Presence Of Mass Transfer Research Articles

Mass transfer and species separation due to oscillatory flow in a Brinkman medium

The problem of mass transfer in presence of oscillatory flow in a porous tube with impermeable boundary has been investigated in this present study. Before we consider the any governing equations both for the hydrodynamic problem as well as for the mass transfer, we review the mathematical background behind various governing equations following the detailed hierarchy of models that are derived by Rajagopal (2007). This gives a clear motivation on the governing equations that have been assumed in the present problem. We have assumed that the flow inside a cylindrical porous pipe is governed by non-stationary Navier–Stokes equations with a Brinkman term accounting for the resistance offered by the porous medium. The equation gets simplified with an additional assumption that the flow is unidirectional along z-axis. The boundary of the pipe has been considered to be a slip boundary. The solution of the hydrodynamic problem has been obtained considering oscillatory forcing both in velocity and pressure. The corresponding solution has been used to consider the convection diffusion inside this cylindrical pipe. The time dependent mass transfer equation has been treated analytically based on Bessel-Fourier eigen function expansion method. It has been observed that the diffusivity of each species play a vital role to display some interesting behavior. For a given slip coefficient at the boundary, increasing angular frequency or Womersely number, the rate of transport of two different species increases. There exists a particular frequency termed as crossover frequency where the rate of mass transport of two species with different Peclet numbers become the same. The crossover is observed only once within a specific range of a particular parameter displaying the separation of the species. However, this separation is significant for moderate Peclet numbers contributing to the impact of the advection and for large Peclet numbers, such a crossover is not significant as the crossover is mostly depends on the individual diffusivities of the species.

Similarity Theory for Forced Convection over Horizontal Plates

A similarity analysis is performed to study the fluid flow and heat transfer characteristics for the steady laminar forced convection boundary-layer flow past a semi-infinite horizontal plate in the presence of mass transfer, i.e., suction or blowing. The plate is subjected either to a nonuniform heat flux or nonuniform wall temperature. The heat flux is assumed to vary in the following form , whereas the wall temperature is assumed to vary as . Numerical results are obtained for various values of Prandtl number, suction or injection parameter , as well as for various levels of heating or . The effects of various values of Prandtl number , suction or injection parameter , and the index or on velocity profiles, temperature profiles, skin-friction coefficients, and local Nusselt number are presented. The results of the present general theory agree well with previously published results for the case of constant wall temperature (the only case with quantitative solutions that were available in the literature). Subtle new flow physics, such as a sharp reduction in the Nusselt number with increasing Prandtl number when mass injection is present and the Prandtl number is large, has been elucidated.

Slip Effects on Peristaltic Transport in an Inclined Channel with Mass Transfer and Chemical Reaction

An analysis is carried out for the peristaltic flow in an inclined asymmetric channel when no-slip condition does not hold. The whole analysis has been carried out in the presence of mass transfer and chemical reaction. The channel asymmetry is generated because of peristaltic wave train on the walls through different amplitudes and phases. Long wavelength and low Reynolds number assumption is adopted in the whole mathematical analysis. Expressions for the stream function and longitudinal pressure gradient have been developed. Numerical integration is performed for the analysis of pressure rise per wavelength. Longitudinal velocity, pumping and trapping phenomena are analyzed in detail via plots.

Slip Effects on Peristaltic Transport in an Inclined Channel with Mass Transfer and Chemical Reaction

An analysis is carried out for the peristaltic flow in an inclined asymmetric channel when no-slip condition does not hold. The whole analysis has been carried out in the presence of mass transfer and chemical reaction. The channel asymmetry is generated because of peristaltic wave train on the walls through different amplitudes and phases. Long wavelength and low Reynolds number assumption is adopted in the whole mathematical analysis. Expressions for the stream function and longitudinal pressure gradient have been developed. Numerical integration is performed for the analysis of pressure rise per wavelength. Longitudinal velocity, pumping and trapping phenomena are analyzed in detail via plots.

Simulation studies on a rotating ring disk electrode system: Role of supporting electrolyte in determination of relevance of ionic migration

Most of the past theoretical works with the rotating ring disk electrode (RRDE) system have been restricted to situations where supporting electrolyte concentration is large enough so that the effects of migration of ionic species in the solution becomes negligible. In this work, effects of ionic migration have been investigated for a RRDE system by solving the differential equations describing mass transfer in presence of ionic migration using numerical technique. Two cases were considered for simulation, presence and absence of migration of ionic species. Results indicate that in presence of migration, collection efficiency of a RRDE system increases for all electrode geometries and concentration boundary layer thickness reduces. Results also indicate that collection efficiency is dependent on electrode geometries. The system chosen for simulation is copper sulfate solution of 0.1 (M) concentration with little supporting electrolyte. It is also noticed that migration effect remains important for supporting electrolyte concentration as high as 0.1 (M). Limiting current condition was assumed. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1390–1399, 2013

Unsteady three dimensional flow of couple stress fluid over a stretching surface with chemical reaction

The unsteady three-dimensional flow of couple stress fluid over a stretched surface is investigated. Analysis has been performed in the presence of mass transfer and chemical reaction. Nonlinear flow analysis is computed by a homotopic approach. Plots are presented and analyzed for the various parameters of interest. A comparative study with existing solutions in a limiting sense is made.

Combined Heat and Mass Transfer by Natural Convection from a Semi-Infinite Plate Submitted to a Magnetic Field with Hall Currents

:The present work is concerned with the MHD unsteady free convection flow from a vertical semi-infinite plate of an incompressible electrically conducting fluid. The effects of the viscous dissipation and the Hall currents are analyzed. The unsteady governing equations are reduced to a system of ordinary differential non-dimensional equations and the resulting equation system is solved numerically by using the Network Simulation Method. This numerical method is based on the electrical analogy, where only previous spatial discretization is necessary to obtain a stable and convergent solution with very low computational times. To solve the system of algebraic equations with time as continuous function, an electric circuit simulator is used. Numerical results for velocities, temperature, concentration and current terms are illustrated graphically. We have observed that the Grashof number for heat transfer (Gr) and mass transfer (G*) accelerate the velocity of the flow field at all points. But the increase in velocity of the flow field is more significant in presence of mass transfer. The effect of Schmidt number Sc on mass transfer process is a decrease of concentration distribution as a result of decrease of the concentration boundary layer thickness.

Viscous potential flow analysis of electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer

Viscous potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer in presence of a horizontal electric field has been carried out. Stability criterion is given by a critical value of relative velocity of two fluids as well as critical value of the applied electric field. Various graphs with respect to physical parameters, such as wave-number, viscosity ratio, ratio of dielectric constants of two fluids, heat transfer coefficients have been drawn and effect of various parameters have been described.

Stable isotope fractionation to investigate natural transformation mechanisms of organic contaminants: principles, prospects and limitations

Gas chromatography-isotope ratio mass spectrometry (GC-IRMS) has made it possible to analyze natural stable isotope ratios (e.g., (13)C/(12)C, (15)N/(14)N, (2)H/(1)H) of individual organic contaminants in environmental samples. They may be used as fingerprints to infer contamination sources, and may demonstrate, and even quantify, the occurrence of natural contaminant transformation by the enrichment of heavy isotopes that arises from degradation-induced isotope fractionation. This review highlights an additional powerful feature of stable isotope fractionation: the study of environmental transformation mechanisms. Isotope effects reflect the energy difference of isotopologues (i.e., molecules carrying a light versus a heavy isotope in a particular molecular position) when moving from reactant to transition state. Measuring isotope fractionation, therefore, essentially allows a glimpse at transition states! It is shown how such position-specific isotope effects are "diluted out" in the compound average measured by GC-IRMS, and how a careful evaluation in mechanistic scenarios and by dual isotope plots can recover the underlying mechanistic information. The mathematical framework for multistep isotope fractionation in environmental transformations is reviewed. Case studies demonstrate how isotope fractionation changes in the presence of mass transfer, enzymatic commitment to catalysis, multiple chemical reaction steps or limited bioavailability, and how this gives information about the individual process steps. Finally, it is discussed how isotope ratios of individual products evolve in sequential or parallel transformations, and what mechanistic insight they contain. A concluding session gives an outlook on current developments, future research directions and the potential for bridging the gap between laboratory and real world systems.

First integrals of equations of motion of a droplet in the presence of mass transfer to the carrier medium

Analysis is performed of first integrals in the limiting Stokes and Newtonian modes of motion of a droplet for two cases, namely, that of the droplet moving in its own vapor in the presence of phase transitions and that of the droplet moving in dusty gas without phase transformations but in view of the capture of dust particles. Expressions are found for the lengths over which the processes of condensation, complete evaporation of droplet, and deposition of particles occur. Comparison is made of the lengths and times of complete evaporation of droplet in the Stokes and Newtonian modes of droplet motion. Asymptotic formulas are obtained for these quantities, which correspond to low and high superheating of vapor, as well as formulas for the limiting diameters of droplet in the cases of condensation of vapor or capture of particles.

EXPERIMENTAL INVESTIGATION OF PHASE INVERSION OF LIQUID-LIQUID SYSTEMS IN A SPRAY EXTRACTION COLUMN

An experimental study of the phase inversion behavior of liquid-liquid dispersion has been conducted in a spray extraction column for systems of toluene / water, n-hexane/water, CCl4/water, toluene /water + glycerol (25 % wt), toluene + CCl4 (25 % wt) / water and toluene / acetic acid (5 % wt)/water. The effects of physical properties, mass transfer and column geometry on phase inversion have been investigated. The results show that the dispersed phase hold up sufficient for phase inversion increases in o/w dispersion and decreases in w/o dispersion by increasing interfacial tension. Also, it was found that by increasing the viscosity of aqueous phase, dispersed phase hold up decreases at phase inversion point in both o/w and w/o dispersions. The tendency to phase inversion increases in o/w dispersion with an increase in density difference of two phases. It was observed that dispersed phase hold up at phase inversion point decreases in the presence of mass transfer, when the direction of mass transfer is from dispersed phase to continuous phase. The results show that dispersed phase holdup increases with drop size at phase inversion point and column diameter has an important effect on phase inversion because of wall effect.

An exact analytical solution of the Falkner-Skan equation with mass transfer and wall stretching

In this paper, an exact analytical solution of the famous Falkner-Skan equation is obtained. The solution involves the boundary layer flow over a moving wall with mass transfer in presence of a free stream with a power-law velocity distribution. Multiple solution branches are observed. The effects of mass transfer and wall stretching are analyzed. Interesting velocity profiles including velocity overshoot and reversal flows are observed in the presence of both mass transfer and wall stretching. These solutions greatly enrich the analytical solution for the celebrated Falkner-Skan equation and the understanding of this important and interesting equation.

Reverse combustion: Kinetically controlled and mass transfer controlled conversion front structures

Under most conditions for reverse fixed bed combustion, transport effects of heat and gaseous species to and within fuel bed particles are important phenomena that limit the conversion rate. At present there is only one model that (1) claims to take transport limitations into account and (2) for which analytical solutions are given. Here, we present a numerical study of reverse combustion analysis on the basis of this model to show the effect of transport limitations on the reaction front structure and the consequences of these effects for the applicability and accuracy of the analytical solution procedure. A parameter set for coal combustion was used to perform the study. Results of numerical simulations indicate that the model solutions contain two limiting cases: kinetically controlled and mass-transfer-controlled conversion front structures. The kinetically controlled solutions consist of a preheat zone at the upstream side of the front and a thin reaction zone at the downstream side. The mass-transfer-controlled solutions consist of a wide reaction zone with a maximum source term situated at the upstream part of the front. The analytical solution to the model equations is shown to give correct predictions in the kinetically controlled case only. In the presence of mass transfer, the solution predicts the trend of decreasing front velocity with increasing transport limitations correctly but does not show the correct functional dependence on the parameter describing transport limitations. In addition, the predictions become highly inaccurate. This is related to the fact that the effect of transport limitations is not accounted for in the analytical solution method. Therefore, numerical methods should be used to obtain generally valid solutions.

Kinetic Study of the Effect of Benzoic Acid Derivatives on Copper Electrodeposition

The effect of anodic oxygen bubbles on the rate of mass transfer in presence of benzoic acid, p-nitro, p-chloro and p-aminobenzoic acids were studied by measuring the limiting current of cathodic deposition of copper from acidified copper sulphate solution using lead anode. It is found that the rate of deposition decreases by adding organic substances. The rate of deposition depends on the type of inhibitor as well as its concentration. The ability of inhibitors to decrease the limiting current is as follows: p-nitrobenzoic > p-chlorobenzoic > benzoic > p-aminobenzoic acid. The thermodynamic parameters prove that the reaction is diffusion controlled.

Modeling Homogeneous Combustion in Bubbling Beds Burning Liquid Fuels

This paper introduces a model for the description of the homogeneous combustion of various fuels in fluidized bed combustors (FBC) at temperatures lower than the classical value for solid fuels, i.e., 850°C. The model construction is based on a key bubbling fluidized bed feature: A fuel-rich (endogenous) bubble is generated at the fuel injection point, travels inside the bed at constant pressure, and undergoes chemical conversion in the presence of mass transfer with the emulsion phase and of coalescence with air (exogenous) bubbles formed at the distributor and, possibly, with other endogenous bubbles. The model couples a fluid-dynamic submodel based on two-phase fluidization theory with a submodel of gas phase oxidation. To this end, the model development takes full advantage of a detailed chemical kinetic scheme, which includes both the low and high temperature mechanisms of hydrocarbon oxidation, and accounts for about 200 molecular and radical species involved in more than 5000 reactions. Simple hypotheses are made to set up and close mass balances for the various species as well as enthalpy balances in the bed. First, the conversion and oxidation of gaseous fuels (e.g., methane) were calculated as a test case for the model; then, n-dodecane was taken into consideration to give a simple representation of diesel fuel using a pure hydrocarbon. The model predictions qualitatively agree with some of the evidence from the experimental data reported in the literature. The fate of hydrocarbon species is extremely sensitive to temperature change and oxygen availability in the rising bubble. A preliminary model validation was attempted with results of experiments carried out on a prepilot, bubbling combustor fired by underbed injection of a diesel fuel. Specifically, the model results confirm that heat release both in the bed and in the freeboard is a function of bed temperature. At lower emulsion phase temperatures many combustible species leave the bed unburned, while post-combustion occurs after the bed and freeboard temperature considerably increases. This is a well-recognized undesirable feature from the viewpoint of practical application and emission control.

Effects of radiation on flow past an impulsively started infinite vertical plate with mass transfer

The effect of radiation on the flow past an impulsively started vertical plate in the presence of mass transfer is analyzed. The fluid is a gray, absorbing-emitting, and nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. A rise of the velocity due to the presence of a foreign mass is observed. An increase in the Schmidt number (Sc < 1) and in the radiation parameter N leads to a decrease in the velocity. The skin friction increases due to the presence of a foreign mass when Sc < 1 and decreases at Sc = 1.

Stability of a thin liquid film flowing on a vertical wall in the presence of mass transfer through the free surface

We have studied the problem of the description of a thin liquid film flowing on a vertical wall in the presence of mass transfer through the free surface and have constructed a class of self-similar solutions in the case of a distributed nonstationary mass flux. The stability of the obtained self-similar flows with respect to small nonstationary harmonic perturbations of the liquid parameters has been studied and it is shown that the presence of a negative mass flux through the surface (evaporation) produces a destabilizing action on the flow. Similar to the case of a stationary flowing film of constant thickness, the self-similar flows are unstable with respect to perturbations of any frequency. In the case of evaporation, the development of instability has the character of an “explosion”: in the linear approximation, the amplitudes of perturbations exhibit infinite growth within a finite time (the time of evaporation of the liquid film). On the contrary, the presence of a positive mass flux through the surface (condensation, gas absorption, etc.) leads to the stabilization of the flow, whereby the amplitudes of perturbations exhibit limited growth in time over the entire film length and remain on the level of initial values. Moreover, in this case, there is a certain interval of frequencies in which small perturbations exhibit decay. It will be shown below that, using a feedback control, it is possible to stabilize the initially unstable self-similar film flows.

Novel Analytical Solution for a Simulated Moving Bed in the Presence of Mass-Transfer Resistance

A novel analytical solution for a simulated moving bed (SMB) with a linear adsorption equilibrium isotherm in the presence of mass transfer was derived. The proposed solution is based on the equivalent steady-state true moving bed (TMB) analogy. This analytical solution allows for the calculation of the liquid and solid concentration profiles in all sections of the SMB. The analytical solution was used in the prediction of the “separation volume” for glucose/fructose separation. Emphasis was placed on the effects of the liquid/solid velocity ratios in sections I and IV (γI and γIV, respectively) on the performance of the SMB. The value of γI more significantly affects the SMB performance than the value of γIV and should be tuned carefully in a narrow zone of values. The main advantage of the presented solution is the rapid determination of the separation volume in the presence of mass-transfer limitations, according to the required purity of the extract and raffinate.

Caffeine Extraction with a Karr Reciprocating Plate Column

AbstractA Karr reciprocating plate column was used in extracting caffeine from the methylation mother solution of a caffeine synthesis plant with chloroform as the extractant. Pilot tests were carried out in a 38 mm diameter column to determine holdup, flooding and mass transfer at various reciprocation velocities. Results show that the holdup in the presence of mass transfer is higher than that in the absence of mass transfer, and the height of the equivalent theoretical stage (HETS) was 0.57 m for a 99.9 % recovery at the optimum reciprocation velocity. The Karr empirical correlation for scale‐up was used to predict the column height in the design of the industrial process. A 0.4 m and a 0.6 m diameter column were used to treat 2.5 m3/h and 6.0 m3/h methylation mother solution, and the corresponding HETSs were 1.42 m and 1.53 m for a 99.9 % recovery, respectively. The axial dispersion coefficients of the dispersed phase were estimated for the 0.4 m and the 0.6 m diameter columns. For a better recovery the ratio of the axial dispersion coefficient of the dispersed phase to that of the continuous phase was about 2.7–3.0.

Condensation characteristics inside a vertical tube considering the presence of mass transfer, vapor velocity and interfacial shear

Condensation heat transfer in a vertical tube has been investigated analytically by considering the vapor flow and mass transfer. Condensation processes are divided into two sections: the forming film section and the formed film section. The present analysis takes into account the effects of momentum transfer that results from mass transfer and vapor flow on the interfacial shear and hence condensation. Two major parameters that govern the condensation heat transfer the relative velocity ratio B and the momentum transfer factor U, along with a comprehensive factor ω that includes mass transfer, the vapor velocity and the thermophysical properties, are proposed to describe the condensation mechanism. It is shown that the effects of interfacial shear and mass transfer are strongly dependent on the thermophysical properties of the working fluids and the operating temperatures. The theoretical predictions are in good agreement with the experimental data from other investigations for the upward vapor flow in water cases.