Mathematical analysis of viscometric (polymer) flow fields in capillaries: Taylor dispersion revisited

• Published in: Journal of engineering mathematics Vol. 45; no. 3-4; pp. 269 - 282
• Main Authors: Cook, L P, Nwankwo, E, Schleiniger, G, Wood, B
• Format: Journal Article
• Language: English
• Published: 01-04-2003
• ISSN: 0022-0833
• DOI: 10.1023/A:1022650317386

A general formulation for capillary flow of two miscible fluids - one a dilute plug of polymer fluid inserted into a fully developed Poiseuille flow of the other, a Newtonian stream - is examined for its long time behavior. Phenomenologically, the system evolves from an initial state, that of a plug within the boundaries of sharp, well defined fronts inside a Newtonian stream, to a more homogenized state in the very long time scale. This problem was addressed by G.I. Taylor but with regard to a system of two Newtonian fluids, leading to the well-known results commonly described as 'Taylor axial dispersion'. In this paper, a general and systematic perturbation analysis is presented from which Taylor's result is recovered as a special case of a more general solution which applies to fluids incorporating elastic properties. In particular, the influence of viscoelasticity and (polymer) diffusivity on the observed pressure profile in the capillary conduit is examined. This effect is clearly separated out for small Peclet number flows using asymptotic and numerical analysis. The results identify the influence of fluid viscosity, elasticity, and diffusivity on the observed pressure profile and form the basis for the improved characterization of polymeric elasticity using capillaries - a finding that is of significant scientific and commercial interest. These results were obtained by the authors as a class of observations resulting from the perturbation analysis of forced-flow capillary devices in viscoelastic fluid property investigation.