Bolus Contaminant Dispersion in Oscillatory Tube Flow With Conductive Walls

1993 ◽  
Vol 115 (4A) ◽  
pp. 424-431 ◽  
Author(s):  
Yahong Jiang ◽  
James B. Grotberg
Keyword(s):  
Total Mass ◽  
Functional Dependence ◽  
Asymptotic Methods ◽  
Effective Diffusivity ◽  
Expansion Method ◽  
Axial Dispersion ◽  
Dimensionless Frequency ◽  
Straight Tube ◽  
Derivative Expansion ◽  
Small Conductance

Dispersion of a bolus contaminant in a straight tube with oscillatory flows and conductive walls is solved by using a derivative-expansion method. Using asymptotic methods when small conductance exists, the axial dispersion, as measured by the time-averaged effective diffusivity, increases over the insulated case, as long as the dimensionless frequency (Womersley parameter), α, is smaller than a critical value. When α exceeds this value, axial dispersion is diminished by wall conductance. The functional dependence of this critical α on the system parameters is investigated. We examine the radial wall transport both for total mass and localized flux, which is found to be independent of velocity field, and compute the time-dependent total mass of wall transport and asymptotic Sherwood number for large times as a function of the wall conductance.

Augmentation of Axial Dispersion by Intermittent Oscillatory Flow

1998 ◽  
Vol 120 (3) ◽  
pp. 405-415 ◽  
Author(s):  
G. Tanaka ◽  
Y. Ueda ◽  
K. Tanishita
Keyword(s):  
Stationary Phase ◽  
High Frequency ◽  
Oscillatory Flow ◽  
Effective Diffusivity ◽  
Axial Dispersion ◽  
High Frequency Oscillation ◽  
Gas Transfer ◽  
Straight Tube ◽  
Gas Dispersion ◽  
Molecular Diffusivity

The efficiency of axial gas dispersion during ventilation with high-frequency oscillation (HFO) is improved by manipulating the oscillatory flow waveform such that intermittent oscillatory flow occurs. We therefore measured the velocity profiles and effective axial gas diffusivity during intermittent oscillatory flow in a straight tube to verify the intermittency augmentation effect on axial gas transfer. The effective diffusivity was dependent on the flow patterns and significantly increased with an increase in the duration of the stationary phase. It was also found that the ratio of effective diffusivity to molecular diffusivity is two times greater than that in sinusoidal oscillatory flow. Moreover, turbulence during deceleration or at the beginning of the stationary phase further augments axial dispersion, with the effective diffusivity being over three times as large, thereby proving that the use of intermittent oscillatory flow effectively augments axial dispersion for ventilation with HFO.

scholarly journals Second harmonic resonance in magnetohydrodynamic jet

1994 ◽  
Vol 35 (3) ◽  
pp. 323-334 ◽  
Author(s):  
H. K. Khosla ◽  
R. K. Chhabra
Keyword(s):  
Steady State ◽  
Second Harmonic ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Resonant Interaction ◽  
Spatial Behaviour ◽  
Derivative Expansion ◽  
Modulated Waves ◽  
Harmonic Resonance ◽  
General Motion

AbstractCoupled nonlinear partial differential equations, which describe a nonlinear resonant interaction between the fundamental and its first harmonic on a magnetohydro-dynamic jet, are derived by the derivative expansion method. We investigate the spatial behaviour of the amplitude and phases. It is shown that the fluid surface is unstable in the neighbourhood of the first resonant wavenumber. In the steady state, it is observed that the general motion consists of both amplitude and phase modulated waves.

AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING

2008 ◽  
Vol 22 (21) ◽  
pp. 3487-3578 ◽  
Author(s):  
JI-HUAN HE
Keyword(s):  
High Energy Physics ◽  
Asymptotic Methods ◽  
Variational Iteration Method ◽  
Expansion Method ◽  
High Energy ◽  
New Developments ◽  
Fractal Approach ◽  
Spinning Process ◽  
Intuitive Grasp ◽  
Energy Physics

This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briefly introduced. Bubble-electrospinning for mass production of nanofibers is illustrated. There are in total more than 280 references.

Bolus Contaminant Dispersion for Oscillatory Flow in a Curved Tube

1996 ◽  
Vol 118 (3) ◽  
pp. 333-340 ◽  
Author(s):  
Yahong Jiang ◽  
James B. Grotberg
Keyword(s):  
Stokes Equations ◽  
Time History ◽  
Local Maximum ◽  
Effective Diffusivity ◽  
Axial Position ◽  
Radius Of Curvature ◽  
Local Concentration ◽  
Straight Tube ◽  
Molecular Diffusivity ◽  
Curved Tube

The dispersion of a bolus of soluble contaminant in a curved tube during volume-cycled oscillatory flows is studied. Assuming a small value of δ (the ratio of tube radius to radius of curvature), the Navier-Stokes equations are solved by using a perturbation method. The convection-diffusion equation is then solved by expanding the local concentration in terms of the cross-sectionally averaged concentration and its axial derivatives. The time-averaged dimensionless effective diffusivity, 〈Deff/D〉, is calculated for a range of Womersley number α and different values of stroke amplitude A and Schmidt number Sc, where D is the molecular diffusivity of contaminant. For the parameter values considered, the results show that axial dispersion in a curved tube is greater than that in a straight tube, and that it has a local maximum near α = 5 for given fixed values of Sc = 1, A = 5 and δ = 0.3. Finally it is demonstrated how the time history of concentration at a fixed axial position can be used to determine the effective diffusivity.

Bolus Contaminant Dispersion in Oscillating Flow in Curved Tubes

1998 ◽  
Vol 120 (2) ◽  
pp. 238-244 ◽  
Author(s):  
D. M. Eckmann
Keyword(s):  
Tidal Volume ◽  
Pulmonary Ventilation ◽  
Effective Diffusion ◽  
Effective Diffusivity ◽  
Radius Of Curvature ◽  
Dimensionless Frequency ◽  
Gas Dispersion ◽  
Artificial Pulmonary Ventilation ◽  
Argon Concentration ◽  
Helical Tubes

The investigation of longitudinal dispersion of tracer substances in unsteady flows has biomechanical application in the study of heat and mass transport within the bronchial airways during normal, abnormal, and artificial pulmonary ventilation. To model the effects of airway curvature on intrapulmonary gas transport, we have measured local gas dispersion in axially uniform helical tubes of slight pitch during volume-cycled oscillatory flow. Following a small argon bolus injection into the flow field, the time-averaged effective diffusion coefficient 〈Deff/Dmol〉 for axial transport of the contaminant was evaluated from the time-dependent local argon concentration measured with a mass spectrometer. The value of 〈Deff/Dmol〉 is extracted from the curve of concentration versus time by two techniques yielding identical results. Experiments were conducted in two helical coiled tubes (δ = 0.031, λ = 0.022 or δ = 0.085, λ = 0.060) over a range of 2 < α < 15, 3 < A < 15, where δ is the ratio of tube radius to radius of curvature, λ is the ratio of pitch height to radius of curvature, α is the Womersley parameter or dimensionless frequency, and A is the stroke amplitude or dimensionless tidal volume. Experimental results show that, when compared to transport in straight tubes, the effective diffusivity markedly increases in the presence of axial curvature. Results also compare favorably to mathematical predictions of bolus dispersion in a curved tube over the ranges of frequency and tidal volume studied.

scholarly journals Asymptotic Methods for Solitary Solutions and Compactons

2012 ◽  
Vol 2012 ◽  
pp. 1-130 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Differential Equations ◽  
Variational Principles ◽  
Nonlinear Differential Equations ◽  
Asymptotic Methods ◽  
Variational Iteration Method ◽  
Expansion Method ◽  
Solitary Solutions ◽  
Fractional Differential ◽  
Intuitive Grasp ◽  
And Variational Principles

This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.

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