Computational study of planar extrudate swell flows with a viscous liquid–gas interface

• Published in: AIChE journal Vol. 68; no. 3
• Main Authors: Mendes Junior, Paulo Roberto C., Siqueira, Ivan R., Thompson, Roney L., Carvalho, Marcio S.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.03.2022; American Institute of Chemical Engineers
• Subjects: Boussinesq equations; Boussinesq–Scriven model; Computer applications; Constitutive equations; Constitutive relationships; Dimensionless numbers; Equations of motion; extrudate swell flows; Finite element method; Free surfaces; interfacial rheology; Interfacial stresses; Mesh generation; Newtonian liquids; Plug flow; Tensors; Viscosity; viscous interfaces
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.17503

We present a computational study of planar extrudate swell flows of Newtonian liquids with a viscous liquid–gas interface. The model consists of the equations of motion coupled with the Boussinesq–Scriven constitutive equation for the interfacial stress tensor. The resulting set of equations is solved with the finite element method coupled with an elliptic mesh generation strategy to capture the free surface. The results show a detailed parametric study in terms of the capillary number and the Boussinesq number, a dimensionless parameter used to measure the ratio of viscous forces at the interface to viscous forces in the bulk liquid. The predictions reveal that the extrudate swells dramatically as the interfacial viscosity grows. The interfacial viscosity slows down the flow both in the bulk liquid and at the interface, and thus the extrudate size increases to conserve mass in the slow plug flow that develops under the free surface.