EFFECTIVE DIFFUSIVITY ASSOCIATED WITH AXIAL TRANSPORT IN INSULATED OPEN-ENDED GORTER-MELLINK DUCTS

Steady, single-phase transport characterized by high eddy diffusivity in axial direction is a special case of vessel transport phenomena which has not been studied systematically so far. In the present paper, experiments are reported for a Gorter-Mellink duct, at zero net mass flow, covering turbulent eddy transport in cold He⁴ pressurized beyond its thermodynamic critical pressure above 4 K. Axial transport in vertical direction is induced by gravitational buoyancy. A new phenomenological equation is proposed on the basis of quantum fluid convection postulated originally for He II below the lambda point (Goner and Mellink, 1949). Our data agree reasonably with the equation.     

A model for velocity and eddy diffusivity distributions in fully turbulent pipe flow

A model was developed for the eddy diffusivity and mean velocity distributions in fully developed turbulent isothermal smooth pipe flow (4 × 10³ < Re < 5 × 10⁶). Reichardt's tworegion eddy diffusivity models were modified so as to fulfill the requirements that the eddy diffusivity be represented by a smooth, continuous curve, and vanish with the third power of the distance from the wall; the continuity equation be satisfied; and the ratio of the bulk velocity to centerline velocity agree with experimental data. The descripition is in excellent agreement with Laufer's experimental mean velocity data and, in general, provides a method of accurately predicting the mean velocity distribution.     

The influence of an anisotropic Langevin dispersion model on the prediction of micro- and nanoparticle deposition in wall-bounded turbulent flows

This paper deals with the issues of stochastic dispersion models and associated best practice responses for the investigation of micro- and nanoparticle deposition in turbulent flows. For such applications, Reynolds averaged turbulence models are widely used in combination with particle Lagrangian tracking, due to their relative simplicity and computational efficiency. Such approaches imply to generate the instantaneous velocity of the fluid at particle location to reproduce the effect of turbulence on particle transport. The default dispersion model used in most CFD codes is an eddy lifetime model, which frequently overestimates the deposition rates. In this work, a simple method is proposed to implement a three-dimensional stochastic dispersion model based on the Langevin equation in the Fluent^® commercial code. Comparisons are provided between this model, complemented by the simulation of Brownian effects, and available numerical data obtained using either an eddy lifetime model or a simple Langevin model. Computations are carried out in horizontal and vertical channel flows and in circular pipe flows as well. The use of the proposed anisotropic Langevin model is shown to improve the accuracy of deposition prediction in the whole range of particle inertia.     

A Method for Estimating the Limiting Current Density in Electrodialysis

Abstract

An equation for estimating the limiting current density (LCD) in the electrodialytic equipment with spacers is derived by using the equation of the flow distribution and by assuming that the eddy diffusivity caused by the spacer is proportional to Re. The empirical constants of the eddy diffusivity in the equation were determined by measurement of LCD using spacers, electrolytes, feed concentrations, operating temperatures, and flow velocities. The results obtained show that LCD in the electrodialysis can be estimated from the equation derived here.     

Mass transfer between an eddy of cavity and adjacent flows

Mass Transfer from a cavity containing an eddy to the main contacting flow was investigated by computer simulation and visualization experiments. The mass transfer between the cavity and the main contacting flow was affected mainly by the rotation of the eddy and correlated as Sh = 2.29 x10^-5Re^2.18 Sc^1.03AR^0.156 where AR is the aspect ratio ranging from 1 to 4. The Reynolds number was varied from 25 to 100 and the Schmidt number from 100 to 10000.     

Estimating the electrical conductivity of cement paste pore solutions from OH, K and Na concentrations

A proposed method for estimating the electrical conductivity of cement paste pore solution at 25 °C is based on the concentrations of OH⁻, K⁺ and Na⁺. The approach uses an equation that is a function of the solution ionic strength, and requires a single coefficient for each ionic species. To test the method, the conductivity of solutions containing mixtures of potassium hydroxide and sodium hydroxide with molar ratios of 4:1, 2:1 and 1:1, and having ionic strengths varying from 0.15 to 2.00 mol/l were measured in the laboratory and compared to predicted values. The proposed equation predicts the conductivity of the solutions to within 8% over the concentration range investigated. By comparison, the dilute electrolyte assumption that conductivity is linearly proportional to concentration is in error by 36% at 1 mol/l and in error by 55% at 2 mol/l. The significance and utility of the proposed equation is discussed in the context of predicting ionic transport in cement-based systems.     

Heat and mass transfer in non-isothermal absorption of gases in falling liquid films Part II: Theoretical description and numerical calculation of turbulent falling film heat and mass transfer

A mixing length turbulence model is presented, which was used for the numerical calculation of turbulent falling film heat and mass transfer coefficients. Numerous proposals of different authors for the prediction of eddy transport coefficients are discussed. Good agreement between calculated heat and mass transport coefficients and experimental data was achieved by the combination of Hubbard, Mills and Chung's proposal for the calculation of eddy transport near the film surface with a modified form of van Driest's, the latter being for the eddy transport near the solid wall. Furthermore, the dependence of the turbulent falling film heat transfer coefficients on the Prandtl number is discussed. It is shown that, besides the Prandtl number, a further dimensionless group must be considered in order to describe the effect of liquid properties on heat transfer.     

颗粒与液相间的湍流涡旋裂变传质模型

湍流在宏观上处于远程混沌无序状态, 而在介微观上处于近程有序状态。从分析湍流场中局 域中涡旋的串级结构出发,通过对N-S方程的涡旋输运形式进行求解, 导出一个具有分形意 义的涡旋群运动表达式,并得到涡旋掠过颗粒表面花费的时间, 然后同Higbie的传质渗透模型相联系,以涡旋的分布函数为权求其数学期望,得到搅拌湍流场中的传质系数表达式,结果与实验数据吻合较好。     

LES of turbulent channel flow of a binary electrolyte

The turbulent diffusion boundary layer in a binary electrolyte was considered at Schmidt numbers of 1, 10 and 100 and exchange current densities between 10^–4 A m^–2 and 10^–2 A m^–2. A numerical scheme was developed for efficient investigation of the dynamics by means of large eddy simulations. The methodology was examined by detailed comparisons with documented data from earlier large eddy and direct numerical simulations and good agreement was found. Application of the methodology to electrochemical mass transfer indicated that the exchange current density seems to have negligible effect on the mean concentration profile but it influences the structure of the fluctuating field in a visible manner.     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

One-equation sub-grid scale (SGS) modelling for Euler-Euler large eddy simulation (EELES) of dispersed bubbly flow

In this work, we have presented a one-equation model for sub-grid scale (SGS) kinetic energy and applied it for an Euler-Euler large eddy simulation (EELES) of a bubble column reactor. The one-equation model for SGS kinetic energy shows improved predictions over the state-of-the-art dynamic procedure. With grid refinement, the amount of modelled SGS turbulent kinetic energy diminishes, as one would expect. Bubble induced turbulence (BIT) at the SGS level was modelled with two approaches. In the first approach an algebraic model was used, while in the other approach extra source terms were added in the transport equation for SGS kinetic energy. It was found that the latter approach improved the quantitative prediction of the turbulent kinetic energy. To the best of authors knowledge, this is the first use of a transport equation for SGS kinetic energy in bubbly flows.     

Characterization of an anisotropic hydrogel tissue substrate for infusion testing

Artificial tissue models that capture specific transport properties are useful for investigating physical phenomena important to drug delivery. In this study, an in vitro tissue model was developed and characterized with the goal of mimicking aligned tissue. An anisotropic porous medium was developed by the construction of a 1% agarose hydrogel implanted with different volume fractions (～ 5, 10, and 20%) of 10‐μm‐diameter glass fibers. The developed substrate was able to capture anisotropic transport after the direct infusion of a macromolecular tracer, Evans blue albumin (EBA). To further characterize the test substrate, the diffusion tensor of water was measured by diffusion tensor imaging, and the ratios of the diffusivities in the directions parallel and perpendicular to the glass fibers were 1.16, 1.20, and 1.26 for 5, 10, and 20% fiber volume fractions, respectively. The hydraulic conductivity was estimated by the measurement of pressure gradients across samples under controlled microflow conditions in the direction parallel to implanted fibers. The hydraulic conductivities at various hydrogel concentrations without fibers and in a 1% hydrogel with various fiber volume fractions were measured; for example, K_∥ = 1.20 × 10^?12 m⁴ N^?1 s^?1 (where K_∥ is the conductivity component in the direction parallel to the glass fibers) for 20% fiber volume fractions. Also, EBA distributions were fit to porous medium transport models to estimate hydraulic conductivity in the direction perpendicular to glass fibers. The estimated ratio of directional hydraulic conductivity, K_∥/K_? (where K_? is the conductivity component in the direction perpendicular to the glass fibers), ranged from approximately 3 to 5, from 6 to 10, and from 40 to 90 for 5, 10, and 20% fiber volume fractions, respectively. These agarose hydrogel models provided convenient media for quantifying infusion protocols at low flow rates. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

The trail of perfumes

A methodology is proposed for modeling the diffusion of fragrances released from a moving source. First, we started with a one‐dimensional model considering molecular diffusion of α‐pinene in air as the only mass transport mechanism. The validation was performed in a diffusion tube, and a system was developed to move the scented source along the axial direction. Results showed that experimental data fitted well with the numerical simulation, suggesting this model as a valid tool to describe the trail of a fragrance released from a moving source for low Re of the order of 10. In the case of a person walking at the speed of 1.34 m/s in a room or corridor inside a building, three‐dimensional models are required and mass transport of the perfume to the surrounding air will be dominated by turbulent diffusion or eddy diffusion D_t which is two orders of magnitude higher than molecular diffusion. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2890–2897, 2018     

Theoretical investigations of electronic structure and charge transport properties in polythiophene‐based organic field‐effect transistors

Regioregular poly(3‐hexylthiophene) (P3HT) is a hole transport polymer material used in organic field‐effect transistors (OFETs) and can reach mobilities as high as 0.1 cm² V^?1 s^?1. Factors that affect the charge mobility and the transport mechanisms of P3HT‐based OFET systems are therefore of great importance. We use quantum mechanical methods to interpret the charge mobility and the transport properties of self‐assembled P3HT molecules along the intra‐chain and inter‐chain directions. Our approach is illustrated by a hopping transport model, in which we examine the variation of charge mobility with torsional angle and the intermolecular distance between two adjacent thiophene segments. We also simulate packed P3HT structures via molecular dynamics (MD) simulations. The MD results indicate that the resultant mobility along the π?π inter‐chain direction is significantly less than that along the intra‐chain direction. Accordingly, the main charge‐transfer route within the P3HT ordered domains is an intra‐chain rather than an inter‐chain one. The calculation result for the inter‐chain hole mobility is around 10^?2 cm² V^?1 s^?1, which is consistent with experimental data from P3HT single fibril. Copyright © 2009 Society of Chemical Industry     

GAS ABSORPTION INTO WAVY AND TURBULENT FALLING LIQUID FILMS IN A WETTED-WALL COLUMN

Experiments are conducted for gas absorption in a long wetted-wall column. Liquid-side mass transfer coefficients are measured for absorption of CO₂ and O₂ into falling water films on the outside of a stainless steel pipe 2.72 cm OD and 183 cm absorption length. The liquid film Reynolds number ranges from 129 to 10500 which encompasses the wavy-laminar, wavy-transition and turbulent flow regimes. The experimental data are correlated by a dimensionless equation of the form kt = (k_tD) (v²/g) ^1/3 = a-Re^p-Sc^1/2. The correlation is well supported by a viscosity-damped turbulence model at the gas-liquid interface which tends to confirm that viscosity is probably the major mechanism causing eddy damping and not surface tension as proposed by Levich and Davies. The form of the above correlation also represents previous experimental work at different temperatures and for different gases quite well.     

Modeling the transport of multiple corrosive chemicals in concrete structures: Synergetic effect study

The synergetic effect of multiple corrosive chemicals in concrete structures has been investigated using a mathematical model with a set of one-dimensional linear diffusion equation that belongs to the equation of continuity. Combining the method of Laplace transform with the substitution method, and using the convolution theorem, the analytical solution of the one-dimensional linear diffusion equation can be solved. Based on the equation of continuity and the reduction of corrosive chemical concentration through the mechanical driving force with second-order kinetics, a system of transport equations may be employed to elucidate the synergetic effect of two contaminants such as Cl⁻ and CO₂, Cl⁻, and SO₄²⁻, and CO₂ and SO₄²⁻. The computer package “Mathematica” was used to show the synergetic effect of multiple corrosive chemicals in concrete structures. The numerical results of concrete structure subjected to multiple corrosive chemicals shed some light on the synergistic behavior of Cl⁻ and CO₂, Cl⁻, and SO₄²⁻, and CO₂ and SO₄²⁻ versus their individual behavior. These results prove that the proposed model may really describe the synergetic effect of multiple corrosive chemicals in concrete structures. However, it is still recommended that experiments should be performed to choose suitable parameters for numerical simulations.     

Liquid Membrane Separations of Metal Cations Using Macrocyclic Carriers

Abstract

The selectivity in water and methanol solvents of macrocyclic crown ether ligands toward univalent and bivalent cations is well known. Incorporation of these ligands into chloroform liquid membranes separating water and salt solution phases results in a system showing selective cation transport. The cation transport rates of single cations across these liquid membranes have been correlated with equilibrium constant values for cation-macrocycle interaction in methanol. This correlation has been extended to binary cation mixtures of Cs⁺ with Li⁺, Na⁺, K⁺, and Rb⁺. A model for cation transport from these cation mixtures has been reduced to an equation which gives good agreement between measured and predicted transport rates across our liquid membranes.     

Radial distribution of diffusivity in the core of turbulent pipe flow

Tests are described which yield the radial distribution of the turbulent diffusivity for enthalpy (eddy diffusivity) for fully-developed flow of water in a smooth straight pipe, with Reynolds number 10⁵. It is found that this closely resembles the distribution of the turbulent diffusivity for momentum (eddy viscosity), with an average value of turbulent Prandtl number of 0·977. This is somewhat greater than the value predicted by the Jenkins model.     

Numerical simulation of a dissolution process in a stirred tank reactor

A dissolution process of solid particles suspended in a turbulent flow of a Rushton turbine stirred tank is studied numerically by large eddy simulations including passive scalar transport and particle tracking. The lattice-Boltzmann flow solver and the Smagorinsky subgrid-scale model are adopted for solving the stirred tank flow. To the LES a finite volume scheme is coupled that solves the convection-diffusion equation for the solute. The solid particles are tracked in the Eulerian flow field through solving the dynamic equations of linear and rotational motion of the particles. Particle-particle and particle-wall collisions are included, and the particle transport code is two-way coupled. The simulation has been restricted to a lab-scale tank with a volume equal to . A set of 7×10⁶ spherical particles in diameter are released in the top part of the tank (10% of the tank volume), resulting in a local initial solids volume fraction of 10%. The particle properties are such that they resemble those of calcium chloride beads. The focus is on solids and scalar concentration distributions, particle size distributions, and the dissolution time. For the particular process considered, the dissolution time is found to be at most one order of magnitude larger than the time needed to fully disperse the solids throughout the tank.