Displacement of a liquid in a capillary tube by gas injection occurs in many situations, like enhanced oil recovery, coating of catalytic converters and gas-assisted injection molding. Generally the liquid being displaced is a polymeric solution or dispersion, that are not Newtonian. Viscoelastic forces alter the force balance in various parts of the flow and consequently change the amount of liquid left attached to the capillary wall. In order to model the effect of the rheological properties in this important flow, the mechanical behavior of the flowing liquid has to be well described by an appropriate constitutive model. Here, the Oldroyd-B differential constitutive equation that approximate viscoelastic behavior of dilute polymer solutions was used, together with momentum and continuity equation, to model the two-dimensional free surface flow near the gas-liquid interface. The equation system was solved with the Finite Element Method. The resulting nonlinear system of algebraic equations was solved by Newton’s method. The results show the effect of the viscoelastic character of the liquid on the free surface shape and the film thickness attached to the capillary wall.

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