Abstract
The displacement of a fluid in a capillary tube by gas injection occurs in many practical applications like enhanced oil recovery, coating of catalytic converters and gas-assisted injection molding. This situation has been extensively studied both by theory and experiments in the case of Newtonian fluids. However, the complete understanding of the effects of the rheological properties of the displaced fluid in this type of flow is still under investigation. Recent work has shown that, at a given Capillary number, the amount of shear thinning liquid deposited on the tube wall falls with decreasing power-law exponent, but a singular perturbation method was not able to capture this effect. The flow of viscoelastic liquids has also been analyzed experimentally by measuring the fractional coverage of the tube wall and by Particle Tracking Velocimetry. The main conclusion was that the flow near the interface presents strong extensional deformation and that the viscoelastic behavior of the liquid leads to larger deposited liquid layer on the wall. Flow simulation with non Newtonian liquids for this situation is rare. The presence of the free surface and the non linearities of the constitutive model make the problem extremely complex. In this work, the complete two dimensional solution of the free surface flow is obtained using the Galerkin finite element method. The rheological character of the liquid is modelled by two different constitutive equations: a simple Generalized Newtonian Liquid model, to analyze the effect of shear sensitive liquids; and a new algebraic constitutive relation that is capable of describing variable shear and extensional viscosity, first normal stress coefficient and second normal stress coefficient. This equation is used to analyze the effect of the viscoelastic properties of the liquid on the flow field.
Effect of kinetic and configurational thermostats on calculations of the first normal stress coefficient in nonequilibrium molecular dynamics simulations