Direct numerical simulations of mass transfer in square microchannels for liquid-liquid slug flow

Microreactors for the development of liquid-liquid processes are promising technologies since they are supposed to offer an enhancement of mass transfer compared to conventional devices due to the increase in the surface/volume ratio. But impact of the laminar flow should be negative and the effect is still to be evaluated. The present work focuses on the study of mass transfer in microchannels by means of 2D direct numerical simulations. We investigated liquid-liquid slug flow systems in square channel of depth. The droplet velocity ranges from 0.0015-0.25 m/s and the ratio between the channel depth and the droplet length varies between 0.4 and 11.2. Droplet side volumetric mass transfer coefficients were identified from concentration field computations and the evolution of these coefficients as a function of the flow parameters and the channel size is discussed. This study reveals that mass transfer is strongly influenced by the flow structure inside the droplet. Moreover, it shows that the confinement of the droplets due to the channel size leads to an enhancement of mass transfer compared to cases where the droplets are not constrained by the walls.     

Effects of crystal growth rate and heat and mass transfer on solute distribution

The effects of crystal growth rate and heat and mass transfer on solute distribution during solidification of binary melt have been theoretically investigated on the basis of a new theory of solute distribution proposed by the present authors. The solute distribution factor f at the solid-liquid (SL) interface is in inverse proportion to the one-half power of the dimensionless growth rate U. The growth rate U is in proportion to the second power of the normalized concentration difference between the SL interface and bulk melt. A new transport factor K, which describes heat and mass transfer in melt, gives an important contribution to the crystal growth and the solute distribution at the SL interface. The transport factor is used successfully to control the solidification of melt. The flow structure in melt exerts essential influence on the solid purity.     

Heat and mass transfer of single droplet/wet particle drying

A theoretical model, which considers the fully unsteady character of both heat and mass transfer during the drying of single droplet/wet particle, is presented. The model enables prediction of pressure and fraction distributions of air-vapour mixture within the capillary pores of the wet particle crust. The simulations of the drying process of a single silica droplet under different conditions show a permanent rising of pressure within the capillary pores, but the corresponding vapour fraction remains less than unity. The comparison between the drying histories of the silica droplet, predicted by the present model with the data, calculated by the model which assumes a quasi-steady-state mass transfer and linear pressure profile within the capillary pores, shows inconsiderable differences between the droplet/wet particle temperature and mass time-changes. At the same time, the present model predicts pressure build-up and temperature rising within the particle wet core. However, in the studied cases the temperature of the wet core temperature does not exceed the liquid saturation temperature and therefore no boiling of liquid within the particle wet core is observed.     

Correlations for mass transfer coefficients over blunt boards based on modified boundary layer theories

Correlations for skin friction, heat and mass transfer coefficients on the surfaces of blunt-edged flat plates have been established, based on modified boundary layer theories which take account of the influence of separation and reattachment flows. The calculated velocity profiles, skin friction, heat and mass transfer coefficients show good agreement with the data measured by previous authors.     

Mathematical simulation of mass transfer processes under heterogeneous reactions in polydisperse porous media

Submitted is a theoretical study of mass transfer processes in polydisperse porous media in the presence of chemical reactions. Kinetic regime of methane pyrolysis in a porous carbon skeleton considering external and internal diffusion resistances for different initial distributions of particles forming the porous medium is investigated. Derived is a general analytical expression describing the influence of the inner reaction surface variation on the degree of the pore filling for an arbitrary initial particle size distribution. Expressions defining the time of pores filling by pyrocarbon based on approximate and exact solutions of the equation for the probability density function (PDF) of particle size distribution are received. Dependence of pore filling time on effective diffusion coefficient and initial particle size distribution using both solutions for PDF-equation is compared. It is shown, that the dominant factor influencing the pore filling time is the dispersion of particle size distribution.     

Transient convective mass transfer for a fluid sphere dissolution in an alternating electric field

In this study, we considered mass transfer in a binary system comprising a stationary fluid dielectric sphere embedded into an immiscible dielectric liquid under the influence of an alternating electric field. Fluid sphere is assumed to be solvent-saturated so that an internal resistance to mass transfer can be neglected. Mass flux is directed from a fluid sphere to a host medium, and the applied electric field causes a creeping flow around the sphere. Droplet deformation under the influence of the electric field is neglected. The problem is solved in the approximations of a thin concentration boundary layer and finite dilution of a solute in the solvent. The thermodynamic parameters of a system are assumed constant. The nonlinear partial parabolic differential equation of convective diffusion is solved by means of a generalized similarity transformation, and the solution is obtained in a closed analytical form for all frequencies of the applied electric field. The rates of mass transfer are calculated for both directions of fluid motion—from the poles to equator and from the equator to the poles. Numerical calculations show essential (by a factor of 2/3) enhancement of the rate of mass transfer in water droplet-benzonitrile and droplet of carbontetrachloride-glycerol systems under the influence of electric field for a stagnant droplet. The asymptotics of the obtained solutions are discussed.     

Theoretical modelling of the effect of surface active species on the mass transfer rates in bubble column reactors

The complex composition of the liquid media in bubble column reactors makes their understanding and theoretical modelling challenging. In this work we have studied the effect of surface tension and contaminants, salts, on the mass transfer rates from a theoretical point of view, looking for a deeper understanding on the effect of surface active species which usually reduce surface tension and modify bubble surface behaviour. The specific contact area is obtained using a population balance where the effect of the presence of contaminants is addressed by the proper theoretical closures for bubble coalescence efficiency, for partially and fully immobile surfaces, and bubble break-up. Meanwhile, the contribution of contaminants to the liquid-film resistance is implemented as function of the coverage of the surface of the bubbles. It was found that the degree of bubble surface coverage not only affects bubble coalescence but also their break-up. The ion strength defines bubbles stability and the critical Weber number can be predicted as function of ion strength. Furthermore, the mass transfer rates are function of the surface coverage by the electrolytes. The model was able to predict k_La taking into account the fact that the concentration profiles surrounding individual bubbles are not completely developed due to the presence of other bubbles, in agreement with previous results from the literature.     

Optimal experimental protocol for identification of dissolution parameters in presence of fast reaction

To model the reactive solid phase contribution, knowledge of the solubility and mass transfer should be extracted from empirical measurements. Often unknown factors may complicate the interpretation of the data. In this paper we consider an example of this kind and present a practical procedure that allows one to avoid these difficulties. A simplified model is derived for the mass transfer and kinetics. This model provides the insight that leads to an optimal protocol for estimation of the parameters of interest.     

Predicting inter-phase mass transfer for idealized Taylor flow: A comparison of numerical frameworks

Four numerical frameworks were derived to investigate the impact of underlying assumptions and numerical complexity on the predicted mass transfer between a Taylor bubble and liquid slug in circular capillaries. The separate influences of bubble velocity and film length, slug length, and bubble film thickness on k_La were compared to empirical and CFD-based predictions from existing literature. Reasonable agreement was obtained using a Slug Film model, which accounted for diffusion-limited mass transfer between the slug film and circulating bulk without the need for an iterative numerical solution. Subsequent investigation of the relative contributions of film and cap mass transport for industrially relevant conditions suggests that both mechanisms need to be accounted for during the prediction of k_La.     

A numerical study of mass transfer of ozone dissolution in bubble plumes with an Euler-Lagrange method

In this paper we study the mass transfer process of ozone dissolution in a bubble plume inside a rectangular water tank, as a model problem for a water purification system. The effect of bubble diameter and plume structure on mass transfer efficiency of ozone in bubble plumes is investigated numerically. In order to capture the detailed plume structure, the interaction between liquid and bubbles is treated by a two-way coupling Euler-Lagrange method. The motion of the continuous phase (a mixture of liquid and gas bubbles) is solved using a finite difference method in an Eulerian framework. The motion of the dispersed phase (bubbles) is tracked individually in a Lagrangian approach. The ozone transfer process from bubbles to liquid is computed by modelling the mass transfer rate of individual bubbles. Our numerical results show a nonlinear dependence of the ozone dissolution efficiency on the initial bubble size. The dissolution efficiency varies rapidly when the initial bubble size reaches certain value while the change of efficiency is much slower at other bubble sizes. Therefore, for a given tank size it is not necessary to generate bubbles much smaller than the optimal size. This result is of importance for engineering since it is difficult to generate small bubbles in practice. Our results also show that the instantaneous dissolution rate of ozone could be increased by increasing the initial volumetric fraction of ozone inside bubbles even up to 20% while maintaining the dissolution efficiency.     

Optimization of square microneedle arrays for increasing drug permeability in skin

Microneedles array is a new transdermal drug delivery technique designed to create holes in the epidermis and penetrate the stratum corneum, thus avoiding the high resistance of this barrier. Microneedles have been shown to increase the skin permeability of drugs with no or little pain. However, the skin permeability of epidermis while using microneedle arrays has yet to be fully studied. In some cases, microneedle and microneedle array designs which were developed based on certain criteria (e.g., material of the microneedles) have to be related to other criteria (e.g., drug permeability in skin, skin thickness, etc.). Therefore, in order to determine the optimum design of the microneedle arrays, the effect of different factors (e.g., number of the microneedle, surface area of the patch, etc.) along with skin permeability by using microneedles should be determined accurately. In this work, an optimization framework for transdermal delivery of high molecular weight drug from microneedle is presented. The outputs of this framework have allowed us to identify the optimum design of various microneedles. Data from this optimization algorithm is then used to predict skin permeability of high molecular weight injected into the skin from a microneedle system. The effect of the optimized microneedles on blood drug concentration has been determined. The outcome of this study is useful to propose an optimum design based on different measurement (e.g., variation of skin thickness) for transdermal delivery of drugs.     

Water transport through a PEM fuel cell: A one-dimensional model with heat transfer effects

Models play an important role in fuel cell design/development. The most critical problems to overcome in the proton exchange membrane (PEM) fuel cell technology are the water and thermal management. In this work, a steady-state, one-dimensional model accounting for coupled heat and mass transfer in a single PEM fuel cell is presented. Special attention is devoted to the water transport through the membrane which is assumed to be a combined effect of diffusion and electro-osmotic drag. The transport of heat through the gas diffusion layers is assumed to be a conduction-predominated process and heat generation or consumption is considered in the catalyst layers. The analytical solutions for concentration and net water transport coefficient are compared with recent published experimental data. The operating conditions considered are various cathode and anode relative humidity (RH) values at and 2 atm. The studied conditions correspond to relatively low values of RH, conditions of special interest, namely, in the automotive applications. Model predictions were successfully compared to experimental and theoretical I-V polarization curves presented by Hung et al. [2007. Operation-relevant modelling of an experimental proton exchange membrane fuel cell. Journal of Power Sources 171, 728-737] and Ju et al. [2005a. A single-phase, non-isothermal model for PEM fuel cells. International Journal of Heat and Mass Transfer 48, 1303-1315]. The developed easy to implement model using low CPU consumption predicts reasonably well the influence of current density and RH on the net water transport coefficient as well as the oxygen, hydrogen and water vapour concentrations at the anode and cathode. The model can provide suitable operating ranges adequate to different applications (namely low humidity operation) for variable MEA structures.     

A dynamic forward mixing model for evaluating the mass transfer performances of an extraction column

It is well known that the droplet behavior of the dispersed phase in extraction equipments has a strong influence on the mass transfer performances. It is, and will continuously be a key project for design and scaling up of extraction columns. In this work, a dynamic mass transfer model, considering the effect of forward mixing led by the drop size distribution and the axial mixing of the continuous phase, has been developed, by which the axial mixing characteristic can be easily evaluated when a stimulus-response dynamic curve is obtained. In order to test the mass transfer model and to study in the effect of droplet coalescence on mass transfer performance, a typical experimental system of 30% tributyl phosphate (in kerosene)-nitric acid-water with interface intension of 0.00995 N/m was chosen to investigate the mass transfer in a coalescence-dispersion pulsed-sieve-plate extraction column (CDPSEC) with 150 mm in diameter. The two-point dynamic method was applied to get the stimulus-response curves. With these results the axial mixing of the CDPSEC were evaluated. The calculated results showed that the response curves could be predicted with the new mass transfer model very well. The model has marked advantages over the traditional diffusion model. It is closer to the practice, easier to solve for the mathematical equations and boundary conditions, and has only one parameter to be optimized. The calculated results also showed that the influence of local coalescence of droplets on mass transfer performances is obvious.     

Experimental study of gas–liquid mass transfer coupled with chemical reactions by digital holographic interferometry

This work deals with the development of a new experimental tool and an original procedure to study the gas–liquid absorption process coupled with chemical reactions in the liquid phase. This absorption is realized inside a Hele-Shaw cell and digital holographic interferometry is used to visualize the formation and the development of the diffusion layer during the mass transport in the liquid phase in the vicinity of the gas–liquid interface. An image processing code is developed to extract quantitative information from the raw experimental results. The experimental results are compared to a mass transfer model in the liquid phase of the Hele-Shaw cell and some physico-chemical parameters of this model are estimated from this comparison using on a non-linear least-square fitting method. The developed procedure is used to study the gaseous CO₂ absorption in NaHCO₃–Na₂CO₃ aqueous solution. Calibration curves are determined and experiments are realized for several couples of NaHCO₃–Na₂CO₃ initial concentrations. The estimated values of the physico-chemical parameters for each experiment are presented and they are compared to the values calculated from correlations found in the literature. A reasonable agreement is observed, which tends to show that the methodology is promising and could be applicable to other systems.     

A new equation for estimating the height of the mass transfer unit in extraction columns

In this study, a new equation for estimating the height of the mass transfer unit, H_oxp, for mutually insoluble extraction systems was developed. The equation's accuracy and robustness were tested by comparing the predicted results with experimental data in the literature. With the same apparent interfacial tension, the mass transfer unit height decreased hyperbolically with the increase of the overall interphase volume mass transfer coefficient, despite the differences of column dimensions, experimental systems and operating conditions.     

A new model for mass transfer in direct contact membrane distillation

The mass transfer process in direct contact membrane distillation (DCMD) for three kinds of membranes was measured. Water fluxes at different temperatures and the membrane distillation coefficients (MDC) for each membrane were obtained directly from experimental data. The fact that the MDC values of membranes with larger pore size increase with temperature indicates that Poiseuille flow plays an important role in the process of mass transfer through the membrane. Based on this conclusion, a three-parameter model, named the Knudsen diffusion-molecular diffusion-Poiseuille flow transition (KMPT) model, was developed to predict MDC and water flux for membrane distillation. The parameters of the KMPT model for each membrane employed in this study, by which MDC at various temperatures can be determined, were evaluated by a nonlinear regression. The values of MDC and water fluxes for each membrane predicted by KMPT model agree well with that obtained directly from the experiment results. A large contribution of Poiseuille flow to mass transfer was observed and can be attributed to the distribution of large pores in the membranes. The KMPT model also provides a method for estimation of the effect pore size using the ratio of the MDCs; the ratio of the Poiseuille flow to molecular diffusion MDC provides the best estimation.     

Effect of pulp fiber suspensions on the rate of mass transfer controlled corrosion in pipelines under turbulent flow conditions

The present study aimed to investigate the corrosion behavior of a pipeline carrying dilute pulp fiber suspensions (0.1–0.3% consistency). To examine the role played by pulp fibers on the rate of diffusion controlled corrosion of metals an accelerated test which involved the diffusion controlled dissolution of copper in acidified dichromate was used under turbulent flow conditions. Different concentrations of pulp fibers at different solution velocities were studied. The rate of mass transfer controlled corrosion of copper was found to increase by increasing solution velocity and decrease by increasing pulp consistency. The data in the presence and absence of the pulp slurry were correlated by dimensionless equations.