Abstract
The multimode diffusion approximation for solute dispersion in transversely bounded shear flows owes its origin to the formal method of eigenmode expansion. It is put forth upon the premise that a quasi-steady condition termed the Taylor limit of equilibrium exists in the course of time when equilibrium estimates of the residual terms of the concentration distribution can be realistically made contingent to the evolution of their primary counterparts. By applying the Green's function for the diffusion equation, this paper provides a qualifying account for the establishment of the Taylor limit. A method of successive approximations is derived for the determination of the principal mode coefficient functions with the inclusion of bulk reaction and longitudinal diffusion. The resulting equations governing the evolution of these mode coefficient functions are truncated to conform to the multimode diffusion type and the special Taylor-limit results given by Smith are easily deduced. Examples are given to illustrate the attainment of a convergent solution.
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Yu, J.S., Chang, W.S. Taylor limit of equilibration and the multimode diffusion approximation. J Eng Math 28, 297–310 (1994). https://doi.org/10.1007/BF00128749
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DOI: https://doi.org/10.1007/BF00128749