfer rate. A lumped parameter model is developed to study the dissolution dynamics of CO2 slugs in the aqueous solution. The experimental data in this controlled study and the model developed are used to predict the liquid side volumetric mass transfer coefficient. The enhancement of mass transfer due to chemical reaction in the liquid phase is also quantified. The effect of various parameters like gas and liquid flow rates, concentration of NaOH on system behaviour is examined. An empirical correlation for dimensionless mass transfer coefficient is obtained from the experimental data which can be used to design absorption columns.

Stochastic Modeling of Turbulent Scalar Transport at Very High Schmidt Numbers

AbstractA stochastic modeling approach, the so‐called One‐Dimensional Turbulence (ODT), is used to study passive scalar transport in incompressible, fully‐developed, turbulent channel flows up to very high Schmidt numbers Sc = ν/Γ ∼ 104 (kinematic viscosity ν, scalar diffusivity Γ). Good agreement is obtained between ODT and Direct Numerical Simulation (DNS) results with respect to the mean, the fluctuation statistics, and the dimensionless mass transfer coefficient K+. ODT yields the mass transfer coefficient to become independent of the Reynolds number at high Schmidt numbers, which is similar to reference laboratory measurements and DNS. The present ODT results exhibit the power law K+ ∝ Sc−0.65 with a scaling exponent that is only slightly larger than in the reference laboratory measurements and DNS. The results obtained suggests that ODT can be a versatile tool for turbulent transport modeling in a wide range of physical parameters. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling slug flow and mass transfer in inclined pipes

An experimental and numerical study of the gas projectile mass transfer when moving in an inclined pipe has been carried out. The mathematical model is based on the smoothed particle hydrodynamics method and verified by experimental data. The dependence of the velocity of the gas projectile motion and effective dimensionless mass transfer coefficient on the pipe inclination angle has been found. The simulated and calculated from experimental data bubble profiles have been compared.

Effects of nanocarbon on the hydraulic parameters and the solute transport process for disturbed loessial soil

Due to its strong absorbability and significant specific surface area, the existence of nanocarbon in loessial soil could significantly affect the physical and chemical properties of the soil. The effects of nanocarbon on the hydraulic properties and solute transport parameters of the soil were investigated in this study. The soil water characteristic curves (SWCCs) were obtained using the centrifuge method in the loessial soil with various nanocarbon contents by weight (0, 0.1, 0.5, 0.7, and 1 %). Based on the soil columns experiment (5 cm in inner diameter and 20 cm in length), the saturated hydraulic conductivity (Ks) and the solute transport process for soil with different nanocarbon contents were also measured. The primary results were shown as follows: the water retention capacity increased with an increase in nanocarbon content, whereas the Ks value and the unsaturated hydraulic conductivity (K) decreased. The relationship between the Ks value and the nanocarbon content could be described by an exponential function. The Brooks–Corey and the van Genuchten models provided a good description of the SWCC of the disturbed loessial soil with various nanocarbon contents. Generally, the residual water content (θr) and the empirical parameter (α) increased with an increasing nanocarbon content, whereas the pore size distribution parameter (n) decreased. Application of nanocarbon in the soil could enhance available water capacity, and the obtained nanocarbon use amount was 0.746 % from the study. The classical convection–dispersion equation (CDE) and the mobile and immobile model (MIM) fitted the chloride transport process in the soil well. Furthermore, the average pore water velocity (v), the Peclet number (Pe), the retardation factor (R), the mobile water fraction (β), and the dimensionless mass transfer coefficient (ω) decreased, whereas the dispersion (λ) increased with the nanocarbon contents. In addition, ω could be expressed by a multiple regression equation related to the nanocarbon content and the v and β values.

Study of MHD Corrosion of RAFM Steel in Laminar and Turbulent PbLi Flows in a Wall-Normal Magnetic Field

The present study addresses corrosion of RAFM steel in the flowing eutectic alloy PbLi in a special case of the 1-D magnetohydrodynamic Hartmann flow, where the liquid metal flows in a wall-normal magnetic field. For this flow, the effect of a magnetic field on corrosion and transport of corrosion products are studied analytically, using a self-similar mass transfer model, and numerically. The results are presented in the form of the dimensionless mass transfer coefficient (the Sherwood number, Sh) as a function of dimensionless flow parameters, the Reynolds (Re) and the Hartmann (Ha) numbers. In turbulent flows, Sh decreases as Ha increases due to turbulence suppression by a magnetic field. In laminar flows, Sh slightly increases with the magnetic field due to formation of steep velocity gradients at the Hartmann wall. The obtained results are then applied to analysis of corrosion for a family of PbLi blankets.

Non-Darcy natural convection from a vertical plate with a uniform wall temperature and concentration in a doubly stratified porous medium

In this paper, non-similarity solutions for natural convection heat and mass transfer along a vertical plate with a uniform wall temperature and concentration in a doubly stratified porous medium saturated by a fluid are obtained. The Darcy–Forchheimer-based model is employed to describe the flow in the porous medium. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by using pseudo-similarity variables. The resulting system of nonlinear partial differential equations is then solved numerically by using the Keller-box method. The effects of the buoyancy parameter, Forchheimer number, and thermal and solutal stratification parameters on the dimensionless velocity, temperature, concentration, and heat and mass transfer coefficients are studied.

Statistical evaluation of a liquid desiccant dehumidification system using RSM and theoretical study based on the effectiveness NTU model

In the present study the performance of an air dehumidifier using lithium bromide (LiBr) as a desiccant was investigated. Response surface methodology (RSM) was used to assess individual and interactive effects of the six main factors (velocity, temperature and humidity of air, flow rate, temperature and concentration of desiccant) on dehumidification mass rate. A reduced quadratic statistical model was derived to predict dehumidification mass rate. The maximum dehumidification mass rate was obtained 0.154g/s under the optimal conditions of an air velocity of 4.1m/s, desiccant flow rate of 0.035kg/s, air humidity ratio of 0.0185kg/kg, desiccant concentration of 0.48kg/kg, air temperature of 29.5°C, and desiccant temperature of 21.8°C. The effectiveness number of transfer unit (NTU) model was employed to describe the coupled heat and mass transfer. The results of the model and the experimental data show good agreement. Dimensionless mass and heat transfer coefficients correlations are proposed; the average absolute differences between the predicted values and the experimental findings for Sh and Nu numbers were calculated as 2.14% and 5.27%, with the discrepancies mainly within ±9% and ±13%, respectively.

Numerical investigation of oxygen mass transfer in a helical-type artery bypass graft

Local oxygen lack in arterial walls (hypoxia) plays a very important role in the initiation, progression and development of intimal hyperplasia (IH) and thrombosis. Aiming to find out whether a helical-type artery bypass graft (ABG) is hypoxia beneficial, a numerical study was carried out to compare oxygen transport between a helical-type ABG and a conventional-type ABG. The dimensionless mass transfer coefficient (Sherwood number) was introduced to evaluate the oxygen mass transfer distribution and detailed oxygen wall flux was computed. The results show that the intrinsic geometry of a helical-type ABG resulted in improved hypoxia and the oxygen-depleted fluid located proximally to the occluded section as compared with that of a conventional-type ABG. However, benefits aside, distinct double low regions (low wall shear stress (WSS) and hypoxia) which might be most prone to IH and more localised and thicker boundary layer of oxygen-depleted fluid were observed at the helical-type ABG. This may explain why the helical flow plays a detrimental role at some locations in the human body. In addition, it was observed that although low WSS region was always accompanied with low oxygen supply, the oxygen transport rate did not adjust simultaneously with flow. The change in oxygen distribution usually lagged behind the flow change. A physiological WSS region may be associated with hypoxia condition. This study captured the qualitative trend of oxygen distribution in ABGs and the effect of helical geometry on reducing hypoxia, which is useful in the structural design of swirling flow vascular devices.

Role of aerosols in enhancing SVOC flux between air and indoor surfaces and its influence on exposure

Indoor surfaces play an important role in the transport of, and exposure to, semi-volatile organic compounds (SVOCs) in buildings. In this study, we develop a model that accounts for SVOC transport mediated by particles and find that, due to large gas-particle partition coefficients along with large differences in Brownian and gas diffusivities, SVOC transport across concentration boundary layers is significantly enhanced in the presence of particles. Two important dimensionless parameters, Bim,g and Bim,g/Bim,p, were identified: Bim,g is the ratio of 1) the characteristic time for the SVOC to transport across the concentration boundary layer to 2) the characteristic time for boundary layer to either be “swept” of SVOCs by particles or “saturated” by release of SVOCs from particles. This parameter can be regarded as a dimensionless mass transfer coefficient. Bim,g/Bim,p characterizes the SVOC mass associated with particles, relative to SVOCs in the gas-phase. Analysis on monodisperse particles shows that flux can be enhanced by as much as a factor of 5 over transport in the absence of particles, for a large particle/gas partition coefficient (log Kpart = 13), small particles (dp ∼ 0.1 μm) and a small free stream velocity (U∞ = 0.01 m s−1). As particle diameter decreases, flux enhancement tends to increase. However, as particles become very small (e.g., dp < 0.05 μm), flux enhancement for SVOCs with log Kpart = 13 decreases slightly. Particles larger than 2 μm do not significantly influence the flux. An exponential correlation is found to fit the results for polydisperse particles associated with typical indoor environments, cooking and smoking. Two illustrative examples are used to show that, 1) the timescale for di(2-ethylhexyl) phthalate (DEHP) to approach equilibrium between the gas and a surface is shortened from 3.0 years to 0.45 years; and 2) in the presence of particles, the gas-phase DEHP concentration and emission rate are predicted to be as much as 4 times higher by our model than that by prior model estimates. Particle mediated gas-phase transport of SVOCs can result an increase in occupant exposure by a factor of 4–10.

Overall mass transfer coefficients and controlling regimes in catalytic monoliths

It is well known that the performance of a catalytic monolith is bounded by two limits: the kinetic regime at low temperatures (or before ignition for the case of exothermic reactions) and the external mass transfer controlled regime at sufficiently high temperatures (or after ignition). The washcoat diffusional resistance can also be significant over an intermediate range of temperatures. The transition temperatures at which the controlling regime changes from kinetic to washcoat diffusion to external mass transfer depend on the various geometric properties of the monolith, flow properties, the catalyst loading and washcoat properties. We present analytical criteria for determining these transition temperatures. These are derived using the recently developed low-dimensional model and the concepts of internal and external mass transfer coefficients. The criteria are more general than those in the literature and are useful in analyzing the experimental data. Further, we present an explicit expression for the experimentally measurable dimensionless apparent mass transfer coefficient ( Sh app ) in terms of individual transfer coefficients in each phase. It is shown that Sh app can be lowered by orders of magnitude compared to the theoretical upper bound obtained in the limit of external mass transfer control. Low values of Sh app are obtained due to a small value of effective diffusivity in the washcoat, low catalyst loading or a reaction with low activation energy. The analytical criteria may be used for the design of monolith properties and experimental conditions so that the performance of the monolith approaches the upper limit defined by the external mass transfer controlled limit.

On the use of internal mass transfer coefficients in modeling of diffusion and reaction in catalytic monoliths

We utilize the recently developed concept of internal or intraphase mass transfer coefficient to simplify the problem of diffusion and reaction in more than one spatial dimension for a washcoated monolith of arbitrary shape. We determine the dependence of the dimensionless internal mass transfer coefficient (Shi) on washcoat and channel geometric shapes, reaction kinetics, catalyst loading and activity profile. It is also reasoned that the concept of intraphase transfer coefficient is more useful and fundamental than the classical effectiveness factor concept. The intraphase transfer coefficient can be combined with the traditional external mass transfer coefficient (She) to obtain an overall mass transfer coefficient (Shapp) which is an experimentally measurable quantity depending on various geometric and transport properties as well as kinetics. We present examples demonstrating the use of Shapp in obtaining accurate macro-scale low-dimensional models of catalytic reactors by solving the full 3-D convection–diffusion–reaction problem for a washcoated monolith and comparing the solution with that of the simplified model using the internal mass transfer coefficient concept.

Experimental and theoretical study of gas/solid mass transfer in metallic filters as supports for micro-structured catalysts

Commercial sintered metallic micro-fibers have been investigated in view of their adoption as enhanced catalyst carriers. The material herein studied has high porosity (86%) and very high interfacial area (22 400 m 2/m 3), thus appearing promising for application in fast, mass-transfer limited catalytic processes. It was catalytically activated by calcination and impregnation with Pt, and tested in the model reaction of CO oxidation. The observed activity was very high: at T>500 °C, under diffusional control, CO conversions in excess of 90% were achieved at space velocities in the order of 10 6 h −1. Dimensionless mass transfer coefficients extracted from these data, accounting also for axial dispersion, exhibited. However, negative deviations from those expected either for a single infinite cylinder or from extrapolation of previous correlations for open-celled foams at higher Reynolds numbers. According to an original and unifying theoretical approach herein proposed, such deviations are quantitatively explained by accounting for the limitations to boundary layer development due to the proximity of other fibers in the densely packed system. The key point is to assume a pseudo ordered locally parallel assembly of cylinders with average distance related to the fiber diameter and to the void fraction.

Mass transfer of a rising bubble in molten glass with instantaneous oxidation–reduction reaction

The mass transfer around a rising bubble has been studied within the field of glass melting processes. Due to the large value of liquid viscosity, creeping flow was used. The rising bubble is assumed to have a clean interface with a total mobility and the exact solution of Hadamard or Rybczynski was used to define the velocity field around the bubble. The mass transfer of oxygen in the soda–lime–silica glass melt where oxidation–reduction reactions of iron oxides occur is also described. The dimensionless mass transfer coefficient, Sherwood number, was determined as a function of the Péclet number based on the terminal rise velocity of the bubble. Two different techniques have been used: the first based on the boundary layer theory and the second using a finite element method. In order to take into account the oxidation–reduction reaction in a unified framework, a modified Péclet number has been defined as a function of two dimensionless numbers. The first is strongly linked to the equilibrium constant of the chemical reaction and the second is the glass saturation, defined as the ratio of oxygen concentration in the bulk to that at the bubble surface. The Sherwood number, taking into account the chemical reactions, increases with iron content as well as with glass reduction (i.e. small saturation level). From an application point of view, the determination of a modified Péclet number is important because it is possible to use a similar expression (determined without the reaction) by replacing the classical Péclet number by the modified one proposed herewithin.

Experimental investigation of convective mass/heat transfer in short minichannel at low Reynolds numbers

An experimental investigations of convective mass/heat transfer in short circular channel with small inner diameter at Re numbers ranging from 20 to 250 were performed. Mean values of convective mass transfer coefficients were measured using electrochemical technique – limiting current method. The results of dimensionless mass transfer coefficient Sh were compared with conventional theory. It was observed the increase of experimental Sh in compare with data from classical correlation relative to channels of conventional size. The heat transfer correlation was obtained on the basis of mass/heat transfer analogy. Chilton–Colburn analogy was applied. The effects were compared with the available literature experimental thermal balance results.

On the relationship between Aris and Sherwood numbers and friction and effectiveness factors

We present a general solution of the diffusion–reaction problem for linear kinetics and an expression for the effectiveness factor ( η ) in terms of the shape normalized Thiele modulus ( Φ ) for a catalyst particle of arbitrary shape and with an arbitrary activity profile. We also show that the Sherwood number ( Sh Ω ) or the dimensionless mass transfer coefficient between the interior of a particle or region (denoted by Ω ) and its boundary ( ∂ Ω ) is related to the effectiveness factor and Thiele modulus by η = 1 / ( 1 + Φ 2 / Sh Ω ) . Further, the coefficients in the expansion of η in terms of Φ (the Aris numbers, Ar i ) are related to the asymptotic Sherwood number ( Sh Ω ∞ ) obtained in the limit of slow reaction. We show that the curve Sh Ω versus Φ is universal for most common particle or channel geometric shapes and for the case of uniform activity is described by the two asymptotes Sh Ω = Sh Ω ∞ = 1 / Ar 1 for Φ ⪡ 1 and Sh Ω ≈ Φ for Φ ⪢ 1 . For two-dimensional ducts we show that the friction factor times Reynolds number ( fRe) is equal to 8 Sh Ω ∞ and provide a physical interpretation of this result. In the second part of this work, we derive low-dimensional models for solving multicomponent nonlinear diffusion–reaction problems using the concept of an internal mass transfer coefficient. We also present low-dimensional models for catalytic reactors using external and internal mass transfer coefficients. Finally, the Aris/Sherwood numbers are presented for some commonly used catalyst particles in packed-bed reactors and washcoat shapes in catalytic monoliths.