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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v35.i5.60
pages 475-492

Dispersion in Oscillatory Couette Flow with Absorbing Boundaries

B. S. Mazumder
Fluvial Mechanics Laboratory Physics and Applied Mathematics Unit Indian Statistical Institute Kolkata - 700108, India
Suvadip Paul
Physics & Applied Mathematics Unit, Indian Statistical Institute Calcutta, India

RESUMO

This paper presents the longitudinal dispersion of passive contaminant released in an incompressible viscous fluid flowing between two infinite parallel plates, where the contaminant undergoes irreversible heterogeneous reaction with the boundary walls. The flow is driven by the oscillation of the upper plate in its own plane with a constant velocity as well as by an imposed constant pressure gradient. This type of flow may be termed unsteady generalized Couette flow. A finite difference implicit scheme has been adopted to solve the unsteady convection-diffusion equation for all time periods based on the Aris method of moments. The influence of applied constant pressure gradient, oscillation of the upper plate, and the absorption parameter at both walls on dispersion is discussed. The dispersion coefficients are obtained for three different flow situations: plane and generalized Couette flow, unsteady generalized Couette flow, and for comparison, the combined effect of steady and unsteady Couette flows, separately. The most striking result is that unlike the case of parallel flow under periodic pressure gradient, the double-frequency period in the dispersion phenomena does not vanish, even for the high frequency of upper-plate oscillation for the case of unsteady generalized Couette flow. The axial distributions of mean concentration are determined from the first four central moments using Hermite polynomial representation for the periodic flow with or without nonzero mean flow.


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