Summary: Flow of a two component fluid in a capillary is studied analytically and numerically to obtain an understanding of the basic parameters and their effect on the advection-diffusion flow process. One fluid (the solvent) is Newtonian, and the other is a dilute polymer plug (the solution) introduced into the flowing solvent. The polymer plug is modeled as a Maxwell fluid. The ultimate goal is characterization of industrially manufactured polymers in real time, at-line.
Experimentally, the evolution of a dilute plug introduced into a fully developed capillary solvent flow is tracked by observing the pressure drop downstream. The volumetric flow rate is held constant. While the pressure plateau has been identified with the intrinsic viscosity of the polymer, in this work, we relate the leading edge behavior of the plug/plateau to the elasticity and diffusivity of the polymer. The combination of these three parameters should unambiguously characterize the polymer chains in solution.
In this paper, asymptotic expansions of the equations governing the flow and advection-diffusion are carried out in terms of a dilution parameter \(\epsilon\) (\(\ll 1\)). The resulting initial-boundary value problems are solved numerically in order to characterize the effect of polymer properties on the observed pressure profile.