Dispersion In Oscillatory Flow Research Articles

Taylor dispersion in oscillatory flow in rectangular channels

This paper focuses on exploring the effect of the side walls on dispersion in oscillatory Poiseuille flows in rectangular channels. The method of multiple time scales with regular expansions is utilized to obtain analytical expressions for the effective dispersivity D3D⁎. The dispersion coefficient is of the form D3D⁎/Pe2=f(Ω≡ωh2/D,Sc≡D/ν,χ≡w/h) where Pe≡<u>h/D, <u> is the root mean square of the cross-section averaged velocity, ω is the angular velocity, 2w and 2h are, respectively, the width and the height of the cross-section, D is the solute diffusivity, and ν is the fluid kinematic viscosity. The analytical results are compared with full numerical simulations and asymptotic expressions. Also effect of various parameters on dispersion coefficient is explored. For small oscillation frequency Ω the dispersion coefficient approaches the time averaged dispersion of the Poiseuille flow and for large Ω, D3D⁎ scales as Pe2/Ω2 where Pe=<u>h/D. Due to its relative simplicity, the 2D model is frequently utilized for calculating dispersion in channels. However at small dimensionless frequencies the 2D model can significantly underestimate the dispersion, particularly for channels with large χ. At large Ω the dispersion coefficient predicted from the 2D model becomes reasonably accurate, particularly for channels with large χ. For a square channel, the 2D prediction is reasonably accurate for all frequencies. The results of this study will enhance our understanding of transport in microscale systems that are subjected to oscillating flows, and potentially aid technological advances in diverse areas relevant to microfluidic devices.

On Taylor dispersion in oscillatory channel flows

We revisit Taylor dispersion in oscillatory flows at zero Reynolds number, giving an alternative method of calculating the Taylor dispersivity that is easier to use with computer algebra packages to obtain exact expressions. We consider the effect of out-of-phase oscillatory shear and Poiseuille flow, and show that the resulting Taylor dispersivity is independent of the phase difference. We also determine exact expressions for several examples of oscillatory power-law fluid flows.

The effect of wall absorption on dispersion in oscillatory flow in an annulus: application to a catheterized artery

The effect of the irreversible boundary reaction on the dispersion of a tracer in an annular region in presence of oscillatory flow is studied. The solution of the mathematical model, based on the generalized dispersion model, brings out the dispersive transport following the injection of a tracer in terms of the three effective transport coefficients, the exchange, the convection and the dispersion coefficients. The model is applied to a specific problem in clinical medicine – dispersion of solutes in blood flow in a catheterized artery. The model predicts that the oscillatory flow augments the mass transfer and that an increase in the frequency parameter helps in the longitudinal dispersion of the dye. But the presence of the catheter and increase in the catheter size inhibit the dispersion process. Also, there is more absorption of solute at the wall as the catheter size increases.

Effect of Wall Conductivity on Axial Gas Dispersion in Oscillatory Flow.

High-frequency oscillation (HFO) is an artificial respiratory system based on small tidal volume and high frequency. Axial gas dispersion in an oscillatory flow occurs due to the interaction between radial mixing and radially nonuniform axial velocity profile. Furthermore, the dispersion can be improved by intermittent oscillatory flow. Most previous studies employ the insulating trachea wall model. However, an actual airway wall has conductivity and absorptivity of flowing gaS. In the present study, numerical simulation of CO2 gas transport in an oscillatory flow through an infinitely long straight airway was carried out to reveal the effect of wall conductivity on axial CO2 gas transport in oscillatory flow. The ratio of resultant effective diffusivity to the effective diffusivity of the insulating wall was markedly enhanced if β<1, due to the gas exchange on the wall. The maximum ratio was more than 200 in this computation. Furthermore, by employing intermittent oscillatory flow, CO2 gas transport resistance was improved in all airway regions, because of radial diffusion during stationary period in thick airways and wall gas exchange in thin airways.

A study of fluid dispersion in oscillatory flow through a baffled tube

AbstractPrevious studies show that axial dispersion in steady laminar flow can be substantially reduced by superimposing fluid oscillation in a baffled tube. In this paper, experimental observations on fluid dispersion for oscillatory flow in a baffled tube are obtained in a series of concentration measurements using high spatial resolution local conductivity probes, and two models—the continuous stirred tank (CST) with feedback and the plug flow with axial dispersion—are used to analyse the concentration curves and determine the fluid dispersion for such a system. The CST with feedback model combines the algorithms from Mecklenburgh and Hartland with the evaluations of unbiased moments from Anderssen and White to determine the dimensionless dispersion coefficient, D/uL, and the backmixing coefficient, F. The plug flow with axial dispersion model, on the other hand, utilises the axial diffusion model by replacing the molecular diffusion coefficient to the axial dispersion coefficient. This model uses an upstream concentration measurement together with an imperfect pulse technique to predict a downstream concentration profile, and thereby determine a best fit value for the dispersion coefficient D/uL. The axial dispersion results show that there is generally more dispersion predicted using the plug flow with axial dispersion model than when using the CST with feedback model for all the oscillatory Reynolds numbers and Strouhal numbers tested. The difference in the calculated D/uL between the two models is discussed.

Effect of Intermittency on Axial Dispersion in an Asymmetrical Oscillatory Flow.

Axial dispersion in oscillatory flow is one of the important factors influencing the gas transport during HFO. Recently, the requirements for HFO have become diversified. The mucus clearance is one of the important steps for HFO. It was proven that the difference of flow rates between inspiration and expiration of oscillation was effective for mucus clearance. According to our latest study, the dispersion in an oscillatory flow can be improved by introducing a stationary period right after the diffusing particle experiences the largest movement, because of its lateral mixing effect during the stationary period. In this study, the numerical simulation of gas transport in an asymmetrical oscillatory laminar flow in a straight circular pipe was carried out for improvement of gas transport. The presence of the stationary period enhances axial gas transport in an asymmetrical oscillatory flow, and the maximum ratio of effective diffusivity to molecular diffusivity is double that of sinusoidal oscillatory flow.

Numerical Analysis of Axial Dispersion in an Intermittent Oscillatory Flow.

Ventilation by high-frequency oscillation (HFO) has gained widespread attention in clinical medicine because of its potential benefits to respiratory insufficiency. The axial dispersion in oscillatory flow is one of the important factors influencing gas transport during HFO. In this study, the gas transport in sinusoidally oscillatory and intermittent laminar flow in a straight circular pipe was numerically simulated to reveal the mechanism of dispersion. The diffusion of substance was simulated according to the random walk technique and its diffusive nature was evaluated by tracking the path of marked particles. The presence of a stationary period enhances the axial gas transport in the oscillatory flow, and the maximum ratio of effective diffusivity to the molecular diffusivity is twice that of sinusoidal oscillatory flow.

Effect of Turbulence on the Taylor Dispersion in Oscillatory Flow.

The effective use of high-frequency oscillation (H. F. O.) requires precise knowledge of the Taylor dispersion of gas on the oscillatory flow. In this study, axial gas transport and turbulent characteristics were measured on the oscillatory flow at and near resonance frequency, in a straight circular pipe to simulate the trachea. The velocity profiles are measured by a hot wire anemometer. The effective dispersion coefficient was determined by the measurement of the carbon dioxide concentration which was dispersed from the injection point. The turbulence appeared at the frequency near the resonance and turbulent intensity and kurtosis achieved maximum values at the beginning of the deceleration phase. Furthermore, the integral scale was enlarged and the lateral mixing of carbon dioxide was enhanced by the large turbulent diffusion coefficient.

Stochastic resonance for dispersion in oscillatory flows.

We discuss the dispersion of particles suspended in time-periodic flows. It is found that this dispersion becomes maximal if the stochastic process describing the intrinsic random motion of the suspended particles is in ``resonance'' with the time-periodic flow. Furthermore, the dispersion coefficient is found to be proportional to the spectrum of the stochastic process, evaluated at the frequency of the flow. The dispersion is calculated for several cases of interest, including a two-layer, non-Markovian model and field flow fractionation.

Dispersion in Oscillatory Flow Superimposed on Steady Flow in Open Channel

ABSTRACTThe dispersion in an oscillatory flow superimposed on a steady flow is analyzed theoretically. On the assumption that for flow in an open channel with variable depth the transverse profile of the velocity is similar to that of steady flow, the mass conservation equation reduces to an eigenvalue problem. The distributions of concentration and dispersion coefficients are calculated numerically for the flows in channels with triangular and parabolic cross-sections. The dispersion coefficient is expressed as a function of two non-dimensional parameters, which are the ratio of the velocity of the steady flow to the amplitude of the oscillatory flow, and the ratio of the period of oscillation to the characteristic time scale of the cross-sectional turbulent mixing. It is found that the dispersion is determined by the combined effects of so-called shear effect and turbulent mixing in the transverse direction, and that the shear effect increases the dispersion coefficient whereas the transverse mixing dec...

Enhanced dispersion in oscillatory flows

Measurements of the dispersion coefficient in oscillating pipe flows for a wide range of Womersley numbers, tidal displacements, and tube radii are presented. The results are shown to be in good agreement with those of a recent laminar dispersion theory for oscillatory flows.

Numerical simulation of contaminant dispersion in estuary flows

The paper examines in detail the dispersion of a passive contaminant in steady and oscillatory turbulent shear flow in a two-dimensional channel. The aim of this examination is to understand dispersion in estuaries. A new method of analysing and predicting concentration distributions has been developed from work of Sullivan ( J. Fluid Mech . 49, 551–576 (1971)). A random walk technique is used, the contaminant being represented by a large number of marked particles whose paths are tracked as they move through the fluid. The technique seeks to model the physics of dispersion more realistically than the standard diffusion equation, and results from the simulation, with input based on data taken in the Mersey, show it to be a useful and versatile method of studying dispersion in oscillatory flows.

Contaminant dispersion in oscillatory flows

If the time scale for cross-sectional mixing is comparable with or larger than the flow period, then, after each flow reversal, there can be a substantial time span in which the contaminant cloud is contracting. Thus, the apparent longitudinal-diffusion coefficient is negative. This means that the contaminant dispersion cannot be modelled by a diffusion equation, because negative diffusivities imply the spontaneous development of infinite concentrations. Here it is shown how this periodic contracting and expanding can be modelled by a delay-diffusion equation (Smith 1981) \[ \partial_t\overline{c} + \overline{u}\partial_x\overline{c} = \overline{\kappa}\partial^2_x\overline{c} + \int_0^{\infty} \partial_{\tau}D\partial^2_x\overline{c}(x-X,t-\tau)\,d\tau, \] where is the bulk velocity, X(t, τ) a coordinate displacement, and D(t, τ) the diffusion coefficient at time τ after discharge. The recent memory ∂τD is always positive and diffusive in character, so singularities cannot arise. However, when τ is large this memory function can be negative because of reversed flow at earlier times. Particular attention is given to estuarial flows and results are derived for the dependence of D upon the water depth and upon the width of the estuary.