Taylor dispersion in the presence of time-periodic convection phenomena. Part I. Local-space periodicity

M. Shapiro*, H. Brenner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Generalized Taylor dispersion theory is herein extended to circumstances for which the transport of dissolved or suspended chemically reactive (as well as inert) solutes is affected by carrier-solvent flow fields and/or external forces that are time periodic in both their global and local microscale spaces (and possess commensurate frequencies). The local-space- and time-averaged solute transport process is characterized by three time-independent, but frequency-dependent microscale phenomenological coefficients - K̄*, Ū*, and D̄*, representing the mean chemical reaction rate, velocity vector, and dispersivity dyadic of the solute, respectively. These macroscale transport coefficients are expressed in terms of time-periodic eigenfunctions and corresponding eigenvalues using a recently developed solution scheme. This scheme permits the analysis of phenomena involving time-periodic transport coefficients on a par with that for the classical case of time-independent microscale phenomenological coefficients. The analysis generalizes to time-periodic local-space phenomena a previous treatment, in which only the global-space coefficients were allowed to vary periodically with time. This greatly enlarges the scope of potential applications of the analysis. In addition to the time-averaged phenomenological coefficients K̄*, Ū*, and D̄*, comparable instantaneous coefficients are defined governing the local-space-averaged instantaneous solute concentration. In contrast with their time-averaged counterparts, K̄*, Ū*, and D̄*, the latter instantaneous transport coefficients are shown to depend upon the initial solute distribution within the local space. Because of coupling between the local- and global-space transport processes in oscillatory flows and/or oscillatory external force fields, all harmonics of the resulting global-space solute velocity field contribute to the mean convective solute transport. This phenomenon may result, for example, in zero solvent-nonzero solute net macroscale transport (or vice versa). The driving frequency of the local-space time-periodic transport process may be used to parametrically control the macroscale solute reactivity rate coefficient, as well as the solute's mean velocity and dispersivity about that mean. A companion paper (Part II) [Phys. Fluids A 2, 1744 (1990)], provides an example, albeit for the nonreactive case.

Original languageEnglish
Pages (from-to)1731-1743
Number of pages13
JournalPhysics of fluids. A, Fluid dynamics
Volume2
Issue number10
DOIs
StatePublished - 1990
Externally publishedYes

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