Gas-displacement of non-Newtonian liquids in capillary tubes

The displacement of a non-Newtonian liquid by a gas in a capillary tube is studied. The complete solution of the differential equations that govern this free-surface flow is obtained using the Galerkin finite element method. The non-Newtonian behavior of the displaced liquid is modeled by two different constitutive equations, namely, (1) a simple Generalized Newtonian Liquid model, to analyze the effect of shear-rate sensitive liquids, and (2) the algebraic constitutive relation proposed by Thompson et al. [Thompson, R.L., Souza Mendes, P.R., Naccache, M.F., 1999. A new constitutive equation and its performance in contraction flows. J. Non-Newt. Fluid Mech. 86, 375–388], which is capable of predicting decoupled shear and extensional viscosities as well as non-null normal stress differences. Among other results, the predictions suggest that the increase of liquid film on the tube wall is related to the purely elastic extensional viscosity rather than to normal stress differences.