Effects of ultrafiltration permeation rates on the hydrodynamics of a minichannel/slit laminar flow

It is experimentally studied herein the effect on pressure drop of scaling down the characteristic length of laminar flows in impermeable rectangular minichannels, its height, to values ranging from 700 to with the bottom wall possessing different roughness values. Results are compared to the analytical solution of the Hagen-Poiseuille flow confirming the presence of surface phenomena unobserved in macroscale flows. A fictitious viscosity, μ_rough, dependent on the surface roughness may be used to model such surface phenomena. This viscosity is obtained from μ_rough=μ_app-μ, μ_app being the apparent viscosity used in the theory that matches the experimental data. From the experiments and theory values of μ_rough ranging from 0.516μ to 0.915μ are obtained. Additionally, effects of suction on pressure drop in the same minichannel, but with permeation through membranes with different roughness values, are also experimentally characterized and analyzed viewing the identification of its attenuating or amplifying trends. Results clearly show that suction reduces the effects of surface phenomena on the pressure drop approaching more closely the Hagen-Poiseuille flow solution. Also, the assumption of fully developed flow is assessed through the numerical calculation of the entrance lengths of the studied minichannel flows and the results elucidated that such hypothesis constitutes a fair approximation: for the most adverse operating conditions, the maximum entrance length is only 17.7% of the channel length.     

Experimental study of mass transfer limited reaction—Part I: Use of fibre optic spectrometry to infer asymmetric mass transfer coefficients

Mass transfer coefficients, often quantified using empirical correlations in chemical engineering, are useful in predicting the final concentration of the reactants [(Fogler 1992). In: Amundson (Ed.)., Element of Chemical Reaction Engineering, International Series in the Physical and Chemical Engineering, Princeton-Hall]. In the present work, we propose an inverse methodology to estimate mass transfer coefficients from the experimentally measured concentrations of the reactants. The potential of the inverse methodology is that asymmetric mass transfer coefficients of all the premixed reactants can be inferred, which has not been reported so far in literature. In general, only the slowest transfer coefficient estimate has been feasible before. We first review the potential reactions satisfying the required criteria and then discuss multi-component spectrum analysis to decipher the concentrations of the reactants from the absorbance spectrum of the reaction mixture using the principle of additivity. We show that linear additivity does not hold if there is any interaction between the reacting species. In that case, we use a non-linear calibration for the concentrations of the reactants. The mass transfer coefficients inferred using the inverse methodology are validated by solving the forward problem and could be potentially used to study transport limited characteristics of heterogeneous reactions.     

Numerical study of a hybrid membrane cell with semi and fully permeable membrane sub-sections

Hybrid membrane cells with up to 128 sections, each one comprising a fully and a semi-permeable membrane sub-section and, the limit case of a cell with an infinite number of membrane sections were studied by numerical methods. These hybrid cells separate a feed stream into two parts: a solvent stream which crosses the semi-permeable membranes and a concentrate stream which crosses the fully permeable membranes. The concentrate stream has a cleaning effect on the mass boundary layer over the semi-permeable membranes. The numerical results show that concentration polarization in hybrid cells is much lower than the polarization in conventional cells. Additionally, a highly concentrated solution is recovered. The cell with an infinite number of membrane sections (n) has the best performance: the lowest polarization and the highest concentration in the concentrate stream. As n increases to infinite, the concentration in the concentrate stream tends to the concentration over the semi-permeable membrane, i.e., to the maximum concentration inside the mass boundary layer. The number of membrane sections needed to achieve a performance similar to that of a cell with an infinite number of sections is very high, greater than 128. The velocity of the concentrate stream also plays an important role. As this velocity is increased (until an upper limit), the cleaning effect of the boundary layer intensifies but the purity of the concentrate stream decreases (dilution effect). An intermediate value for the velocity of the concentrate stream (between the lower and upper limit) should be used to optimize both effects.     

Hydrodynamics and mass transfer in a packed column: Case of toluene absorption with a viscous absorbent

Volatile organic compounds (VOCs) cause nuisance to humans and the environment. Recent legislation encourages industrialists to set up equipment for treating their VOC-loaded gaseous effluents. This piece of research studies the absorption process, using a viscous organic absorbent (di(2-ethylhexyl) adipate=DEHA) to treat a toluene-loaded vent gas, in terms of hydrodynamics and mass transfer. It is shown that DEHA does not lead to an excessive pressure drop. Correlations predicting hydrodynamic parameters from previous literature are summarised and tested against experimental results. It is shown that acceptable prediction accuracy can be achieved for counter-current pressure drop and liquid hold-up. Treatment efficiency for the toluene-loaded vent gas is shown to be very good. Calculation of mass transfer constants (k_La) enables to test literature correlations against the experimental results. The mass transfer is supposed to be limited by the liquid-side resistance. Our experimental results showed that the k_La of the system depends on the liquid velocity but also on the gas velocity. This behaviour has also been observed by the few authors who have used viscous fluids in their experiments, but is contrary to all the authors who have work on low-viscosity fluids. It is therefore clear that the influence of viscosity on the phenomenon is considerable. Not one current correlation is currently accurate in the case of a viscous absorbent.     

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.     

Hydrodynamics and mass transfer in a novel multi-airlifting membrane bioreactor

A novel multiple-airlifting membrane bioreactor is built with four sintered stainless steel tubular filters as the risers and downcomers. This work investigates the hydrodynamics including gas holdup, liquid velocity, liquid circulation and mixing times by aerating different number of risers (one to three) at superficial gas velocities of 0.02-0.07 m/s The mass transfer phenomena, including oxygen mass transfer (k_La) and effective molecular diffusivity of lactic and acetic acids through the walls of tubular filters, are also investigated. It is found that gas holdup in individual risers increases linearly with the superficial gas velocity, and performs independently under multiple-airlifting conditions. The vessel-based gas holdup and liquid velocity in downcomer(s) increase with aeration rate of individual risers as well as the number of risers. The liquid velocity in downcomers reaches an upper limit (about 0.6 m/s), because of flow resistance or energy loss of liquid circulation. The oxygen mass transfer coefficient (k_La) is primarily affected by gas holdup and the number of risers, and to some extent influenced by liquid velocity. The novel airlifter configuration results in good liquid mixing in the bioreactor that quickly reaches new steady state in response to a sudden pH change from acid addition.     

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.     

Investigation of laminar flow in a stirred vessel at low Reynolds numbers

Many mixing applications involve viscous fluids and laminar flows where the detailed as well as overall flow structures are important. In order to understand the fluid dynamic characteristics of low Re laminar flows in mixing vessels, the flow induced by a Rushton impeller for three Re namely, 1, 10 and 28, was studied both experimentally and computationally. It was found that for the highest Re, the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re a reciprocating motion with negligible net pumping was observed. This behaviour has not been reported in the literature in the past and represents a highly undesirable flow pattern from the standpoint of effective mixing. The CFD results successfully reproduced this behaviour. In order to elucidate the physical mechanism responsible for the observed flow pattern, the forces acting on a fluid element in the radial direction were analysed. The analysis indicated that for the lowest Re, the material derivative of radial velocity near the blade tip is small thus a balance exists between pressure and viscous forces; the defining characteristic of creeping flow. The velocity and pressure forces are in phase because the velocity is driven by the pressure field generated by the rotation of the impeller. Based on these findings, a simplified analytic model of the flow was developed that gives a good qualitative as well as quantitative representation of the flow.     

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.     

Heat and mass transfer correlations and bifurcation analysis of catalytic monoliths with developing flows

We review and compare the literature correlations for estimating the heat and mass transfer coefficients as well as pressure drop in catalytic monoliths with simultaneously developing velocity, concentration and temperature profiles. We present accurate correlations for estimating the local Nusselt and Sherwood numbers for developing flows with constant flux (slow reaction) and constant wall concentration or temperature (fast reaction) cases for a channel of arbitrary shape. These new correlations need only a single parameter, namely, the asymptotic value, which depends on the channel geometric shape. We establish the accuracy of the proposed correlations by comparing the predicted values with the exact numerical values available for a few cases. We use the new correlations to analyze the effect of flow conditions near the inlet of the channel on the ignition and extinction behavior of catalytic monoliths used in combustion and after-treatment applications as well as laboratory experiments. It is shown that the bifurcation behavior, such as the number and location of the ignition/extinction points, the number of stable steady-states and the hysteresis locus is sensitive to the flow conditions in the entry region, and hence the heat and mass transfer correlations used, especially for large values of the transverse Peclet number (high space velocities or very short monoliths) or adiabatic temperature rise or when the axial catalyst loading is not uniform.     

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.     

Experimental study of mass transfer in a dense bubble swarm

We consider the liquid-side mass transfer coefficient k_L in a dense bubble swarm for a wide range of gas volume fraction (0.45%≤α_G≤16.5%). The study is performed for an air–water system in a square column. Bubble size, shape and velocity have been measured for different gas flow rates by means of a high speed camera. Gas volume fraction and bubble velocity have also been measured by a dual-tip optical probe. Both of these measurements show that the bubble vertical velocity decreases when increasing α_G in agreement with previous investigations. The mass transfer is measured from the time evolution of the dissolved oxygen concentration, which is obtained by the gassing-out method. The mass transfer coefficient is found to be very close to that of a single bubble provided the bubble Reynolds number is based on the average equivalent diameter 〈d_eq〉 and the vertical slip velocity 〈V_z〉.     

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.     

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.     

Consequences of an asymmetrical confinement in the transfer phenomena for a cylinder at low Reynolds numbers

In most of the systems where heat or mass transfer occur geometrical symmetries are often present. In this paper, we wish to know if the global flux transferred to cylindrical particles in motion (sedimentation, etc.) could be influenced when introducing some geometrical disturbance breaking the general symmetry of the system. To answer this question, we numerically investigate the simple configuration of a single cylindrical particle moving at constant speed between two parallel walls when the particle is off the symmetry plane and when the thermal boundary conditions are of the Dirichlet or Neumann type. When the geometrical disturbance of the system increases, the results show that the backflow that appears in such confined situations yields a non-intuitive evolution of the transfer in convective regimes. In this case a minimum of the flux appears off the symmetry plane. However, in purely diffusive regimes, we find a monotonical evolution of the transfer.     

Bubbling process in stirred tank reactors II: Agitator effect on the mass transfer rates

Several impellers, perforated plates and geometrical configurations were tested in order to evaluate the effect of the particular hydrodynamics generated by each impeller on the mass transfer rates and to optimize the performance of the tank. Theoretical and empirical equations have been used or proposed, based on the experimental data, to study the oxygen transfer rates from air bubbles generated in a non-standard stirred tank. The empirical equations obtained depend on the impeller type, its position and the design of the perforated plate because of their effect on the bubbles. The optimal position of the impeller depends on the physical effect of the impeller on the bubbles. Higher mass transfer coefficients were obtained close to the perforated plates. Not only the dispersion but also the break up of the bubbles favors the mass transfer rates. In short, although the Rushton turbine is efficient and stable with its relative position, other impellers show very interesting results for lower power inputs.     

Numerical simulation of mass transport in a filter press type electrochemical reactor FM01-LC: Comparison of predicted and experimental mass transfer coefficient

This paper studies flow characteristics and their effect on local mass transfer rate to a flat plate electrode in a FM01-LC electrochemical reactor. 3D reactor simulations under limiting current and turbulent flow conditions were performed using potassium ferro-ferricyanide electrochemical system with sodium sulfate as supporting electrolyte. The model consists of mass-transport equations coupled to hydrodynamic solution obtained from Reynolds-averaged Navier–Stokes equations using standard k–? turbulence model, where the average velocity field, the turbulence level given by the eddy kinetic energy and the turbulent viscosity of the hydrodynamic calculation were used to evaluate the convection, turbulent diffusion and the concentration wall function. The turbulent mass diffusivity was evaluated by Kays–Crawford equation using heat and mass transfer analogies, while wall functions, for mass transport, were adapted from Launder–Spalding equations. Simulation results describe main flow properties, concentration profiles throughout the entire volume of the reactor and local diffusion flux over the electrode. Overall mass transfer coefficients estimated by simulation, without fitting parameters, agree closely with experimental coefficients determined from limiting current measurements (1.85% average error) for Re between 187 and 1407.     

Hydrodynamics and volumetric gas-liquid mass transfer coefficient of a stirred vessel equipped with a gas-inducing impeller

Hydrodynamic and mass transfer characteristics of a gas-liquid stirred tank provided with a radial gas-inducing turbine were studied. The effect of the rotation speed and the liquid submergence on global hydrodynamic and mass transfer parameters such as the critical impeller speed, the induced gas flow rate, the gas holdup, the power consumption and the volumetric gas-liquid mass transfer coefficient were investigated. The experiments are mainly conducted with air-water system. In the case of critical impeller speed determination, two liquid viscosities have been used. The volumetric gas-liquid mass transfer coefficient k_La has been obtained by two different techniques. The gas holdup, the induced gas rate and the volumetric gas-liquid mass transfer coefficient are increasing functions with the rotation speed and decreasing ones with the liquid submergence. The effects of these operating parameters on the measured global parameters have been taken into account by introducing the dimensionless modified Froude number and correlations have been proposed for this type of impeller.