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Transient Taylor–Aris dispersion for time-dependent flows in straight channels

  • Søren Vedel (a1) and Henrik Bruus (a1)
Abstract
Abstract

Taylor–Aris dispersion, the shear-induced enhancement of solute diffusion in the flow direction of the solvent, has been studied intensely in the past half century for the case of steady flow and single-frequency pulsating flows. Here, combining Aris’s method of moments with Dirac’s bra–ket formalism, we derive an expression for the effective solute diffusivity valid for transient Taylor–Aris dispersion in any given time-dependent, multi-frequency solvent flow through straight channels. Our theory shows that the solute dispersion may be greatly enhanced by the time-dependent parts of the flow, and it explicitly reveals how the dispersion coefficient depends on the external driving frequencies of the velocity field and the internal relaxation rates for mass and momentum diffusion. Although applicable to any type of fluid, we restrict the examples of our theory to Newtonian fluids, for which we both recover the known results for steady and single-frequency pulsating flows, and find new, richer structure of the dispersion as function of system parameters in multi-frequency systems. We show that the effective diffusivity is enhanced significantly by those parts of the time-dependent velocity field that have frequencies smaller than the fluid momentum diffusion rate and the solute diffusion rate.

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Email address for correspondence: soren.vedel@nanotech.dtu.dk
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

28. M. L. Mehta 2004 Random Matrices, 3rd edn. Pure and Applied Mathematics , vol. 142. Elsevier/Academic Press.

34. R. F. Probstein 1994 Physicochemical Hydrodynamics. An Introduction, 2nd edn. John Wiley and Sons.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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