Taylor dispersion in variable-density, variable-viscosity pulsatile flows

TL;DR

This work addresses how a non-passive scalar, which alters density and transport properties, influences Taylor dispersion in pulsatile pipe flows. It develops a two-time-scale asymptotic framework that separates fast cross-sectional dynamics from slow axial evolution, yielding a one-dimensional, unsteady mixing equation with an effective diffusion coefficient D_eff that incorporates molecular diffusion, steady Taylor dispersion, and oscillatory shear-induced diffusion. The analysis provides explicit cross-sectional solutions for the leading-order flow via functions f and g, establishes solvability constraints, and derives a Lagrangian-coordinate formulation that accurately describes the 1D scalar transport. The resulting model offers a rigorous, generalizable description of variable-density/viscosity effects on scalar dispersion in pulsatile flows, with implications for buoyancy-driven and reactive transport in engineering and environmental contexts.

Abstract

The phenomenon of Taylor or shear-induced dispersion of a non-passive scalar field in a pulsatile pipe flow is investigated, accounting for the scalar field's influence on fluid density and transport coefficients. By employing multiple scale analysis, an effective one-dimensional, unsteady mixing problem for the scalar field is obtained, which includes the diffusion coefficient for shear-induced dispersion. The resulting governing equations are applicable to a range of scalar transport problems in pulsatile pipe flows.