Depletion of cross‐stream diffusion in the presence of viscoelasticity

An effort to analyze the viscoelasticity effects on transverse transport of neutral solutes between two miscible streams in an electrokinetic T‐sensor is presented. The analysis is based on an approximate analytical solution for the depthwise averaged concentration, assuming a channel of large width to depth ratio for which a one‐dimensional profile is sufficient for describing the velocity field. We show that the solution derived is surprisingly accurate even for very small channel aspect ratios and the maximum error reduces to only about 1% when the aspect ratio is 5. The developed model reveals that the mixing length for a viscoelastic fluid may be by far larger than that for a Newtonian fluid. Moreover, the Taylor dispersion coefficient for electroosmotic flow of viscoelastic fluids, which its determination is a main part of the analysis, is found to be an increasing function of both the elasticity level and the EDL thickness. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4533–4541, 2015     

Bridging the gap between Graetz's and lévêque's analyses for mass/heat transfer in a channel with uniform concentration or flux at the wall

A new approximate solution which bridges the gap between the classical theories of Graetz and Lévêque for heat/mass transfer in channel flow is presented. The results include expressions, uniformly valid in the axial direction, for the mixing‐cup concentration (or temperature) profile 〈c〉 when transport towards the wall is slow (Dirichlet limit), and for the Sherwood number Sh when the wall flux can be considered uniform (Neumann limit). The technique employed provides insight into the mathematical structure of both quantities 〈c〉 (or conversion X_R) and Sh identifying explicitly the contributions from fully developed and developing behaviors, while maintaining accuracy in the transition region. Criteria to bound the different convection‐diffusion regimes are suggested, which critically systematize previous results. These results are important for model selection in the design and simulation, among others, of heat exchangers and wall‐coated microreactors where fast heterogeneous reactions occur. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1880–1892, 2012     

Numerical investigation of spinneret geometric effect on spinning dynamics of dry‐jet wet‐spinning of cellulose/[BMIM]Cl solution

In this study, the effect of spinneret geometry, including the entrance angle α of the entrance channel, the length L_s, and the diameter D₀ of the exit channel, on the spinning dynamics of dry‐jet wet‐spinning of cellulose/1‐butyl‐3‐methylimidazolium chloride ([BMIM]Cl) solution was simulated by using finite element method. Based on the mathematical model of dry‐jet wet‐spinning established in our previous work (Xia et al., Cellulose 2015, 22, 1963) the radial and axial profiles of velocity, pressure, and shear rate in the spinneret and the profiles of diameter, temperature, and tensile stress in the air‐gap region were obtained. From the simulated profiles, the effect of spinneret geometric parameters on the flow behavior and the pressure drop of polymer solution in the spinneret and the die‐swell ratio near the spinneret was discussed. The entrance angle α of the entrance channel mainly influences the flow behavior of polymer solution in the spinneret and the die‐swell effect near the spinneret. As the decrease of the entrance angle α of the entrance channel, the vortices in the spinneret could be removed and the die‐swell ratio decreases. The increase of the length L_s of the exit channel results in the increase of pressure drop in the spinneret and the decrease of the die‐swell ratio. It is also found that the increase of the diameter D₀ of the exit channel reduces the flow velocity of polymer solution and decreases the pressure drop in the spinneret at a constant mass flow rate. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43962.     

Development of Two‐point Dynamic Method for Evaluating Extraction Columns

The steady‐state method by measuring the concentration profile along the column height is an effective way, but it is a time and material consumption method for large extraction columns. In order to investigate the axial‐mixing and mass transfer performances in a large pulsed‐sieve‐plate extraction column with the diameter of 150mm, a two‐point dynamic method with mass transfer based on the diffusion model has been developed. The results proved that the two‐point dynamic method has the advantages of good accuracy, simple boundary equations and flexible sampling position over the traditional single‐point dynamic method. It is a reliable tool for studying the axial‐mixing and the mass transfer performances.     

Peak Capacity in Field-Flow Fractionation

Abstract

Field-flow fractionation (FFF) peak capacity values have been computed with only two major assumptions: first, the plate height is supposed the sum of only two contributions, axial molecular diffusion and transversal nonequilibrium, and second, the steric effect has been neglected in the equations of retention and peak broadening.

Several reduced parameters have been defined to generalize the equations and limit the number of variable parameters. It appears that among the already implemented FFF subtechniques for which the elution spectrum is an explicit function of the principal dimension, or mass, of the retained sample (which excludes electrical FFF), sedimentation FFF has some peculiar characteristics due to the fact that the field-induced velocity depends on a particular sample, while in thermal and flow FFF it is the same for all samples of a given type under fixed experimental conditions. For example, in sedimentation FFF, the axial diffusion contribution to the plate height persists at a much larger reduced eluant velocity than for the other techniques.

The effect on the peak capacity of the retention volume, the channel length, the eluant velocity as well as the influence of detection limit and analysis time have been studied. Simple relationships between peak capacity and these parameters are established in the high retention and negligible axial diffusion limits which previal in most experimental situations, and deviations from these limits are discussed. It is shown that for all three     

Deposition of particles in a parallel-plate channel due to electrostatic charge,diffusion and gravitational effects

The deposition of fine particles in channel flow due to the effects of electrostatic charge and diffusion and due to charge and gravity in the direction of flow with uniform and parabolic velocity profiles was investigated using a finite difference analysis. The variations in deposition were determined using an axial parameter which includes a ratio of the electrostatic charge to the diffusion effect. These results were determined along the channel for various values of electrostatic charge.The deposition due to diffusion and charge effect was studied and the range of charge effect was determined for which the diffusion effect may be neglected.Also, the deposition due to charge and gravity was investigated to determine the effect of the velocity profile on the deposition.     

Effect of channel size on liquid‐liquid plug flow in small channels

The hydrodynamic properties of plug flow were investigated in small channels with 0.5‐, 1‐, and 2‐mm internal diameter, for an ionic liquid/aqueous two‐phase system with the aqueous phase forming the dispersed plugs. Bright field Particle Image Velocimetry combined with high‐speed imaging were used to obtain plug length, velocity, and film thickness, and to acquire velocity profiles within the plugs. Plug length decreased with mixture velocity, while for constant mixture velocity it increased with channel size. Plug velocity increased with increasing mixture velocity and channel size. The film thickness was predicted reasonably well for Ca > 0.08 by Taylor's (Taylor, J Fluid Mech. 1961;10(2):161–165) model. A fully developed laminar profile was established in the central region of the plugs. Circulation times in the plugs decreased with increasing channel size. Pressure drop was predicted reasonably well by a modified literature model, using a new correlation for the film thickness derived from experimental values. © 2015 American Institute of Chemical Engineers AIChE J, 62: 315–324, 2016     

Fully developed mixed convection of a binary fluid in a vertical porous channel

This paper reports an analytical and numerical study of mixed convection heat and mass transfer of a binary fluid in a vertical parallel plate channel filled with a porous medium. The thermal conditions applied on the walls of the system are uniform heat fluxes. Both the cases of double‐diffusion and Soret‐induced convection are considered. The governing equations for the porous medium rely on Darcy's model. The governing parameters for the problem are the Rayleigh number, Ra, Peclet number, Pe, Lewis number, Le, buoyancy ratio, φ, aspect ratio of the channel $A = L'/H'$ and the constant a (a = 0 for double diffusive convection and a = 1 for Soret induced convection). The resulting problem, in the limit of fully developed mixed convection, is solved analytically in closed form. A numerical solution of the full governing equations is demonstrated to be in good agreement with the analytical model. The temperature and velocity fields and the Nusselt and Sherwood numbers are obtained in terms of the governing parameters. The possible existence of reversed flows in the channel is discussed. © 2011 Canadian Society for Chemical Engineering     

Liquid‐Solid Mass Transfer Behavior of a Stirred‐Tank Reactor with a Fixed Bed at Its Bottom

The mass transfer behavior of a new batch stirred tank with a fixed bed of Raschig rings at the bottom was studied using diffusion‐controlled dissolution of copper in acidified dichromate. Variables studied, amongst others, were the impeller rotation speed, Raschig ring diameter, fixed‐bed height, and impeller geometry. The rate of mass transfer from the fixed bed to the solution increased with increasing impeller rotation speed, decreasing particle size, and decreasing bed height. The axial‐flow turbine is more efficient in increasing the rate of mass transfer than the radial‐flow turbine. The presented reactor is especially useful for conducting diffusion‐controlled liquid‐solid catalytic reactions involving reactants that need to be dispersed first, such as sparingly soluble solid particles.     

Solution properties of comb‐like polymers consisting of dimethylsiloxane monomer units

A series of comb‐like polymers consisting of dimethylsiloxane monomer units and differing by side‐chain length have been studied in hexane solution using analytical ultracentrifugation, translational diffusion and viscometry. Analysis of the hydrodynamic parameters and their molar mass dependences based on the Fixman–Stockmayer theory or wormlike spherocylinder model shows that with side chain lengthening, the Kuhn segment length A of the polymers under study increases from the value of A for linear polydimethylsiloxane to values typical for semi‐rigid chain polymers A = 8–10 nm. © 2016 Society of Chemical Industry     

The chemical reactor omnibook : by Octave Levenspiel,published by Oregon State University Bookstores,Corvallis, OR 97330, U.S.A. 1979; 670 pp., $20.00 + $1.75 p&p.

The deposition of aerosols with gravity in a vertical channel from the inlet to a distance of 50 channel widths was investigated numerically for developing, fully developed, and uniform laminar flows. The relative importance of sedimetation as compared to Brownian diffusion was determined by the parameter σ = v_gh/D where v_g is the settling velocity, h is half the channel width and D the particle diffusivity. A finite difference solution was found for the concentration distribution whereby various values of σ are presented for the penetration over the axial distance.     

Boundary layer flows with Dufour and Soret effects: I: Forced and natural convection

Similarity solutions of laminar boundary layer flows in forced and natural convection are examined aiming at the evaluation of the coupled effects of heat and mass transport. Momentum, energy and mass balance equations are simultaneously solved under the assumption of the validity of constitutive equations for the heat and mass fluxes of dilute solutes obeying linear forms in accordance with the thermodynamics of irreversible processes. Forced and natural convection cases depend on different similarity variables, with different exponents for the axial variable and different significant physical properties compose the pertinent dimensionless groups. In the first part of this paper thermal diffusion and diffusion thermo effects are studied for the boundary layer flows about a vertical flat plate in forced and in natural convection, separately. The second part deals with the intermediate cases of non-similar of mixed convection, where it is determined by a one-parameter family of transformations (0???1), which reduce to both extreme cases. The mixed convection will be presented in a forthcoming continuation. A modification of the method of solution based on Adomian's polynomials for the resulting boundary value problem is employed.     

Investigating dry reforming of methane with spatial reactor profiles and particle‐resolved CFD simulations

Dry reforming of methane (DRM) over nickel in a fixed‐bed reactor of spheres was studied experimentally and with CFD simulations. Temperature and mole fraction profiles were measured in a dedicated profile reactor as function of axial coordinate. Particle‐resolved CFD simulations took into account conjugate heat transfer, surface‐to‐surface radiation, and surface reactions described by microkinetics. Energy transport of CFD simulations were verified by studying heat transfer without chemical reactions. DRM experiments could not be reproduced with the original microkinetics formulation, even with the axial temperature profile applied. A detailed analysis of the microkinetics showed that thermodynamic inconsistencies are present, which are amplified by high surface coverage of CO*. After modifying the mechanism the experiments could be reproduced. This study shows how complex interactions between local transport phenomena and local kinetics can be quantified without relying on transport correlations. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4436–4452, 2016     

Wall-flow filters with wall-integrated oxidation catalyst: A simulation study

Diesel soot abatement via diesel particulate filters composed of so-called wall-flow monoliths is well established. Today, due to recent improvements in the production technology full-featured catalyst functionality can be implemented in the filter walls.

This work focuses on a comparison of the reactor performance of the wall-flow filter and the conventional flow-through monolith. To this end a two-dimensional numerical model is set up for each of the two reactor configurations.

Concentration profiles in the wall-flow filter systematically change as a function of flow velocity.

At high flow velocities transport from the inlet channel into the porous wall is nearly entirely dominated by convection. This leads to uniform axial concentration profiles in the inlet and outlet channel and a steep gradient in the porous wall.

At low velocities radial transport into the porous wall is dominated by diffusive transport. This leads to a negligible radial concentration gradient between the inlet and the outlet channel.

Under most operating conditions relevant for an automotive exhaust catalyst the flow velocity is in an intermediate range with contributions of diffusive and convective transport.

The transition from entirely convection dominated transport at high space velocities to increasingly diffusion dominated transport at lower flow velocities is similarly found for first order kinetics and a generalized Langmuir–Hinshelwood–Hougen–Watson (LHHW) rate law.

Wall-flow filters show systematic conversion advantages over the conventional monolith for a first order reaction. For a reaction with LHHW-type kinetics this effect is not generally observed. It is one major result of this work that the relative performance of the two reactor configurations depends on the kinetics of the catalyzed reaction.     

Axial pressure profile in circulating fluidized beds

Design and operation of a circulating fluidized bed requires the knowledge of fluid mechanics. According to heat and mass transfer as well as chemical reactions, the effect of the set superficial gas velocity on the axial pressure profile is of particular interest. The axial pressure profile was measured for a variety of solids, as a function of the superficial gas velocity, in a cylindrical circulating fluidized bed with an inner diameter of 0.19 m and an overall height of 11.5 m. Depending on the solids content and superficial gas velocity, two or one sections can be observed in the plant where the pressure gradient is constant. A pressure profile with one pressure gradient exists only at high gas velocities, so long as the acceleration pressure drop immediately above the gas distributor is negligible. Comparison of measured pressure drops in circulating fluidized beds with those measured in vertical pneumatic conveying led to a state diagram for vertical gas-solid flows. The operation behaviour of different types of circulating fluidized bed plants can be explained with the aid of this diagram.     

Three-dimensional numerical simulation of straight channel PEM fuel cells

The need to model three-dimensional flow in polymer electrolyte membrane (PEM) fuel cells is discussed by developing an integrated flow and current density model to predict current density distributions in two dimensions on the membrane in a straight channel PEM fuel cell. The geometrical model includes diffusion layers on both the anode and cathode sides and the numerical model solves the same primary flow related variables in the main flow channel and the diffusion layer. A control volume approach is used and source terms for transport equations are presented to facilitate their incorporation in commercial flow solvers. Predictions reveal that the inclusion of a diffusion layer creates a lower and more uniform current density compared to cases without diffusion layers. The results also show that the membrane thickness and cell voltage have a significant effect on the axial distribution of the current density and net rate of water transport. The predictions of the water transport between cathode and anode across the width of the flow channel show the delicate balance of diffusion and electroosmosis and their effect on the current distribution along channel.     

Multicomponent gas diffusion in nonuniform tubes

In many technical processes gas, multicomponent diffusion takes place in confinements that are rarely uniform in direction of their long axis (e.g., catalysts pores). Here, we show that in conical tubes multicomponent diffusion is hindered. This effect increases with ratio of inlet to outlet cone radius Λ, indifferent of the orientation of the tube. Based on the Maxwell–Stefan equations, predictive analytical solution for ideal multicomponent diffusion in slightly tapered ducts is developed. In two‐bulb diffusion experiments on a uniform tube, the results of Duncan and Toor (1962) were reproduced. Comparison of model and experiment shows that the solution presented here provides a reliable quantitative prediction of the temporal change of H₂, N₂, and CO₂‐concentration for both tube geometries, uniform and slightly conical. In the demonstrated case (Λ = 3.16), mass diffusion is 68% delayed. Thus, for gaseous diffusion in “real,” typically tapered pores the transport limitation is more serious than considered so far. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1404–1412, 2015     

Mixing of two binary nonequilibrium phases in one dimension

The mixing of nonequilibrium phases has important applications in improved oil recovery and geological CO₂‐storage. The rate of mixing is often controlled by diffusion and modeling requires diffusion coefficients at subsurface temperature and pressure. High‐pressure diffusion coefficients are commonly inferred from changes in bulk properties as two phases equilibrate in a PVT cell. However, models relating measured quantities to diffusion coefficients usually ignore convective mass transport. This work presents a comprehensive model of mixing of two nonequilibrium binary phases in one‐dimension. Mass transport due to bulk velocity triggered by compressibility and nonideality is taken into account. Ignoring this phenomenon violates local mass balance and does not allow for changes in phase volumes. Simulations of two PVT cell experiments show that models ignoring bulk velocity may significantly overestimate the diffusion coefficients. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Current distribution in a rectangular flow channel manufactured by 3‐D printing

The characterization and improvement of a rectangular channel electrolyte flow compartment used in an iron‐air flow battery was carried out by using an arrangement of copper electrodes to measure the current density distribution employing the limiting current technique. The present work addresses the hydrodynamics and mass transport distribution in the compartment and their improvement by an improved electrolyte compartment that results in a more uniform current distribution. The current distribution was evaluated as the ratio between the local and the averaged limiting current densities during the reduction of copper ions over a range of mean linear flow velocity across the electrode surface (2–30 cm s^?1). The initial compartment, showed larger differences between the minimum and maximum currents than the electrolyte compartment that resulted as part of the design process and showed a higher pressure drop at a given mean linear flow velocity. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1144–1151, 2017     

固定床吸附柱放大效应考察─—理论板当量高度分析

从色谱塔板理论公式出发，推导出实测理论板公式及理论极当量高度和吸附热力学、吸附动力学参数之间的关系，并对模型的选择、优化操作线速的选取作了讨论。实验测定了ｄ＿ｐ／ｄ＿ｔ＝４．０／２０．０时，吸附柱内的轴向扩散系数及流体传质系数，并加以关联。对不同压力、流量下的理论板当量高度也进行了检验。