Dispersion in steady and oscillatory flows through a tube with reversible and irreversible wall reactions

2005 ◽  
Vol 462 (2066) ◽  
pp. 481-515 ◽  
Author(s):  
Chiu-On Ng
Keyword(s):  
Dispersion Coefficient ◽  
Tube Wall ◽  
Dispersion Model ◽  
Small Diameter ◽  
Chemical Species ◽  
Taylor Dispersion ◽  
Phase Partitioning ◽  
Dispersion Mechanism ◽  
Effective Dispersion ◽  
Number Flow

An asymptotic analysis is presented for the advection–diffusion transport of a chemical species in flow through a small-diameter tube, where the flow consists of steady and oscillatory components, and the species may undergo linear reversible (phase exchange or wall retention) and irreversible (decay or absorption) reactions at the tube wall. Both developed and transient concentrations are considered in the analysis; the former is governed by the Taylor dispersion model, while the latter is required in order to formulate proper initial data for the developed mean concentration. The various components of the effective dispersion coefficient, valid when the developed state is attained, are derived as functions of the Schmidt number, flow oscillation frequency, phase partitioning and kinetics of the two reactions. Being more general than those available in the literature, this effective dispersion coefficient incorporates the combined effects of wall retention and absorption on the otherwise classical Taylor dispersion mechanism. It is found that if the phase exchange reaction kinetics is strong enough, the dispersion coefficient is probably to be increased by orders of magnitude by changing the tube wall from being non-retentive to being just weakly retentive.

scholarly journals Closed-form expression for the dynamic dispersion coefficient in Hagen-Poiseuille flow

2017 ◽  
Author(s):  
Lichun Wang ◽  
M. Bayani Cardenas
Keyword(s):  
Poiseuille Flow ◽  
Molecular Diffusion ◽  
Numerical Solutions ◽  
Dispersion Coefficient ◽  
Dispersion Model ◽  
Taylor Dispersion ◽  
Breakthrough Curves ◽  
Exact Expression ◽  
Closed Form Expression ◽  
Pore Network Model

We present an exact expression for the upscaled dynamic dispersion coefficient (D) for one-dimensional transport by Hagen-Poiseuille flow which is the basis for modeling transport in porous media idealized as capillary tubes. The theoretical model is validated by comparing the breakthrough curves (BTCs) from a 1D advection-dispersion model with dynamic D to that from direct numerical solutions utilizing a 2D advection-diffusion model. Both Taylor dispersion theory and our new theory are good predictors of D at lower Peclet Number (Pe) regime, but gradually fail to capture most parts of BTCs as Pe increases. However, our model generally predicts the mixing and spreading of solutes better than Taylor’s theory since it covers all transport regimes from molecular diffusion, through anomalous transport, and to Taylor dispersion. The model accurately predicts D based on the early part of BTCs even at relatively high Pe regime (~62) where the Taylor’s theory fails. Furthermore, the model allows for calculation of the time scale that separates Fickian from non-Fickian transport. Therefore, our model can readily be used to calculate dispersion through short tubes of arbitrary radii such as the pore throats in a pore network model.

Gaseous dispersion in laminar flow through a circular tube

1965 ◽  
Vol 284 (1399) ◽  
pp. 540-550 ◽  
Keyword(s):  
Circular Tube ◽  
Dispersion Coefficient ◽  
Straight Tube ◽  
Laminar Regime ◽  
Thermal Conductivity Detector ◽  
Longitudinal Dispersion Coefficient ◽  
Dispersion Coefficients ◽  
Effective Dispersion ◽  
Flow Through ◽  
Gaseous Dispersion

The dispersion of a pulse of ethylene injected into nitrogen, flowing in the laminar régime through straight and curved tubes, has been investigated at pressures of 1.0 and 4.4 atm. From the study of the concentration profiles with a thermal conductivity detector (katharometer) it is found that the experimental results for gas velocities between 1.00 and 16.00 cm/s agree well with the analytical solution to this problem for a straight tube given by Sir Geoffrey Taylor and extended by Aris. In particular, at low velocities, the effective dispersion coefficients tend to the molecular diffusivities. The presence of a bend slightly reduces the effective longitudinal dispersion coefficient and the introduction of constrictions enhances it. Data are also given on a number of other gas pairs. It is concluded that measurements of dispersion provide an accurate and simple way of studying diffusion in gas mixtures.

Subproject PROCLOUD Phase Partitioning of Chemical Species in Mixed Clouds during CIME

2001 ◽  
pp. 90-97
Author(s):  
P. Laj ◽  
A. I. Flossmann ◽  
W. Wobrock ◽  
S. Fuzzi ◽  
G. Orsi ◽  
...  
Keyword(s):  
Chemical Species ◽  
Phase Partitioning

On the dispersion of a solute in pulsating flow through a tube

1960 ◽  
Vol 259 (1298) ◽  
pp. 370-376 ◽  
Keyword(s):  
Diffusion Coefficient ◽  
Pressure Gradient ◽  
Circular Tube ◽  
Dispersion Coefficient ◽  
Pulsating Flow ◽  
Periodic Flow ◽  
Pressure Pulsations ◽  
Effective Dispersion ◽  
Mean Pressure ◽  
Flow Through

The effective dispersion coefficient of a solute in pulsating flow through a circular tube is here found. The case of a viscous flow under a pulsating pressure gradient is treated in detail and it is found that the Taylor diffusion coefficient contains terms proportional to the square of the amplitude of the pressure pulsations. However, the coefficients of these terms tend rapidly to zero, and the effect of pulsation will rarely contribute a fraction of more than 1/128 (the ratio of the amplitude of pressure gradient pulsation to mean pressure gradient) 2 to the total dispersion coefficient. The methods may be applied to diffusion in any periodic flow.

Lagrangian approach to time-dependent laminar dispersion in rectangular conduits. Part 1. Two-dimensional flows

1988 ◽  
Vol 190 ◽  
pp. 201-215 ◽  
Author(s):  
Shimon Haber ◽  
Roberto Mauri
Keyword(s):  
Channel Flow ◽  
Poiseuille Flow ◽  
Open Channel ◽  
Molecular Diffusion ◽  
Dispersion Coefficient ◽  
Brownian Particle ◽  
Open Channel Flow ◽  
Taylor Dispersion ◽  
Time Dependent ◽  
Two Dimensional

Time-dependent mean velocities and dispersion coefficients are evaluated for a general two-dimensional laminar flow. A Lagrangian method is adopted by which a Brownian particle is traced in an artificially restructured velocity field. Asymptotic expressions for short, medium and long periods of time are obtained for Couette flow, plane Poiseuille flow and open-channel flow over an inclined flat surface. A new formula is suggested by which the Taylor dispersion coefficient can be evaluated from purely kinematical considerations. Within an error of less than one percent, over the entire time domain and for various flow fields, a very simple analytical expression is derived for the time-dependent dispersion coefficient \[ \tilde{D}(\tau) = D + D^T\left(1-\frac{1-{\rm e}^{-\alpha\tau}}{a\tau}\right), \] where D is the molecular diffusion coefficient, DT denotes the Taylor dispersion coefficient, τ stands for the non-dimensional time π2Dt/Y/, Y is the distance between walls and a = (N + 1)2 is an integer which is determined by the number of symmetry planes N that the flow field possesses. For Couette and open-channel flow there are no planes of symmetry and a = 1; for Poiseuille flow there is one plane of symmetry and a = 4.

Peculiarities of axial and radial Ge–Si heterojunction formation in nanowires: Monte Carlo simulation

2012 ◽  
Vol 84 (12) ◽  
pp. 2619-2628 ◽  
Author(s):  
Nataliya L. Shwartz ◽  
Alla G. Nastovjak ◽  
Igor G. Neizvestny
Keyword(s):  
Monte Carlo ◽  
Small Diameter ◽  
Chemical Species ◽  
Flux Ratio ◽  
Chemical Vapor ◽  
Growth Conditions ◽  
Drop Diameter ◽  
Nanowire Diameter ◽  
Mc Simulation ◽  
Drop Composition

The process of axial and radial Si–Ge heterostructure formation during nanowire growth by vapor–liquid–solid (VLS) mechanism was studied using Monte Carlo (MC) simulation. It was demonstrated that radial growth can be stimulated by adding chemical species that decrease the activation energy of precursor dissociation or the solubility of semiconductor material in catalyst drop. Reducing the Si adatom diffusion length also leads to Si shell formation around the Ge core. The influence of growth conditions on the composition and abruptness of axial Ge–Si heterostructures was analyzed. The composition of the GexSi1–x axial heterojunction (HJ) was found to be dependent on the flux ratio, the duration of Si and Ge deposition, and the catalyst drop diameter. Maximal Ge concentration in the HJ is dependent on Ge deposition time owing to gradual changing of catalyst drop composition after switching Ge and Si fluxes. The dependence of junction abruptness on the nanowire diameter was revealed: in the adsorption-induced growth mode, the abruptness decreased with diameter, and in the diffusion-induced mode it increased. This implies that abrupt Ge–Si HJ in nanowires with small diameter can be obtained only in the chemical vapor deposition (CVD) process with negligible diffusion component of growth.

The Influence of Pipeline Diameter Variation on the Mixing Volume in Batch Transfers

2002 ◽  
Author(s):  
Felipe Bastos de Freitas Rachid ◽  
Jose´ Henrique Carneiro de Araujo ◽  
Renan Martins Baptista
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Dispersion Coefficient ◽  
Rate Variation ◽  
Governing Equations ◽  
Initial Value ◽  
Diameter Variation ◽  
Constant Diameter ◽  
Effective Dispersion ◽  
Predictor Corrector

Presented in this paper is a new model for estimating mixing volumes arising in batch transfers in multiproduct pipelines, when variations of the line diameter as well as injection and/or withdrawal of products are present. Besides these novel features, the model incorporates the flow rate variation with time and the use of a more precise effective dispersion coefficient, which is considered to depend on the concentration. The governing equations of the model form a non-linear initial-value problem that is solved by using a predictor-corrector finite difference method. A comparison among several cases studied reveals that the pipeline diameter variation can effectively reduce the amount of mixing volume when compared to a similar transfer carried out in a constant diameter line.

scholarly journals THE USE OF FLY ASH AND ZEOLITE MIXTURE AS BACKFILL MATERIAL IN THE RADIOACTIVE WASTE REPOSITORY

2010 ◽  
Vol 5 (3) ◽  
pp. 302-308
Author(s):  
Herry Poernomo ◽  
Noor Anis Kundari ◽  
Burhani J W
Keyword(s):  
Fly Ash ◽  
Radioactive Waste ◽  
Dispersion Coefficient ◽  
Nitrate Solution ◽  
Fixed Bed ◽  
Weight Ratio ◽  
Weight Percent ◽  
Backfill Material ◽  
Fly Ash Zeolite ◽  
Effective Dispersion

An investigation of the contribution of fly ash in the fly ash-zeolite mixture as the backfill material on the shallow land burial of radioactive waste has been done. The experiment objective is to know the effect of zeolite particle size and fly ash-zeolite weight ratio on physical properties such as permeability (K) and dispersion characteristic such as effective dispersion coefficient (De) in the fly ash-zeolite form as backfill material. The experiment was carried out by the fixed bed method in the column filled by the fly ash-zeolite mixture with a fly ash-to-zeolite weight percent ratio of 100/0, 80/20, 60/40, 40/60, 20/80, 0/100 in the water saturated condition flown by uranyl nitrate solution at concentration (Co) of 500 ppm. The concentration of uranium in the effluents in interval 15 minutes represented as Ct was analyzed by spectrophotometer, then using Co and Ct, data effective dispersion coefficient (De) in the backfill material were determined. The experiment data showed that -400 mesh fly ash and -70+80 mesh zeolite on fly ash-to-zeolite with weight percent ratio of 40/60 with K = 5.00x10-5cm/second and De = 1.11.10-5 cm2/second can be used as backfill material. Keywords: backfill material, fly ash, radioactive waste, zeolite

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