Sherwood number in porous microtube due to combined pressure and electroosmotically driven flow

Mass transfer of a neutral solute in a porous microtube is quantified in this study. An analytical expression of the Sherwood number is developed from first principles for combined flow of pressure driven and electroosmotic flow. Similarity solution method is adopted for solution of convective-diffusive species balance equation with coupled velocity profile, within the mass transfer boundary layer. It is observed that the Sherwood number increases with decrease in the Debye length (as the electric double layer becomes more compact) and it becomes constant beyond scaled Debye length of 60. Effects of the Reynolds number, dimensionless suction velocity, ratio of driving force and scaled Debye length have been investigated in detail. The analysis is useful for efficient design of microfluidic devices and flow through porous media.     

Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid: Natural Convection Dominated Regime

A boundary layer analysis is presented for the mixed convection past a vertical wedge in a porous medium saturated with a nano fluid. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient, implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the velocity, temperature, and nanoparticles volume fraction profiles, as well as the friction factor, surface heat and mass transfer rates have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) on these parameters has been discussed.     

Détermination électrochimique du nombre de sherwood minimum pour un milieu macro‐poreux (fritté — lit fixe de grains)

In this work, an electrochemical method used for the determination of solid‐liquid mass transfer coefficients has been applied to the measurement of the Sherwood number for the stationary diffusional mass transfer between a porous material and a stationary liquid in the pores. Such a minimum Sherwood number was determined for sintered metals and for fixed beds of spherical grains. The theoretical aspects are based on the analogy of the problem with competition between molecular diffusion and heterogeneous chemical reaction in a porous catalyst.     

微通道中钒的液-液流型和萃取传质动力学研究

采用伯胺N1923萃取剂在微通道中研究V(V)的液-液流型和萃取传质动力学,以15vol% N1923作为连续相、钒氧酸根水溶液作为分散相,研究不同流速下两不混溶相的流型变化规律及两相停留时间和微通道管径作为流速的函数对传质的影响。随两相流速增大,段塞流长度和比界面面积基本不变,且两相流体由Raydrop微通道流入外接毛细管微通道时由于微通道的扩张会改变两相流动方式,使同一实验条件下在微通道中同时出现多种流型,与此同时两相流速和总体积传质系数(kLa)呈正相关,表明流型在本研究体系中对传质的影响可忽略。在相同管径通道内,停留时间与总体积传质系数呈负相关,表明在两相接触通道入口处发生了显著传质。在相同的两相混合速度和相比下,254 μm的管径传质效果是750 μm的9倍,表明小管径内传质效果更加,循环强度更大。最后将实验总体积传质系数结果与总体积传质系数的经验式进行了关联,有望为实现将微通道放大的绿色冶金技术提供理论基础。     

绕流具有光合生化反应管束的格子Boltzmann模拟

采用格子Boltzmann方法模拟了有机废水溶液绕流表面附着有光合生物膜管束的流动、传质及光合生化反应过程,并分析了管束排列,管间距及Reynolds数对流场、浓度场、平均阻力系数及底物的Sherwood数的影响。结果表明：溶液绕流小管间距时具有较高的Sherwood数,同时阻力系数也较高;与顺排管束相比,绕流叉排管束的平均Sherwood数增大了一倍左右,其增大幅度随Re的增大而增大,而阻力系数仅增大了约10%。一定条件下,绕流叉排管束时,出口处具有较低的底物浓度和较高的产物浓度。结果表明,很小的流场扰动可对浓度场产生较大影响,从而,叉排管束更有利于传输传质及生物降解。     

小曲率蛇形微通道弯头处弹状流流动及传质特性的数值研究

采用CLSVOF（coupled level set and volume of fluid）方法,以空气和水为工作流体对小曲率矩形截面蛇形微通道内气液两相流动进行模拟研究。验证模型的合理性后,研究了曲率对弯通道内压降的影响,曲率及气相速度对弹状流气泡及液塞长度的综合影响;同时深入分析了弯管内气液两相流动的传质特性,包括不同曲率下气泡长度的变化,弯管内液侧体积传质系数与液膜体积传质系数的比较,曲率及气相速度对液相体积传质系数的影响。同时,对比了回转弯道与直微通道传质系数的差异,发现弯微通道可以强化传质。     

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.     

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

A two‐dimensional advection‐diffusion model accompanied with a parabolic velocity profile of Poiseuille flow is considered for the chemical species transport in a tube with a constant wall concentration. The Reynolds decomposition technique is applied to reduce it to an equivalent one‐dimensional model for advective‐dispersive transport in a tube through which the effective advection coefficient, the dispersion coefficient, and the effective Sherwood number are developed for the problem under study. The derived and the classical Taylor models are also compared in order to find the difference between the two arrangements. The reduced‐order model for the transport equation shows that the effective advection coefficient increases, whereas the dispersion coefficient in the tube decreases as compared to the classical Taylor equation. The effective Sherwood number for the steady state form of the developed model is found to be only a function of the Peclet number, which varies in the range of 3.215 ≤ Sh ≤ 4. These results find application in design of experiments and improve our understanding of mass transfer in microfluidic devices.     

Liquid/solid mass transfer in an air-lift loop reactor with a dispersed solid phase

In processes with immobilized cells mass transfer across the boundary layer surrounding the support often plays an important role. Relatively little is known about external mass transfer as a function of the superficial gas velocity in bioreactors such as air-lift loop reactors. In this work ion-exchange resins were used as a solid phase to determine the mass-transfer coefficient in such a reactor. Relations between the Sherwood number and the superficial gas velocity were derived and compared with relations from the literature. Relations in which the Sherwood number is a function of the energy-dissipation rate and relations in which the relative particle velocity is calculated from the rate of free fall of the particle were compared. It was shown that the Sherwood numbers that were functions of the energy-dissipation rates were higher than could be calculated on the basis of the rate of free fall. The Sherwood number obtained was used to calculate the k_l,s of carrageenan gel beads as a solid phase in an air-lift loop reactor. © 1998 SCI.     

具有非均匀内热源的多孔介质中自然对流传热传质的数值研究

采用数值方法分析了具有非均匀分布内热源的竖直同心套管内多孔介质中的传热传质,内热源分布系数M较大时,造成流场中心的逆时针环流向中心挤压。浮力比N由1.5变为-1.5后,流体由顺时针流动变为逆时针流动且流体速度加快。Nusselt数在Z=0.7处出现转折。随M增大内壁面Nusselt数变化范围增大,并且转折点前移。上壁面Sherwood数也呈先增大后减小的趋势,并且在R=0.9处出现转折。     

随机分布纤维束间纵向层流时传质的数值模拟

按层流流动理论模型,对纤维为随机分布的中空纤维膜组件的壳程,在恒定壁面传质量和恒定壁面浓度边界条件下的传质现象进行了数值模拟,并得到了不同装填率下传质Sherwood数关联式。结果表明,纵向层流时,随机分布纤维间的传质仍可分进口段和充分发展段。对于某一给定的纤维束,在传质的充分发展段,传质Sherwood数为一个定值,且较纤维束规则排列时小得多,纤维分布不均一性将导致膜组件的传质能力下降。在传质进口段,传质Sherwood数也较纤维束规则排列时要小,装填率不但对传质系数的关联式Sh=BReaScbf(de/L)的系数B值有影响,且对该式中的Reynolds数的指数a和Schmidt数的指数b值也均有影响。     

Design and operation of gas–liquid slug flow in miniaturized channels for rapid mass transfer

The influences of operating parameters such as channel size, flow rate, and void fraction on the mass transfer rate in the gas–liquid slug flow are investigated to establish a design method to determine the parameters for rapid mass transfer. From the experimental results, the turnover index, including the slug linear velocity, its length, and the channel size that represents the turnover frequency of the internal circulation flow, is proposed. For PTFE tube in which no liquid film exists in slug flow, a master curve is derived from the relationship between the mass transfer coefficient and the turnover index. For each channel material, the Sherwood number is also roughly correlated with the Peclet number. These correlations make it possible to arbitrarily determine a set of operating parameters to achieve the desired mass transfer rate. However, the turnover index and the Peclet number include the slug length, which cannot be controlled directly. The relationship between the slug length and the operating parameters is also investigated. The slug volume mainly depends on the inner diameter (i.d.) of a union tee. At a fixed union tee i.d., the slug length is controlled through the exit i.d. of the channel connected to the union tee and the void fraction. Thus, the final slug length depends on the union tee and exit channel inner diameters. At low flow rates, the gas and liquid collision angle is significant in determining the slug length.     

The effect of the size of square microchannels on hydrodynamics and mass transfer during liquid‐liquid slug flow

The present study investigated the influence of square microchannel (MC) size on hydrodynamics and mass transfer in the liquid‐liquid slug flow regime. Three square MCs with the hydraulic diameters of 200, 400, and 600 μm were used. The employed method for estimating mass‐transfer coefficients remarkably increased the accuracy of the results. The findings revealed that decreasing the MC size improved the interfacial area due to plug length enlargement and deteriorated mass‐transfer resistances because of augmented internal circulations, leading to the considerable enhancement of mass‐transfer coefficients. The increasing effect on the overall mass‐transfer coefficient became greater with flow velocity, showing that size effect on mass‐transfer resistances was more profound at higher flow velocities. The influence of size on the interfacial area was significantly greater than that on mass‐transfer resistances due to the significant increment of wall film length with the decrease in channel size. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Kinetics of Colloidal Particle Deposition to a Solid Surface from Pressure Driven Microchannel Flows

Kinetics of colloidal particles deposition onto a solid surface in hydrodynamic flows was studied. A phenomenological mathematical model was presented to analyze the particle deposition from pressure‐driven flows in a parallel‐plate microchannel. The two‐dimensional mass transport equation incorporating hydrodynamic convection, particle diffusion, gravity force and DLVO colloidal forces (i.e., the van der Waals and electrical double‐layer forces) was solved numerically using a finite difference method to obtain the dimensionless particle deposition rates expressed by the Sherwood number. The numerical predictions of the Sherwood number were compared with the results of videomicroscopic experiments conducted under various physicochemical conditions including electrolyte concentration, particle size and hydrodynamic flow intensity in terms of the Reynolds number, and reasonable good agreement was found.     

Mass transfer of a rising bubble in molten glass with instantaneous oxidation-reduction reaction

The mass transfer around a rising bubble has been studied within the field of glass melting processes. Due to the large value of liquid viscosity, creeping flow was used. The rising bubble is assumed to have a clean interface with a total mobility and the exact solution of Hadamard or Rybczynski was used to define the velocity field around the bubble. The mass transfer of oxygen in the soda-lime-silica glass melt where oxidation-reduction reactions of iron oxides occur is also described.The dimensionless mass transfer coefficient, Sherwood number, was determined as a function of the Péclet number based on the terminal rise velocity of the bubble. Two different techniques have been used: the first based on the boundary layer theory and the second using a finite element method.In order to take into account the oxidation-reduction reaction in a unified framework, a modified Péclet number has been defined as a function of two dimensionless numbers. The first is strongly linked to the equilibrium constant of the chemical reaction and the second is the glass saturation, defined as the ratio of oxygen concentration in the bulk to that at the bubble surface. The Sherwood number, taking into account the chemical reactions, increases with iron content as well as with glass reduction (i.e. small saturation level).From an application point of view, the determination of a modified Péclet number is important because it is possible to use a similar expression (determined without the reaction) by replacing the classical Péclet number by the modified one proposed herewithin.     

MHD MIXED-CONVECTION INTERACTION WITH THERMAL RADIATION AND nTH ORDER CHEMICAL REACTION PAST A VERTICAL POROUS PLATE EMBEDDED IN A POROUS MEDIUM

This article investigates the hydromagnetic mixed convection heat and mass transfer flow of an incompressible Boussinesq fluid past a vertical porous plate with constant heat flux in the presence of radiative heat transfer in an optically thin environment, viscous dissipation, and an nth order homogeneous chemical reaction between the fluid and the diffusing species. The dimensionless governing equations for this investigation are solved numerically by the fourth-order Runge-Kutta integration scheme along with shooting technique. Numerical data for the local skin-friction coefficient, the plate surface temperature, and the local Sherwood number have been tabulated for various values of parametric conditions. Graphical results for velocity, temperature, and concentration profiles based on the numerical solutions are presented and discussed.     

Velocity Distribution inside a Laminated‐Sheet Microchannel Reactor

In a laminated‐sheet microchannel reactor, several microchannel sheets with the same or different structures are mutually laminated together. The effect of microchannel and manifold structure as well as the number of laminated sheets on the velocity distribution among microchannels in each sheet with the same structure is investigated. Results indicate that a large microchannel length, a high‐aspect‐ratio microchannel, and centrosymmetric manifold structure are favorable for a relatively uniform velocity distribution in each sheet. Considering the centrosymmetric manifold structure, a shorter distance from inlet and outlet to microchannels in direction of the microchannel width and a longer distance to the microchannel array in direction of the microchannel length can contribute to a more uniform velocity distribution. The laminated‐sheet number has only a minor impact on the velocity distribution among microchannels in each sheet.     

Numerical study on steady and transient mass/heat transfer involving a liquid sphere in simple shear creeping flow

A numerical method is utilized to examine the steady and transient mass/heat transfer processes that involve a neutrally buoyant liquid sphere suspended in simple shear flow at low Reynolds numbers is described. By making use of the known Stokes velocity field, the convection‐diffusion equations are solved in the three‐dimensional spherical coordinates system. For the mass transfer either outside or inside a liquid sphere, Sherwood number Sh approaches an asymptotic value for a given viscosity ratio at sufficiently high Peclet number Pe. In terms of the numerical results obtained in this work, two new correlations are derived to predict Sh at finite Pe for various viscosity ratios. © 2013 American Institute of Chemical Engineers AIChE J, 60: 343–352, 2014     

Transient gas–liquid mass transfer model for thin liquid films on structured solid packings

This paper describes a model for gas–liquid mass transfer through thin liquid films present on structured packings for gas–liquid operations under dispersed gas flow regime. The model has been derived for two cases: the absorption (or desorption) of a gaseous component into the liquid film and the transfer of the gaseous component through the liquid film to the packing surface where an infinitely fast reaction takes place. These cases have been solved for three bubble geometries: rectangular, cylindrical, and spherical. For Fourier numbers below 0.3, the model corresponds to Higbie’s penetration theory for both cases. The Sherwood numbers for cylindrical and spherical bubbles are 20% and 35% higher, respectively, than for rectangular bubbles. In case of absorption and Fourier numbers exceeding 3, the effect of bubble geometry becomes more pronounced. The Sherwood numbers for cylindrical and spherical bubbles now are 55% and 100% higher, respectively, than for rectangular bubbles. In case of an infinitely fast reaction at the packing surface, the Sherwood number corresponds to Whitman’s film theory (Sh=1$Sh=1$) for all bubble geometries. In this paper also practical approximations to the derived Sherwood numbers are presented. The approximations for both cases and all bubble geometries describe all the model data within an error of 4%. The application of the model has been demonstrated for three examples: (1) gas–liquid mass transfer for a structured packing; (2) gas–liquid mass transfer in a microchannel operated with annular flow; (3) gas–liquid mass transfer in a microchannel with Taylor flow.     

The influence of hydrodynamic and mass transfer entrance effects on the operation of a parallel plate electrolytic cell

Experimental measurements of mass transfer in an electrochemical flow cell of rectangular cross section with different hydrodynamic entrance and electrode lengths have been made. For fully developed flow, average Sherwood numbers under laminar conditions vary with Graetz number to a power 0·30. For turbulent flow, fully developed mass transfer conditions occur about twelve equivalent diameters along the electrode and are best represented by the Chilton-Colburn analogy which predicts Sherwood numbers varying with Reynolds number to a power of 0·8 and Schmidt number to a one-third power. For shorter electrodes Sherwood numbers can be adequately correlated by an expression with Reynolds number to a two-thirds power and dimensionless electrode length to a power of −0·2. For hydrodynamic entrance lengths of not less than eight equivalent diameters, data in the laminar region can be expressed by an emperical boundary layer type of equation which includes terms for the hydrodynamic entrance length and electrode length. In the turbulent regime substantially developed flow occurs after eight entrance lengths and correlations with fully developed flow equations are satisfactory