Molecular diffusion in oscillating laminar flow in a pipe

Purtell, L. P.

doi:10.1063/1.863450

Cited by 19 publications

(7 citation statements)

References 2 publications

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“…His assumption on linearity of the concentration solution was adequate for large time. Purtell (1981) analysed the effect of flow oscillation (without a timemean velocity) due to the periodic pressure gradient on the axial diffusion of a solute in a pipe, considering a small perturbation to the oscillation Reynolds number Re ( = wR2/v), where w is the frequency of oscillation, R is the radius of the tube, and v is the kinematic viscosity of the fluid. His attention was restricted to the initial t Present Address : Mathematics and Statistics Division, Indian Statistical Institute, 203 B.T.…”

Section: Introductionmentioning

confidence: 99%

Effect of boundary reaction on solute dispersion in pulsatile flow through a tube

1992

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This paper examines the streamwise dispersion of passive contaminant molecules released in a time-dependent laminar flow through a tube in the presence of boundary absorption or a catalytic wall reaction, which causes a depletion of contaminant in the flow. A finite-difference implicit scheme has been used to solve the unsteady convective–diffusion equation for all time. Here it is shown how the mixing of the cross-sectionally integrated concentration of contaminant molecules is influenced by the frequency of pressure pulsation and the heterogeneous reaction at the boundary. The behaviour of the dispersion coefficient due to the shear effects of steady, oscillatory, and the combined action of steady and periodic currents have been examined separately. The comparison reveals that for all cases the dispersion coefficient asymptotically reaches a stationary state after a certain time and it decreases with the absorption parameter. The increased wall absorption causes negatively skewed deviations from Gaussianity.

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Section: Introductionmentioning

confidence: 99%

Effect of boundary reaction on solute dispersion in pulsatile flow through a tube

1992

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“…Chatwin [12] studied the diffusion of the solute in oscillatory flow. Purtell [13] studied the impact of flow oscillations on the axial diffusion by a perturbation method. Ng [14], and Mazumder and Paul [15] examined dispersion process in presence of reversible and irreversible reactions in the boundary.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Convective Diffusion with Interphase Mass Transfer in Casson Liquid

Roy

Saha

Debnath

2017

Period. Polytech. Chem. Eng.

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“…Equations (10), (15), and (16) jointly constitute a well-posed problem that can, in principle, be solved. Indeed, Taylor dispersion techniques allow us to circumvent the difficulty of actually solving the microtransport equation (10) in circumstances where only the macroscale transport coefficients are sought. The long-time asymptotic behavior of the zeroth, first, and second global moments of P with respect to Q i suffice to determine the macrotransport properties of the system.…”

Section: Brief Recapitulation Of the Taylor Dispersion Paradigm mentioning

confidence: 99%

Diffusion, sedimentation, and Taylor dispersion of a Brownian cluster subjected to a time-periodic external force: A micromodel of ac electrophoretic phenomena

Haber

Brenner

Shapira

1990

The Journal of Chemical Physics

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A generalized formulation ofthe Fokker-Planck equation is utilized to calculate the mean velocity and dispersivity of a flexible Brownian cluster of rigid particles which is acted upon by a time-periodic external force. It is shown that if the force consists of a nonzero mean part and a "fluctuating" (Le., zero mean) part, their effects are decoupled. Similarly, if a Fourier expansion of the force is carried out, the effect of each term of the expansion can be treated independently of the others. A representative force term of the form F n exp (i1iJ n t) + F n exp ( -iliJ n t) was selected to act upon a flexible dumbbell composed of two identical tethered spheres of radii a, with the inextensible tether acting as an "attractive" internal potential. The dispersion tensor is found to consist of a "parallel" contribution (directed along F n F n + F n F n ) }lnd a "hydrostatic" contribution. This dispersion tensor depen~s linearly upon the scalar (F n ' Fn )aI241rl-"kT (I-" = viscosity), approaches a constant asymptotic value for small nondimensional frequencies fin = 121rl-"a3IiJnlkT, and decreases asymptotically to zero for very large frequencies.

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Molecular diffusion in oscillating laminar flow in a pipe

Cited by 19 publications

References 2 publications

Effect of boundary reaction on solute dispersion in pulsatile flow through a tube

Effect of boundary reaction on solute dispersion in pulsatile flow through a tube

Unsteady Convective Diffusion with Interphase Mass Transfer in Casson Liquid

Diffusion, sedimentation, and Taylor dispersion of a Brownian cluster subjected to a time-periodic external force: A micromodel of ac electrophoretic phenomena

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