Mass transfer from ensembles of fluid spheres to a power-law liquid at moderate Reynolds and Peclet numbers

The steady convective mass transfer from ensembles of mono-size Newtonian fluid spheres to power-law liquids has been studied at moderate Reynolds and Peclet numbers. The species continuity equation segregated from momentum equations has been solved numerically using a finite difference method. A simple cell model has been used to account for the modification of the flow field due to the neighbouring droplets. Extensive numerical results have been obtained which elucidate effects of the Reynolds number (Re_o), Schmidt number (Sc), power-law index (n_o), internal to external fluid characteristic viscosity ratio (k) and the volume fraction of the dispersed phase (Φ) on the rate of mass transfer. The ranges of parameters considered herein are: 1?Re_o?200, 1?Sc?10000, 0.6?n_o?1.6, 0.1?k?50 and 0.2?Φ?0.6. For shear-thinning fluids (n_o<1), the rate of mass transfer is somewhat enhanced whereas for shear-thickening fluids (n_o>1), it decreased as compared to that in Newtonian fluids (n_o=1). A simple predictive correlation has been proposed which can be used to estimate the rate of mass transfer in liquid-liquid systems in a new application involving power-law continuous phase.     

Low to moderate Peclet mass transport in assemblages of spherical particles for a realistic adsorption-reaction-desorption mechanism

A theoretical model and the associated numerical simulations for the mass transport from a moving Newtonian fluid to an assemblage of spherical solid absorbers are presented here. In particular, we present results from the numerical solution of the convection-diffusion equation in the simplified sphere-in-cell geometry and in stochastically constructed 3-D spherical particle assemblages for low to moderate Peclet numbers (Pe < 100) and relatively high porosities (? > 0.7). A realistic adsorption/reaction/desorption mechanism is used to describe the adsorption of diluted mass on the particles surface as opposed to the assumption of instantaneous and Langmuir-type adsorption that has been adopted in previous works. We also attempt to compare the effect of considering different sorption mechanisms in terms of adsorption efficiency. In all cases, the adequacy of the simplified sphere-in-cell approach is tested against the predictions from the numerical study in sphere assemblages. It is found that higher adsorption efficiencies correspond to lower porosities while increasing Peclet numbers lead to lower λ₀ values. Finally, it is shown that the assumption of instantaneous adsorption leads to severe overestimation of the adsorption efficiency in comparison with that obtained by using the more realistic adsorption-reaction-desorption model.     

Mass transfer from a single fluid sphere to power-law liquids at moderate Reynolds numbers

The steady-state convective inter-phase mass transfer from a single Newtonian fluid sphere (free from surfactants) to a continuous phase with power-law viscosity has been studied at moderate Reynolds and Schmidt numbers under the conditions when the resistance to mass transfer in the dispersed phase is negligible. The species continuity equation, segregated from the momentum equations of both phases, has been numerically solved using a finite difference method. The effects of the Reynolds number (Re_o), power-law index (n_o), internal to external fluid characteristic viscosity ratio (k) and Schmidt number (Sc) on the local and average Sherwood number (Sh) have been analysed over the following ranges of conditions: 5?Re_o?200, 0.6?n_o?1.6, 0.1?k?50 and 1?Sc?1000. It has been observed that irrespective of the values of the Reynolds number and of the power-law index, as the value of k increases the average Sherwood number decreases for intermediate to large values of the Peclet number. As the value of the power-law index increases, the rate of mass transfer decreases for all values of the Reynolds number and the characteristic viscosity ratio thereby suggesting that shear-thinning behaviour facilitates mass transfer, whereas shear-thickening behaviour impedes it. Based on the present numerical results, a simple predictive correlation is proposed which can be used to estimate the rate of inter-phase mass transfer of a fluid sphere sedimenting in power-law liquids.     

Numerical investigation of hydrodynamics and mass transfer for in-line fiber arrays in laminar cross-flow at low Reynolds numbers

In this work, mass transfer at the shell side of an in-line hollow fiber array subjected to cross-flow is simulated by applying the domain decomposition method combined with orthogonal grid generation. Two-dimensional Navier-Stokes equations written in stream function-vorticity variables, were separately solved along with a species conservation equation for different arrays. The main factors influencing the concentration fields, local mass transfer rates and global mass transfer rates in the laminar flow of Re=10-200 and Pe=10-300 with pitch to tube diameter ratios of 1.45, 1.50, 1.75, 1.85 and 2.00 are discussed in detail. Mass transfer correlations obtained from the numerical simulations show good agreement with typical empirical correlations proposed earlier.     

Mass/heat transfer from a neutrally buoyant sphere in simple shear flow at finite Reynolds and Peclet numbers

Theoretical analyses of mass/heat transfer from a neutrally buoyant particle in simple shear flow indicate that mass/heat must diffuse across a region of closed streamlines of finite thickness at zero Reynolds number, whereas spiraling streamlines allow the formation of a thin mass transfer boundary layer at small but non‐zero Reynolds numbers (Subramanian and Koch, Phys Rev Lett. 2006;96:134503; Subramanian and Koch, Phys Fluids. 2006;18: 073302). This article presents the first numerical results for mass/heat transfer at finite Reynolds and Peclet numbers. The simulations indicate that fluid particles in the flow‐gradient plane spiral away from the particle for Reynolds numbers smaller than about 2.5 while they spiral toward the particle for higher Reynolds numbers. Solutions of the Navier‐Stokes equations coupled with a boundary layer analysis of mass transfer yield predictions for the rate of mass transfer at asymptotically large Peclet numbers and Reynolds numbers up to 10. Simulations of mass transfer for zero Reynolds number and finite Peclet numbers confirm Acrivos' (Acrivos, J Fluid Mech. 1971;46:233–240) prediction that the Nusselt number approaches a finite value with increasing Peclet number. Simulations at finite Reynolds numbers and Peclet numbers up to 10,000 confirm the theoretical predictions for the concentration gradient at the particle surface at angular positions away from the flow‐gradient plane. However, the wake near the flow‐gradient plane remains too large at this Peclet number to yield a quantitative agreement of the overall rate of mass transfer with the theory for asymptotically large Peclet number. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Effect of blockage on drag and heat transfer from a single sphere and an in-line array of three spheres

The effect of blockage ratio on the steady flow and heat transfer characteristics of incompressible fluid over a sphere and an in-line array of three spheres placed at the axis of a tube has been investigated numerically. The Navier-Stokes and thermal energy equations have been solved numerically using FLUENT for the following ranges of parameters: for a single sphere, 2 ≤ β ≤ 10; 1 ≤ Re ≤ 100; for the three-sphere system, for two values of sphere-to-sphere distance, namely s = 2 and 4. All computations were carried out for two values of the Prandtl number, i.e., 0.74 and 7, corresponding to the flow of air and water respectively. Extensive results on streamline patterns, wake characteristics (angle of separation and recirculation length), drag coefficient and Nusselt number are presented to elucidate the interplay between the blockage and the Reynolds number and their influence on drag and Nusselt number.     

On the interfacial mass transfer and the location of the chemical reaction in a fluid/fluid reacting system at elevated temperatures and pressures

In a two-phase (supercritical fluid–fluid) system, the rate of conversion of a bimolecular reaction A+B→AB reacting in the layer adjacent to the interface and in the bulk phase was determined. The mass transfer associated with the chemical reaction was measured in a stirred and thermostatically controlled cell varying reaction temperature, pressure and stirring speed. As model system, the Diels–Alder reaction between 9-hydroxymethylanthracene and maleic acid was chosen in the solvent pair supercritical propane/water. The cell was developed for high pressures and temperatures. The reaction was monitored in both phases with on line UV-spectroscopy. The experimental results are compared to simulated data obtained by using a film model. An improved theoretical model describing the changes in concentration of the reactants in the two phases is presented.     

Re-evaluation of the Nusselt number for determining the interfacial heat and mass transfer coefficients in a flow-through monolithic catalytic converter

The two-equation porous medium model has been widely employed for modeling the flow-through monolithic catalytic converter. In this model, the interfacial heat and mass transfer coefficients have been usually obtained using the asymptotic Nusselt and Sherwood numbers with some suitable assumptions. However, previously it seemed that there existed some misunderstanding in adopting these Nusselt and Sherwood numbers. Up to now, the Nusselt number based on the fluid bulk mean temperature has been used for determining the interfacial heat and mass transfer coefficients. However, the mass and energy balance formulations in the two-equation model indicate that the Nusselt number should be evaluated based on the fluid mean temperature instead of the fluid bulk mean temperature. Therefore, in this study, to correctly model the heat and mass transfer coefficients, the Nusselt number based on the fluid mean temperature was newly obtained for the square and circular cross-sections under two different thermal boundary conditions (i.e., constant heat flux and constant temperature at the wall). In order to do that, the present study employed the numerical as well as analytical method.     

Hydrodynamic and mass transfer performance of a new aero-ejector with its application to VOC abatement

The aero-ejector, an in-house developed gas-liquid contactor, ensures an improved gas-liquid contact, favorable to a high mass transfer in a small volume: its transfer capacity enables the elimination of 90% of pollutants from gaseous effluents in a single treatment. Through its characteristics, its use as a transfer device into a treatment process has distinct advantages. However, such an application needs modifications to make the contactor suitable for use in an industrial context (efficiency, compactness and low pressure drop). The aim of this research is to improve the contactor geometry in order to enhance its performances. Modifications have resulted in an energy improvement since an inlet gaseous pressure of was reached for a Q_G/Q_L ratio in excess of 10 and with a small loss of transfer efficiency. The study of the effect of operating parameters has identified a sizing criterion, the “useful volume”. This can be used to determine an optimal configuration for the gas-liquid contactor taking into account constraints such as pollutant solubility, pressure drop or compactness.     

Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model

Using an illustrative sphere packing assembly, it is demonstrated that flow structure and wall heat transfer patterns in low aspect ratio fixed bed reactors are more realistically modelled by properly accounting for the discrete void fraction variations. A 3D network-of-voids (NoV) model has been devised to characterise and examine the discrete flow and heat transfer phenomena in a low aspect ratio packed bed with d_t/d_p = 1.93. The model as formulated is deliberately designed to be not too complicated so as not to place severe demands on computational resources. Hence, the model can potentially easily be applied to simulate the typically large sets of tubes (often comprising more than 10,000) in the case of industrial multi-tubular reactors, where every tube is different due to the random insertion of the packing particles. Because of its simplicity, the model offers an opportunity of coupling the individual catalyst pellet level transport with the complex interstitial flows at the reactor scale. Illustrative studies of this NoV model on a random packed bed of spheres predict large variations of discrete in-void angular velocities and consequently wall heat transfer coefficients within a single tube. The wide variations of wall heat transfer coefficients imply that the different angular sections of the tube will transfer heat at radically different rates resulting in potentially large temperature differences in different segments of the tube. This may possibly result in local temperature runaway and/or hot spot development leading to several potentially unanticipated consequences for safety and integrity of the tube and hence the reactor. The NoV model predictions of the overall pressure drop behaviour are shown to be consistent with the quantitative and qualitative features of correlations available in the literature.     

Effect of high pressure on mass transfer kinetics of granny smith apple

The mass transfer kinetics during osmotic dehydration of granny smith apple slices in 60 Brix fructose and sucrose solution was studied at atmospheric pressure and at elevated pressure of 200–600?MPa at 40°C. The moisture and solute fractions in apple slices during osmotic dehydration under high pressure were predicted by Weibull frequency distribution model. The calculated effective moisture diffusivity values of apple slices suspended in fructose and sucrose solution during high-pressure treatment (0.1–600?MPa) were in the range of 6.35?×?10^?10 to 3.60?×?10^?9?m²/s and 7.96?×?10^?10 to 4.32?×?10^?9?m²/s, respectively.     

Effect of fluid rheological properties on mass transfer in a bioreactor

Rheological properties and oxygen mass transfer coefficient (k_L a) were investigated in a stirred reactor (10 dm³) in the course of fermentations producing microbial polysaccharides—pullulan and xanthan. The fermentation broths behaved as pseudoplastic non-Newtonian fluids in both cases. Studies on the relationship between fluid rheological properties and k_L a were also carried out. The oxygen mass transfer coefficient decreases during the fermentation and exponential equations have been obtained to describe the relationship between the oxygen mass transfer coefficient, the agitation speed and the apparent viscosity of the broths. Furthermore, comparison of results between pullulan and xanthan fermentations was investigated. For the xanthan fermentation process, mixing and mass transfer in the reactor were more difficult than those for the pullulan fermentation.     

高级氧化耦合撞击流技术强化废水降解过程的数值模拟

为了探讨应用撞击流技术强化废水高级氧化降解过程,采用控制容积数值分析法通过FLUENT软件分别模拟了气相和液相单相撞击流的流场,为模拟气液两相流的撞击流流场,建立了k1-ε1-kb-εb双流体数学模型,并模拟了气液双流体撞击过程.模拟结果表明,撞击过程形成强烈的湍动,为强化传递提供很好的条件.气液撞击过程中强烈的相互渗...     

Effect of pitch-to-diameter ratio on the natural convection heat transfer of two vertically aligned horizontal cylinders

Natural convection heat transfer experiments were conducted for two parallel horizontal cylinders using various pitch-to-diameter ratios (P/D) from 1.02 to 9 for the Prandtl numbers between 2014 and 8334 and Rayleigh numbers between 7.3×10⁷ and 4.5×10¹⁰. Based upon analogy concept, mass transfer rate were measured instead of heat transfer rates by measuring the limiting current of the cathodic deposition of copper from acidified copper sulfate solution. The mass transfer rates for the lower cylinders were unaffected by the presence of the upper cylinders, and agreed well with the prediction from existing heat transfer correlations developed from a single horizontal cylinder. The Nusselt number ratios of the upper to lower cylinders increased with P/D. The ratios were less than 1 at P/D values less than about 1.5 for laminar flows, but the ratios were almost 1 at a P/D very close to 1 for turbulent flows. The variation of the ratios with P/D becomes steep with higher Prandtl numbers, which is confirmed by numerical simulations using the FLUENT program. The plating pattern that appeared on the surface of the cylinder revealed local mixed convection heat transfer. The area covered by thin lines, denoting the flow separation on top of the upper cylinder, increased for laminar but decreased for turbulent flow due to the laminarization phenomena in turbulent mixed convection.     

Two-point Padé approximation of mass transfer rate at microdisc electrodes in a channel flow for all Péclet numbers

The problem of mass transfer at a microdisc electrodes placed in a parabolic steady channel flow is considered. Under suitable conditions, the transfer rate depends only on the Péclet number (a dimensionless measure of shear rate) and on the geometry of the electrode. We present a calculation of the mass transfer rate for a disc electrode for all Péclet number using two-point Padé approximations. The results are compared with existing analytical and experimental results.     

Ionic mass transfer measurements in the case of submerged multijets impinging on to a flat surface

In the case of submerged multijets impinging on to a flat surface, the limiting current densities were measured at microelectrodes, fixed flush with the target surface using diffusion controlled electrode reactions (i.e. reduction of ferricyanide ion). The height of the multijet distributor from the target surface (Y) was varied from 5 to 9 cm. The numbers of holes of the distributor (N) studied were 76 and 141. The variation of mass transfer data with radial distance reveals the existence of two different regions, i.e. the impingement region and the wall jet region. The mass transfer rate increased with increase in Y in the impingement region. The effect of Y is negligible in the wall jet region. Decrease in N decreases the mass transfer rate in both the regions. The data are correlated separately for the two regions.     

Effect of surfactants on liquid-side mass transfer coefficients in gas-liquid systems: A first step to modeling

This paper focuses on the effect of surfactants on the mass transfer parameters (volumetric mass transfer coefficient k_La and liquid-side mass transfer coefficient k_L). Tap water and aqueous solutions with surfactants (anionic, cationic and non-ionic at concentrations up to are used as liquid phases. The bubbles are generated into a small-scale bubble column having an elastic membrane with a single orifice as gas sparger. To understand the effects of the surfactants on the mass transfer, not only the static surface tension is used, but also the characteristic adsorption parameters like the surface coverage ratio at equilibrium Se. The liquid-side mass transfer coefficient is obtained from the ratio of the volumetric mass transfer coefficient (measured by a chemical method) and the specific interfacial area. These two parameters are obtained simultaneously. The methods used to obtain these parameters are described in Painmanakul et al. [2005. Effects of surfactants on liquid-side mass transfer coefficients. Chemical Engineering Science 60, 6480-6491].Whatever the liquid phase, three zones are found on the liquid-side mass transfer coefficient variation with the bubble diameter. For bubble diameters less than 1.5 mm, whatever the liquid phases, the k_L values are roughly constant at . For bubble diameters greater than 3.5 mm, the k_L values do not vary much with the bubble diameter, but depend on the surfactant concentration. For bubble diameters between 1.5 and 3.5 mm, the k_L values increase from to the value reached at 3.5 mm. This increase depends on the surfactants. Higbie's model does not represent the k_L values for bubble diameters greater than 3.5 mm, even though there is a small amount of surfactant in the liquid phase. Thus, a model is proposed for each zone described above. Explanations are also proposed for the effect of the surfactant on the k_L values for each of the above zones.     

Effects of surface-active agents on mass transfer of a solute into single buoyancy driven drops in solvent extraction systems

Numerical simulation was made of transient mass transfer to a surfactant contaminated buoyancy-driven drop controlled by appreciable resistance in both liquid phases. For this purpose, the momentum equations were formulated and solved in a boundary-fitted orthogonal coordinate system. On the basis of resolved hydrodynamics of the contaminated drop, the transient mass transfer was formulated and solved in the same coordinate system. In order to check the applicability of the numerical scheme, single drop extraction experiments were conducted in a totally closed droplet file column with the terminal effect efficiently eliminated. The MIBK-acetic acid-water system was used with small quantities of SDS (sodium dodecyl sulphate), Triton X-100, or Tween 80 introduced into the continuous phase. For these experimental cases, the flow field and the drag coefficient of a contaminated drop were simulated first. The numerical prediction of the drag coefficient is found in good agreement with the corresponding experimental data. It illustrates that the behavior of a drop approaches that of a rigid sphere and that about 100 times higher bulk concentration of SDS than that of Triton X-100 is required for the same extent contamination of a MIBK drop of the same size. Then the information of the flow field of a contaminated MIBK drop was used in simulating the transient mass transfer of solute into the drop. The resulted extraction fraction and overall mass transfer coefficient are in reasonable coincidence with the experimental data. Both numerical results and experimental data show that overall mass transfer coefficient of a heavily contaminated drop is only about one third of that in the pure system. This can be explained well by the distribution of the local Sherwood number, which drops down abruptly along the rear stagnant surface. Also the interfacial resistance of adsorbed surfactant was incorporated in the mass transfer model and then estimated by the least square fitting the simulation with data. The numerical results also show that Tween 80 presents obvious interfacial resistance on the acetic acid diffusing across the interface, whereas SDS and Triton X-100 show no interfacial resistance. It is suggested that the numerical simulation can be resorted in some solvent extraction systems containing surfactants to conduct numerical experiments and parametric study.     

Bubble coalescence at sieve plates: II. Effect of coalescence on mass transfer. Superficial area versus bubble oscillations

Bubble columns are among the most used equipments for gas-liquid mass transfer processes. This equipment's aim is to generate gas dispersions into a liquid phase in order to improve the contact between phases. Bubble coalescence has always been one of their greatest problems, since it reduces the superficial gas-liquid contact area. However, bigger bubbles can oscillate, and these oscillations increase the mass transfer rate by means of modifying the contact time as well as the concentration profiles surrounding the bubble. In the present work, the coupled effect has been studied by means of two-holed sieve plates with diameters of 1.5, 2 and 2.5 mm each, close enough to allow the coalescence and separated enough to avoid it. The results show that although coalescence decreases mass transfer rate from bubbles the deformable bubble generated can, in certain cases, balance the decrease in mass transfer rate due to the reduction in superficial area. This fact can then be used to avoid the harmful effect of coalescence on the mass transfer rate. Empirical and theoretical equations have also been used to explain the phenomena.