Concentration Boundary Layer Research Articles

Modeling interfacial mass transfer driven bubble growth in supersaturated solutions

A commonly encountered phenomenon in chemical processes is bubble evolution driven by supersaturation. On the continuum scale, this essentially involves interfacial mass transfer resulting in the growth of bubbles and their subsequent detachment from a surface. Analytical approaches to study this phenomenon typically involve estimating the driving force for interfacial mass transfer based on Sherwood number (Sh) correlations and the bulk concentration of dissolved gas. This is often not practical since the bulk concentration is often unknown and Sh correlations are sometimes not available to provide an accurate description of the associated flow fields. With the use of interface-resolved simulations to model these processes, the local distribution of dissolved gas can be obtained by solving for the concentration field. The driving force for interfacial mass transfer can be computed based on Sh correlations (which can be adopted for specific flows and are typically used in “engineering” applications) or the universally applicable Fick’s first law. This paper compares the predictions of these approaches for the well-studied case of a two-dimensional bubble growing in an unbounded supersaturated solution for three different levels of supersaturation. The equivalent two-dimensional simulations are run in a previously developed volume of fluid framework on OpenFOAM® [K. J. Vachaparambil and K. E. Einarsrud, Appl. Math. Model. 81, 690–710 (2020)]. The results show that the choice of an appropriate Sh correlation can provide a reasonable estimate of bubble growth. In a more universal approach, which is relevant when the flow being simulated cannot be captured by a single Sh correlation (e.g., bubble growth/coalescence and detachment) or when existing Sh correlations are not applicable, Fick’s first law can be used to compute the driving force for bubble growth, provided that the concentration boundary layer can be resolved.

Evaluation of the Global S-Entropy Production in Membrane Transport of Aqueous Solutions of Hydrochloric Acid and Ammonia.

The results of experimental studies of volume osmotic fluxes () and fluxes of dissolved substances () in a system containing a synthetic Nephrophan® membrane (Orwo VEB Filmfabrik, Wolfen, Germany) set in a horizontal plane are presented. The membrane separated water and aqueous HCl or ammonia solutions or aqueous ammonia and HCl solutions. It was found that for the homogeneity conditions of the solutions and depend only on the concentration and composition of the solutions. For concentration polarization conditions (where concentration boundary layers are created on both sides), and depend on both the concentration and composition of the solutions and the configuration of the membrane system. The obtained results of the and flux studies were used to assess the global production of entropy for the conditions of homogeneity of solutions (), while and —to assess the global production of entropy for concentration polarization conditions ). In addition, the diffusion-convective effects and the convection effect in the global source of entropy were calculated. The concentration polarization coefficient was related to modified concentration Rayleigh number, e.g., the parameter controlling the transition from non-convective (diffusive) to convective state. This number acts as a switch between two states of the concentration field: convective (with a higher entropy source value) and non-convective (with a lower entropy source value). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.

Performance of a forward osmosis mass exchanger based on detailed mass transfer boundary layer analysis

Forward osmosis-based processes are low energy separation technology that can help in the recovery of fresh water. The design of such systems is approximated either from the simple mass conservations or using the analogy of heat exchanger design correlations. Such relationship has serious drawbacks, particularly at high recoveries, when the impact of mass transfer boundary layer is paramount. Unlike the reverse osmosis, the permeate flux (hence the recovery) is reduced with the convection (Peclet number, Pe). The membrane surface concentration and the thickness of concentration boundary layer on the draw side decreases with Pe. Since, permeate flux increases with the surface concentration, the recovery is dependent on Pe. Besides the relative concentration and flow-rates, the membrane area is influenced by the mass transfer boundary layer, manifested through Pe. The results reported in the Mondal and Field (2018) is a special case when Pe ≪ 1 (negligible convection), leading to maximum recovery. We evaluate the required membrane area and the performance of the forward-osmosis system as a function of the operating conditions, including the Pe. We have identified the range of operating conditions, for which the sizing of FO system is underpredicted in the case of negligible convection and the log-mean concentration difference.

Fluid flow effects on diffusion layer and current density for electrochemical systems

The effects of flow field upon the distribution of ionic concentration, electric potential, concentration boundary layer thickness, and electric current density were investigated. A modified numerical scheme is proposed to simulate the corresponding electrochemical system which is governed by nonlinear partial differential equations. Seven types of geometries and various flow fields with Reynolds numbers up to 2100 are considered. The obtained results indicate the current numerical method can successfully simulate the increase of current density on the cathode as the applied potential cell increases, and that rise will continue until the limiting current density is reached. To predict the effect of fluid flow, the proposed scheme is applied for various Peclet numbers. The increase of current density for Peclet numbers between 1 and 104 is quite evident. But for large Peclet numbers between 104 and 107, the current density increases gradually. The results also show that as the anode size is doubled, the maximum current density occurs at the leading and trailing edges. However, if the cathode size is doubled, the maximum current density occurs at the center regions of it. Knowing the regions where current density is extremum helps electochemical system designers to control the parameters of the corresponding process.

Emissions and Marine Boundary Layer Concentrations of Unregulated Chlorocarbons Measured at Cape Point, South Africa.

Unregulated chlorocarbons, here defined as dichloromethane (CH2Cl2), perchloroethene (C2Cl4), chloroform (CHCl3), and methyl chloride (CH3Cl), are gases not regulated by the Montreal Protocol. While CH3Cl is the largest contributor of atmospheric chlorine, recent studies have shown that growth in emissions of the less abundant chlorocarbons could pose a significant threat to the recovery of the ozone layer. Despite this, there remain many regions for which no atmospheric monitoring exists, leaving gaps in our understanding of global emissions. Here, we report on a new time series of chlorocarbon measurements from Cape Point, South Africa for 2017, which represent the first published high-frequency measurements of these gases from Africa. For CH2Cl2 and C2Cl4, the majority of mole fraction enhancements were observed from the north, consistent with anthropogenically modified air from Cape Town, while for CHCl3 and CH3Cl, we found evidence for both oceanic and terrestrial sources. Using an inverse method, we estimated emissions for south-western South Africa (SWSA). For each chlorocarbon, SWSA accounted for less than 1% of global emissions. For CH2Cl2 and C2Cl4, we extrapolated using population statistics and found South African emissions of 8.9 (7.4-10.4) Gg yr-1 and 0.80 (0.64-1.04) Gg yr-1, respectively.

Flammability and critical parameters at low oxygen extinction limit of stagnation-point diffusion flames with varied stretch rates

Recently, to simulate microgravity flames in a terrestrial environment, low stretched stagnation-point diffusion flames have aroused wide interest, while the extinction behaviors of varied stretched flames at reduced oxygen concentration were scarcely investigated. This issue was accomplished by an investigation in this paper. Firstly, local and total extinction modes with ‘U’-shape boundaries were found to enlarge the unstable area in the flammability map. Furthermore, gas-phase radiation inversely proportional to stretch rate contributed to decreased critical flame temperature with dropped stretch rate. Two different power laws of critical flame standoff distance versus stretch rate existed at quenching and blowoff due to the coupling effects of boundary layer and critical oxygen concentration. Surface energy balance to evaluate the mechanisms of quenching and blowoff demonstrated that, both solid-phase conduction and surface radiation dominated at quenching, while they can be ignored at blowoff. Finally, critical burning rate was obtained from the surface energy balance and found to decrease with declined stretch rate. The similar changing tendencies of flammability and burning characteristics versus stretch rate in this work to the microgravity results implied a low-cost earth-based research method to simulate microgravity flames, and some new findings can provide instructions for fire protection in space.

Role of Variable Conductance on Heat and Mass Transport Mechanism Using Generalized Theory

Abstract Fourier law of heat conduction, its analog Fick's first law, and Newton's law of viscosity are classical laws that are not capable of exhibiting memory effects. Conservation laws based on these classical laws do not give predictions about memory effects on the transport phenomena. Recently, proposed novel laws are called Cattaneo–Christov heat flux. Models are based on the generalization of classical laws of heat conduction, mass diffusion, and Newton's law of viscosity. This investigation considers this generalized theory to model the impact of relaxation phenomenon on the transport of momentum, heat, and mass in Maxwell fluid (viscoelastic fluid) of temperature-dependent viscosity and thermal conductivity in the presence of temperature-dependent mass diffusion coefficients. It is observed from the simulations that memory effects play a key role in controlling momentum, thermal and concentration boundary layer thicknesses. It is also noted that the rate of diffusion of heat and mass has shown an increasing trend when thermal conductivity and mass diffusion coefficients are increased via rise in temperature of the fluid. The generative chemical reaction on the transport of specie relative to the impact on the transport of specie when it is compared with the impact of destructive chemical reaction on the transport of specie.

Numerical Simulation of Carbon Dioxide Absorption by Monoethanolamine Solution with Super Mini Ring Contactor

Carbon capture storage provides an alternative to reducing global warming. In order to reduce the cost of carbon capture storage, high mass transfer packings for CO2 absorption from flue gas is an alternative. The study modeled and numerically simulated CO2 absorption by monoethanolamine solution with super mini ring contactor. The model considered the effect of the mass and momentum transfers, as well the chemical reaction. The simulation results show that the driving force of the reactive absorption is higher than the ordinary absorption in term of the low concentration of CO2 in the liquid phase. The CO2 concentration in the bulk gas is approximately 7.56 mol/m3. It decreases to around 5.75 mol/m3 after crossing the concentration boundary layer.

Numerical simulation and evaluation of spacer-filled direct contact membrane distillation module

Membrane fouling and temperature polarization are the most common issues that cause limitations to membrane distillation (MD) process. Integration of spacers has been proven to resolve those problems by inducing regions of turbulence and giving the required mechanical support to the membrane. In this work, a robust high-fidelity computational fluid dynamics simulation is carried out to assess and quantify the performance of spacer-filled DCMD module and compare it with a baseline spacer-free DCMD module. Mainly, simulations are done to delineate the problem of concentration polarization and by alternating spacers material with different thermal conductivities and different displacement configurations. The performance of these different models is demonstrated in terms of concentration boundary layer development, temperature distributions, temperature polarization coefficient (TPC), mass flux, heat flux, heat transfer coefficient, and thermal efficiency. Results show that concentration polarization can penalize mass flux by nearly 10%, and conductive spacers have favorable effect on the DCMD performance compared to spacer-free in terms of TPC by 50%, mass flux by 35%, heat flux by 31%, thermal efficiency by 1%, and top and bottom membrane surface heat transfer coefficients of, respectively, 19% and 62%. Meanwhile, the stride of the spacers in the range of 1.5–3.5 mm tends to achieve a measurable mass flux. Generally, spacers integration has confirmed the capability of reducing concentration polarization at the membrane surface. These attained improvements will accelerate industrial deployments of MD.

The dependence of evaporation and crystallization kinetics on dynamic and thermal background

AbstractIn technical problems there is often the need to simultaneously describe both non‐stationary evaporation and non‐stationary crystallization of droplets and films. Poor wettability of the wall and high heat fluxes lead to the film rupture and the formation of pools, dry spots, droplets. To date, there are no well‐developed methods for calculating crystallization and evaporation in the presence of the factors. Evaporation and crystallization of a drop are shown to fundamentally differ from those of a thin layer. The rate of evaporation prior to crystallization controls the crystallization kinetics. The evaporation and crystallization rates for the film (under identical conditions) are significantly higher than for the drop. The difference in the thickness of the diffusion and dynamic boundary layers affects the evaporation rate of an aquatic salt solution. For correct simulation of evaporation, it is necessary to take into account the thicknesses of the thermal, diffusion and concentration boundary layers.

The Role of Gravity in the Evolution of the Concentration Field in the Electrochemical Membrane Cell

The subject of the study was the osmotic volume transport of aqueous CuSO4 and/or ethanol solutions through a selective cellulose acetate membrane (Nephrophan). The effect of concentration of solution components, concentration polarization of solutions and configuration of the membrane system on the value of the volume osmotic flux ( in a single-membrane system in which the polymer membrane located in the horizontal plane was examined. The investigations were carried out under mechanical stirring conditions of the solutions and after it was turned off. Based on the obtained measurement results , the effects of concentration polarization, convection polarization, asymmetry and amplification of the volume osmotic flux and the thickness of the concentration boundary layers were calculated. Osmotic entropy production was also calculated for solution homogeneity and concentration polarization conditions. Using the thickness of the concentration boundary layers, critical values of the Rayleigh concentration number (), i.e., the switch, were estimated between two states: convective (with higher ) and non-convective (with lower ). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.

Computational Analysis for Unsteady and Steady Magnetohydrodynamic Radiating Nano Fluid Flow past a Slippery Stretching Sheet Immersed in a Permeable Medium

This work gives an account of unsteady and steady radiating magnetohydrodynamics (MHD) nanofluid flow over a slippery stretching sheet embedded in a porous medium. A widely used similarity variables of such flows reduces a governing partial differential equations (PDEs) into a new set of partial differential equations (PDEs) in which a dependent variable is a function of two independent variables rather than three. At the same time, third order PDEs are converted into a second order PDEs by defining a new variable wherever it is deemed necessary. For the time integration, we perform first order explicit Euler method and spatial derivatives are approximated by the finite difference formulas in the context of node-centered finite volume method. It is revealed that for the unsteady flow the temperature of the nanofluid is higher near the surface without thermophoresis parameter Nt and reduced significantly when Nt is present. We also show that the concentration boundary layer thickness decreases with an increase of Darcy number Da.

MHD slip flow and convective heat transfer due to a moving plate with effects of variable viscosity and thermal conductivity

PurposeThe steady two-dimensional laminar boundary layer flow, heat and mass transfer over a flat plate with convective surface heat flux was considered. The governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations and then solved numerically by Runge–Kutta method with the most efficient shooting technique. Then, the effect of variable viscosity and variable thermal conductivity on the fluid flow with thermal radiation effects and viscous dissipation was studied. Velocity, temperature and concentration profiles respectively were plotted for various values of pertinent parameters. It was found that the momentum slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the momentum slip.Design/methodology/approachNumerical Solution is applied to find the solution of the boundary value problem.FindingsVelocity, heat transfer analysis is done with comparing earlier results for some standard cases.Originality/value100

A computational study of burning of vertically oriented leaves with various fuel moisture contents by upward convective heating

Pyrolysis and combustion of a solid fuel representing a vertically oriented leaf of manzanita (Arctostaphylos glandulosa) were computationally investigated. Various fuel moisture content (FMC) values corresponding to four manzanita leaf treatments studied experimentally by others, were considered. The fuel was exposed to an upward stream of hot gases in a computational configuration resembling the experimental setup where leaves were burned. Time evolution of the normalized mass of the leaves was used to validate the simulations against the experimental data. Examining the time history of heat release rate confirmed that increasing FMC delays ignition time. The ignition times in simulations were in good agreement with those determined by empirical correlations for all FMCs. The burnout times were somewhat shorter in simulations than the empirically-determined ones. Simulations showed that thermal, momentum and concentration boundary layers are formed on the leaf faces. The boundary layers played a significant role in heating, and subsequent moisture evaporation and pyrolysis of the leaves. Within the leaves, an evaporation front propagating inward from the edges, was detected. A considerable amount of liquid moisture remained in the leaf after ignition. Accumulation of water and fuel vapor around the leaf, as a consequence of the leaf moisture evaporation and pyrolysis, displaced oxygen, decreasing the oxygen concentration therein. A post ignition time was characterized by a high temperature zone around the leaf. At such times, oxygen consumption by gas phase combustion resulted in a noticeable decrease in oxygen concentration around the leaf. The flaming pattern after ignition was qualitatively in agreement with previously reported experimental observations.

Numerical study on the moisture transfer characteristics of membrane-based liquid desiccant dehumidifiers: Resistance distribution and concentration polarization

Membrane-based liquid desiccant dehumidifiers have received increasing attentions due to their main advantage of preventing liquid carryover in air handling process, but the low dehumidification efficiency limits their further applications. The underlying mechanism of their moisture transfer deterioration is not entirely clear yet, and further efforts are needed to effectively identify and reduce the mass transfer resistances in the dehumidification process. In this work, considering impressionable transmembrane permeation flux, the resistance distribution of moisture transfer in the quasi-counter flow flat-plate membrane-based liquid desiccant dehumidifier is studied by a three-dimensional conjugate heat and mass transfer model. The velocity, temperature and concentration fields in dehumidifying process are analyzed in baseline condition, especially on the membrane surfaces. Analogy to a thermal circuit, the normalized moisture transfer resistances through gaseous, solid and liquid phases are defined to describe their relative importance. Causes of these normalized resistances in variable conditions are analyzed in terms of concentration polarization and boundary layer theory. Furthermore, the resistance variation is compared with the latent effectiveness, to reveal their inherent relation. The results suggest that moisture transfer resistances are mostly originated from the membrane and air side, and thus dehumidifying enhancement is more likely to emerge from the air-side concentration polarization alleviation in synergy with the appropriate improvement of membrane porosity. Among all operating parameters, the air inlet temperature and solution flow rate have relatively limited effect on the total resistance, while increasing solution concentration, followed by decreasing solution temperature, can significantly reduce the moisture transfer resistances at a nondecreasing latent effectiveness. In addition, the latent effectiveness shows a similar variation tendency to that of the air-side moisture transfer resistance, but it cannot reflect the total resistance variation. These results can help researchers and designers make decisions on where and how to improve the performance of membrane-based liquid desiccant dehumidifiers.

Flow analysis of biconvective heat and mass transfer of two-dimensional couple stress fluid over a paraboloid of revolution

In this paper, two-dimensional non-Newtonian couple stress fluid flow over the upper horizontal surface of a paraboloid (uhsp) (shaped like a submarine or any aerodynamical automobile) is investigated. At the freestream, a stretching of the fluid layer is assumed along with catalytic surface reaction which tends to induce the flow in the fluid-saturated domain. The problem is modeled by engaging laws of conservation for mass, momentum, heat and concentration. Velocity components are converted to stream functions and similarity transformations to reduce the dependent and independent variables in the partial differential equation describing the flow. Stream functions ideally satisfy continuity equation and transformation to reduce the PDEs to the system of coupled nonlinear ODEs. The numerical solution of these equations is obtained using the shooting-RKF method. The graphical results show that both the lateral and horizontal velocities decrease by increasing the couple stress material parameter and cause the temperature to rise. The thermal boundary layer decreases subject to the thickness parameter and has appositive effects on concentration boundary layer. Finally, numerical results have also been tabulated.

Variable viscosity and thermal conductivity effects on Williamson fluid flow over a slendering stretching sheet

PurposeThe purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in the presence of radiation and chemical reaction. All pertinent flow parameters are discussed and their influence on the hydrodynamics, thermal and concentration boundary layer are presented with the aid of the diagram.Design/methodology/approachThe governing partial differential equations are reduced into a system of ordinary differential equations with the help of suitable similarity variables. A discrete version of the homotopy analysis method (HAM) called the spectral homotopy analysis method (SHAM) was used to solve the transformed equations. SHAM is efficient, and it converges faster than the HAM. The SHAM provides flexibility when solving linear ordinary differential equations with the use of the Chebyshev spectral collocation method.FindingsThe findings revealed that an increase in the variable thermal conductivity hike the temperature and the thermal boundary layer thickness, whereas the reverse is the case for velocity close to the wall.Originality/valueThe uniqueness of this paper is the exploration of combined effects of heat and mass transfer on MHD Williamson fluid flow over a slendering stretching sheet. The Williamson fluid term in the momentum equation is expressed as a linear function and the viscosity and thermal conductivity are considered to vary in the boundary layer.

Finite Element Analysis of Variable Viscosity Impact on MHD Flow and Heat Transfer of Nanofluid Using the Cattaneo–Christov Model

In this mathematical study, magnetohydrodynamic, time-independent nanofluid flow over a stretching sheet by using the Cattaneo–Christov heat flux model is inspected. The impact of the thermal, solutal boundary and gravitational body forces with the effect of double stratification on the mass flow and heat transfer phenomena is also observed. The temperature-dependent viscosity impact on heat transfer through a moving sheet with capricious heat generation in nanofluids have studied, and the viscosity of the fluid is presumed to deviate as the inverse function of temperature. With the appropriate transformations, the system of partial differential equations is transformed into a system of nonlinear ordinary differential equations. By applying the variational finite element method, the transformed system of equations is solved. The properties of the several parameters for buoyancy, velocity, temperature, stratification, and Brownian motion parameters have examined. The enhancement in the concentration and thermal boundary layer thickness of the nanofluid sheet due to the increment in the viscosity parameter, also increased the temperature and concentration of nanoparticles. Moreover, the fluid temperature declined with the increasing values of thermal relaxation parameter. This displays that the Cattaneo–Christov heat flux model provides a better assessment of temperature distribution. Moreover, confirmation of the code and precision of the numerical method has inveterate with the valuation of the presented results with previous studies.

Optimization of heat transfer properties on ferrofluid flow over a stretching sheet in the presence of static magnetic field

The main emphasis of the present research is to investigate the composite effects of magnetization force and rotational viscosity on two-dimensional ferrohydrodynamic non-conducting nanofluid flow over a stretching sheet under the influence of the stationary magnetic field. Microrotation of magnetic fluid and rotation of nanoparticles are also considered. Shliomis model is used in the problem formulation, and then the similarity transformation is applied to transform partial differential equations into a set of nonlinear-coupled ordinary differential equations in dimensionless form. Transformed nonlinear-coupled differential equations are solved through the finite element method using COMSOL Multiphysics under the mathematical modeling. Results for velocity distribution, temperature distribution, concentration distribution and angular velocity distribution are obtained after considering the effects of Maxwell parameter, ferromagnetic interaction number, thermal Grashof number, solutal Grashof number, Brownian motion parameter, thermophoresis number, chemical reaction parameter, radiation absorption coefficient, heat generation/absorption parameter, Prandtl number and Schmidt number in the flow. It has been observed that magnetic energy transforms into kinetic energy, thermal boundary layer and concentration boundary layer in the presence of considered physical parameters.

Heat Absorption Effect on Free Convection Flow Past a Vertical Porous Pipe with Mass Transfer

This study investigates heat absorption on free convection flow past a vertical porous pipe with mass transfer. The governing equations are the continuity, momentum, energy and diffusion equations. The equations in dimensionless form were transformed into ordinary differential equations (ODEs) and solved analytically using perturbation method. Approximate solutions for the velocity, temperature and concentration were determined. Results are presented graphically showing the effects of various parameters on the fluid flow. It is observed that the velocity becomes higher when thermal Grashof number and sustentions paramètre are increased. Also, increase in magnetic parameter, Schmidt number and Prandtl number lead to fall in the velocity of the fluid. The temperature of the fluid rises also with increase in heat generation but reduces for increased values of Prandtl number. Consequently, the concentration boundary layer decreases with increasing values of Schmidt number. Furthermore, increase in suction/injection has a retarding and accelerating effect on the velocity, temperature and concentration of the fluid respectively.