Effect Of Axial Diffusion Research Articles

Instabilities of the Belousov-Zhabotinsky Reaction in a Taylor Vortex Flow Reactor with Constant Axial Flow.

Instabilities of the Belousov-Zhabotinsky reaction were investigated in a Taylor vortex flow reactor with constant axial flow regarded as a one-dimensional open reaction-diffusion system. The effective axial diffusion coefficient was used as one of the controlling parameters, and changed by varying the rotating speed of the inner cylinder. Effluent from an isothermal continuous stirred tank reactor was supplied as the feed into the test reactor so as to clearly specify the inlet condition of concentration oscillation. The feed rate was changed as another controlling parameter. Irregular disturbances appeared at low-concentrations of Ce4+ when the inlet condition was singly periodic oscillation, whereas no remarkable irregular oscillation could be found when the inlet condition was dynamical equilibrium. The spatio-temporal oscillation patterns were successfully described qualitatively by a numerical simulation based on the ‘Coupled Map Lattice’ method using an Oregonator reaction model. The numerical results also suggested that complex spatial and temporal behavior occurred under the inlet condition of singly periodic oscillation.

Coupled transport and dispersion of multicomponent reactive solutes in rectilinear flows

Simultaneous transport of two-component solution in flows in tubes and channels, coupled via a matrix wall reaction coefficient, is considered. Expressions for long-time effective axial matrix solute properties are derived in the particular case of a channel formed by two parallel plates. These matrix coefficients include effective axial solute reactivity, velocity and diffusivity. These coefficients are systematically investigated both analytically and numerically for a two-component species, having different molecular diffusivities and moving in a plane Poiseuille flow between two parallel walls, on which surfaces they undergo coupled surface reactions. It is shown that for small coupling reactivity coefficient the species initially behave like uncoupled constituents, the dispersive transport of which can be studied via single-species solution scheme. At large times the species transport becomes coupled and all constituents are characterized by the same nonmatrix transport properties. These properties constitute leading modes of the corresponding matrix coefficients, governing the species transport for earlier times. Physically, in this situation the effective properties of both constituents are controlled by the (microscale) molecular diffusivity of the slowest component.

Hydrodynamic voltammetry with channel microband electrodes: axial diffusion effects

The strongly implicit procedure is used to simulate the response of channel electrodes under conditions where diffusional effects in the direction (axis) of solution flow are significant. The cases of flow rate dependence of the steady-state transport limited current, potential step transients and ECE processes are considered and the conditions identified under which axial diffusion effects are considerable.

Effect of Axial Diffusion and Fiber Deformation on the Performance of Purge Gas Permeator

Mathematical models were developed for the purge gas permeator assuming that deformation and axial diffusion were taking place during permeation. Then a comparative study for the plug flow model, deformation model, and diffusion−deformation model was done in order to establish the significance of incorporating axial diffusion and fiber deformation in the mathematical model of the purge gas permeator. The study showed that all three models were predicting nearly the same performance; hence, the simpler plug flow model is good enough and reasonably accurate for investigation of purge gas permeator.

Channel microband electrodes: a complete working surface for potential step transients

The strongly implicit procedure is used to simulate the chronoamperometric transient resulting from a potential step at a channel microband electrode. A working surface is presented which permits the analysis of data recorded at any flow rate, including cases where axial diffusion effects are significant, and for cells of arbitrary geometry.

Reversible axial segregation of rotating granular media.

Experimental measurements of axial segregation of binary mixtures of granular media combined in a horizontal cylinder and rotated like a drum mixer are reported. While in the traditional axial segregation effect the mixture of two different sizes of granular media will separate into bands of relatively pure single concentrations along the axis of rotation, in special cases the homogeneous mixed state can be restored simply by decreasing the speed of rotation. Systematic variation of the relative diameters of the components reveal three classes of behavior: no segregation at any rotation speed, a nonreversible axial segregation, and an axial segregation at high speeds that reverses back into the mixed state at low speeds. Measurements of the dynamic angle of repose of the mixed and segregated phases as a function of rotation speed support a model for the axial segregation effect that involves a diffusion equation with an effective axial diffusion coefficient that can be negative under the conditions for which segregation occurs.

On the eigenvalues basic to the analytical solution of convective heat transfer with axial diffusion effects

AbstractThe integral transform method is employed in the analytical solution of the non‐classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.

Shear-augmented dispersion in non-Newtonian fluids.

The rate of spread of a passive species is modified by the superposition of a velocity gradient on the concentration field. Taylor (18) solved for the rate of axial dispersion in fully developed steady Newtonian flow in a straight pipe under the conditions that the dispersion be relatively steady and that longitudinal transport be controlled by convection rather than diffusion. He found that the resulting effective axial diffusivity was proportional to the square of the Peclet number Pec and inversely proportional to the molecular diffusivity. This article shows that under similar conditions in Casson and power law fluids, both simplified models for blood, and in Bingham fluids the same proportionalities are found. Solutions are presented for fully developed steady flow in a straight tube and between flat plates. The proportionality factor, however, is dependent upon the specific rheology of the fluid. For Bingham and Casson fluids, the controlling parameter is the radius of the constant-velocity core in which the shear stress does not exceed the yield stress of the fluid. For a core radius of one-tenth the radius of the tube, the effective axial diffusivity in Casson fluids is reduced to approximately 0.78 times that in a Newtonian fluid at the same flow. Using average flow conditions, it is found that the core radius/tube radius ratio is 0 (10(-2)) to 0 (10(-1)) in canine arteries and veins. Even at these small values, the effective diffusivity is diminished by 5% to 18%. For power law fluids, Pec2 dependence is again found, but with a proportionality constant dependent upon the power law exponent n.(ABSTRACT TRUNCATED AT 250 WORDS)

Effect of axial solid heat conduction and mass diffusion in a rotary heat and mass regenerator

This research analyzes the effect of axial heat conduction and mass diffusion on the performance of a solid desiccant wheel. A one-dimensional transient heat and mass transfer model which contains four nonlinear partial differential equations is developed. The equations are solved using a full-implicit finite-difference thod. A limiting case with a zero solid diffusion resistance is considered. Three different regeneration temperatures, namely 26, 50 and 85 C, are considered. The parameter, ( λ 4 2 Ntu/Bi), is found to be the most important factor governing the axial heat conduction and mass diffusion effect.

Analysis of effective axial diffusion in branching networks

AbstractDiffusional transport in a network of branching conduits is considered. The branching network is idealized as an ensemble of identical branching segments. Starting with the general species continuity equation, multiscale perturbation analysis is used to derive a one‐dimensional, effective transport equation for species concentration. The macrotransport equation contains an effective diffusion coefficient, D*, which arises naturally from the analysis. D* can be computed from a local diffusion problem posed on an individual branching segment of the ensemble network. The local relations defining D* bear clear similarity to their counterparts for transport in spatially periodic porous media. Although this study was originally directed toward describing gas diffusion in the peripheral airspaces of the lung, the results provide insight for other transport processes occurring in branching networks.

Axial tissue diffusion can account for the disparity between current models of hepatic elimination for lipophilic drugs.

An assumption of previous models of hepatic elimination is that there is negligible axial diffusion in the liver. We show, by construction of a stochastic model and analysis of published data, that compounds which are readily diffusible and partitioned into hepatocytes may undergo axial tissue diffusion. The compounds most likely to be affected by axial tissue diffusion are the lipophilic drugs for which the cell membranes provide little resistance and which are highly extracted, thereby creating steep concentration gradients along the sinusoid at steady state. This phenomenon greatly modifies the availability of the compound under conditions of altered hepatic blood flow and protein binding. For moderately diffusible compounds, these relationships are similar to those predicted by the simplistic venous-equilibrium model. Hence, the paradoxical ability of the venous-equilibrium model to describe the steady-state kinetics of lipophilic drugs such as lidocaine, meperidine, and propranolol may be finally resolved. The effects of axial tissue diffusion and vascular dispersion on hepatic availability of drugs are compared. Vascular dispersion is of major importance to the availability of poorly diffusible compounds, whereas axial tissue diffusion becomes increasingly dominant for highly diffusive and partitioned substances.

Transient response method for evaluating the rate constants of reactions over immobilized enzymes

The transient response method was utilized to evaluate the rate constants of reaction over immobilized enzyme. Glucose oxidation catalyzed by the immobilized glucose oxidase in a fixed-bed reactor was selected as an example. A theoretical model including the effects of axial dispersion, film diffusion, and intraparticle diffusion was established for the reactor. The individual rate constant of each elementary step of this enzymatic reaction was determined through direct fitting of the experimental response data to the model.

Axial diffusion and Michaelis-Menten kinetics in oxygen delivery in rat peripheral nerve

Our simulation of the release, diffusion, and consumption of oxygen in the capillaries and surrounding tissue of peripheral nerve now includes axial diffusion in blood and in surrounding tissue, in addition to bulk flow of blood and radial diffusion of oxygen out of the capillary. Our simulation assumes that the oxygen consumption of nerve tissue obeys Michaelis-Menten kinetics rather than zero-order kinetics as had been assumed in the Krogh model. We can calculate the oxygen tension at all points in the capillary and surrounding tissue as a function of distance from the center of the nearest capillary and distance along the capillary from the arterial to the venous end. Using average measured values for microcirculatory parameters in rat nerve, we calculated a distribution of oxygen tension values that agrees with experimentally measured distributions. The effects of axial diffusion and of Michaelis-Menten kinetics on the oxygen distributions were noticeable under normal conditions, but these effects were much more important in situations in which oxygen delivery was adversely affected.

A study of the separation behavior of different membrane columns with respect to ternary gas mixtures

The simulation model of the continuous membrane column (CMC) and the two-membrane column (TMC), including the axial diffusion effects, has been extended for multicomponent gas mixtures. The model equations have been solved with the orthogonal collocation method and the simulation results have been verified by experimental data. By introducing a measure specifying the extent of mixing at the feed location, it has been demonstrated that maximum separation using the CMC can be achieved by minimizing the mixing at this point. A parametric study of the effect of a third species on the separation behavior has been carried out for the TMC. It has been shown that the third species is mainly concentrated in one product stream, if the two membranes possess reverse selectivities towards this component. If the third species is most permeable in both membranes, a ternary gas mixture can be separated in this column.

Axial dispersion of submicron particles in capillary hydrodynamic fractionation

AbstractIn the present investigation, Taylor's analysis of the axial dispersion of a solute in a Newtonian fluid undergoing laminar flow through a circular tube was applied to dispersions of colloidal particles, in which effects of size exclusion, inertial and colloidal forces, and wall retardation must be considered. The results indicate that the product of the particle Reynolds and Peclet numbers determines the importance of the inertial forces on both the effective axial diffusion coefficient and the height of a theoretical plate.The height of a theoretical plate as a function of the eluant ionic strength and average velocity, particle diameter, and tube diameter was determined experimentally. Close agreement with the numerical calculations from the diffusion equation was obtained. The height of a theoretical plate was found to attain a maximum value when the product of Reynolds and Peclet numbers was approximately 10.5.

Steady laminar heat transfer in the entry region of circular tubes with axial diffusion of heat and momentum

The simultaneous development of the velocity and temperature profiles in circular tubes is analysed, accounting for axial diffusion of both momentum and heat. The axisymmetric problem is formulated in variational form by the weighted residuals Galerkin method and then numerically solved by the finite element method. Results obtained in the case of vanishing axial diffusion effects satisfactorily compare with previous boundary layer solutions ; in the presence of axial diffusion effects the solutions presented in the literature are scanty and do not always agree. The isothermal flow results, presented for Reynolds numbers ranging from 1 to 1000, show the appearance of the overshoots in the axial velocity profile, as well as the dependence on the axial coordinate and Reynolds number of the various axial momentum transfer processes—radial diffusion at the wall, convection and axial diffusion. The non-isothermal flow results, presented for the Prandtl number ranging from 0.1 to 100 and the Péclet number from 5 to 500, point out the effect of axial diffusion of momentum and, above all, of heat, on the convective heat transfer rate.

Adsorption on activated carbon of p-nitrophenol from aqueous solution

A method of the fixed-bed adsorption on activated carbon has been used in the removal of p-nitrophenol from water. The range of low concentrations of a break-through curve has been analyzed. On the basis of a three-stage model of the process the equations describing the initial stage of the adsorption dynamics and concentration distribution in the bed at low concentrations of the break-through curve have been derived. The equations were used to determine the effective kinetic coefficient and to evaluate the effect of axial diffusion on the process kinetics. A method for determination of the time for protective action of the adsorbent layer has been proposed.

Analytical solution for the ideal model of chromatography in the case of a Langmuir isotherm

An exact solution of the ideal model of chromatography for one compound is derived in the case of Langmuir isotherm (C/sub s/ = aC/sub m//(1 + bC/sub m/), where C/sub s/ is the amount of solute sorbed per unit mass of packing material, in equilibrium with a concentration C/sub m/ in the mobile phase). A set of reduced coordinates can be chosen that permits the representation of the elution profiles as a set of curves that are a function of only the reduced sample size. The reduced time is (t - t/sub O/)/(t/sub R,O/ - t/sub O/), which provides a time scale independent of the first isotherm parameter, a. The reduced ordinate is bC/sub m/. The reduced sample size is the loading factor, i.e., the ratio of the sample size to the amount of sample that would completely saturate the column. With the parameters of the isotherm known, it is easy to predict the elution band profile for any sample size. With the sample size known, it is easy to calculate the parameters of the best Langmuir isotherm. From these the profile of the elution band of any sample size can be predicted. The bands eluted from real columns havingmore » several thousands of theoretical plates are so sharp that the effects of axial diffusion and of the radial resistance to mass transfer introduce only very small deviations that can be corrected easily by using a dimensionless plot. This method is rigorous. It is more general than the empirical approaches recently suggested. It is easier to use and provides more accurate predictions.« less

Boundary layer solutions to the Green's function for the extended Graetz problem

Limiting solutions are developed for the Green's function of the extended Graetz problem of mass (or heat) transfer, satisfying absorption boundary conditions, in flat channels. A differential equation directly satisfied by the Green's function of the transmission flux is derived. For finite Peclet numbers, the non-existence of similarity solutions is pointed out. Both uniform and parabolic velocity profiles are considered. While all orders of boundary layer solutions are obtained for the former case, only leading terms are derived for the latter, based on the approximation of a linearized profile near the wall. It is concluded that for sources confined close to the absorbing boundary, the axial diffusion effects cannot be ignored even at relatively large Peclet numbers.

Axial diffusion and wall permeability effects in perfused capillary-tissue structures

Attempts to experimentally examine oxygen supply and distribution in the isolated perfused heart and brain have renewed interest in mathematical models of artificially perfused capillary-tissue structures. The need to understand histograms of Po 2 measurements from these isolated-perfused organ studies (modified Lagendorf preparations) has required that existing mathematical models and their boundary conditions be re-examined in the context of these experiments. A unifying system of equations and boundary conditions are examined here for the purpose of studying the effects of anisotropic diffusion, and capillary vessel wall permeability on both the capillary and tissue substrate supply. The mathematical models are explored for parameters of physiologic interest, and some comparisons are made with experimental determinations. The comparisons with data suggest an anisotropic transport of oxygen in the tissue that is unexplained by known physiologic mechanisms.