Steady bubble rise and deformation in Newtonian and Bingham fluids and conditions for their entrapment
Advancing the chemical engineering fundamentals
Rheology (T2-4)
Keywords: Bubble rise, Bingham fluids, Finite element methods, Elliptic mesh generation
We examine the buoyancy-driven rise of a bubble in a Bingham fluid assuming axial symmetry and steady flow. Bubble pressure and rise velocity are determined, respectively, by requiring that its volume and center of mass remain constant. The continuous constitutive model suggested by Papanastasiou is used to describe the viscoplastic behavior of the material. The flow equations are solved numerically using the mixed finite-element/Galerkin method. The nodal points of the computational mesh are determined solving a set of elliptic differential equations to follow the often large deformations of the bubble-surface. The accuracy of solutions is ascertained by mesh refinement and by predicting very accurately previous experimental and theoretical results for Newtonian fluids. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties. Besides the yield surface away from the bubble which surrounds it, unyielded material can arise either behind the bubble or around its equatorial plane in contact with the bubble. As the Bingham number increases, the yield surface at the equatorial plane and away from the bubble merge and the bubble gets entrapped. When the Bond number is small and the bubble cannot deform from spherical the critical Bingham number is 0.143, i.e. it coincides with the critical Bingham number for the entrapment of a solid sphere in a Bingham fluid. As the Bond number increases allowing the bubble to squeeze through the material easier, the critical Bingham number increases as well.
Presented Thursday 20, 15:40 to 16:00, in session Rheology (T2-4).
