ON THE GAS PENETRATION IN PERIODICALLY CONSTRICTED CIRCULAR TUBES FILLED WITH VISCOELASTIC LIQUIDS
Advancing the chemical engineering fundamentals
Polymer Science & Engineering - I (T2-12a)
Keywords: Gas Penetration, Viscoelastic Liquid, Liquid Displacement, Viscoelastic Instabilities, Numerical Simulation
The displacement of a viscous liquid by a gaseous phase is a problem of fundamental importance in the Polymer and Chemical industry. There are many practical applications and physical operations, such as the enhanced oil recovery, the monolith reactors, the pulmonary airway reopening, the gas-assisted injection molding, which have as a common basic feature the effective displacement of a liquid by gas. Here we examine numerically the displacement of viscoelastic liquids by pressurized air from harmonically undulated tubes of finite length. This unsteady process gives rise to a long open bubble of varying radius, increasing length and surrounded by the liquid. The viscoelastic part of the liquid stresses follows either the exponential PTT or the Oldroyd-B constitutive law. In general, the thickness of the liquid film that remains on the tube wall is non-uniform. Under creeping flow conditions, it varies periodically, but with a phase difference from the tube radius. The liquid fraction remaining in each periodic segment of the tube increases as the ratio between the minimum and maximum of the tube radius, S, decreases, whereas it tends to an asymptotic value for straight tubes, as S->1 or as the wavelength of the tube undulation increases, although here the flow is accelerating. The liquid fraction also depends strongly on the solvent viscosity and the exponential parameter of the PTT model, eptt. It increases as any of the two parameters decreases and tends to the Newtonian limit as eptt takes large enough values. At high values of the Reynolds number, Rep, the film thickness increases with the axial distance, and the periodicity of the velocity and stress fields ahead of the bubble tip, which exists under creeping flow conditions, is broken. At even higher Reynolds numbers, recirculating vortices develop inside each tube expansion and when also decreases significantly, nearly isolated bubbles are formed in each tube segment, while the free surface exhibits short wavelength instability due to the combination of inertia and elastic forces.
References
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2.Dimakopoulos, Y., and Tsamopoulos, J., A quasi-elliptic transformation for moving boundary problems with large anisotropic deformations, J. Comput. Phys., Vol. 192, pp. 494–522, 2003a.
3.Dimakopoulos, Y., and Tsamopoulos, J., Transient displacement of a Newtonian fluid by air in straight or suddenly constricted tubes, Phys. Fluids, Vol. 15 (7), pp. 1973-1991, 2003b.
4.Dimakopoulos, Y., and Tsamopoulos, J., Transient displacement of Newtonian liquid by air in periodically constricted circular tubes, AIChE J., Vol. 52 (8), pp. 2707-2726, 2006.
Presented Tuesday 18, 12:00 to 12:20, in session Polymer Science & Engineering - I (T2-12a).
