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On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid

Published online by Cambridge University Press:  19 January 2016

D. Fraggedakis ,
M. Pavlidis ,
Y. Dimakopoulos  and
J. Tsamopoulos
D. Fraggedakis
Affiliation:
Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras, Patras 26500, Greece
M. Pavlidis
Affiliation:
Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras, Patras 26500, Greece
Y. Dimakopoulos
Affiliation:
Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras, Patras 26500, Greece
J. Tsamopoulos*
Affiliation:
Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras, Patras 26500, Greece
*
†Email address for correspondence: [email protected]
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Abstract

We examine the abrupt increase in the rise velocity of an isolated bubble in a viscoelastic fluid occurring at a critical value of its volume, under creeping flow conditions. This ‘velocity discontinuity’, in most experiments involving shear-thinning fluids, has been somehow associated with the change of the shape of the bubble to an inverted teardrop with a tip at its pole and/or the formation of the ‘negative wake’ structure behind it. The interconnection of these phenomena is not fully understood yet, making the mechanism of the ‘velocity jump’ unclear. By means of steady-state analysis, we study the impact of the increase of bubble volume on its steady rise velocity and, with the aid of pseudo arclength continuation, we are able to predict the stationary solutions, even lying in the discontinuous area in the diagrams of velocity versus bubble volume. The critical area of missing experimental results is attributed to a hysteresis loop. The use of a boundary-fitted finite element mesh and the open-boundary condition are essential for, respectively, the correct prediction of the sharply deformed bubble shapes caused by the large extensional stresses at the rear pole of the bubble and the accurate application of boundary conditions far from the bubble. The change of shape of the rear pole into a tip favours the formation of an intense shear layer, which facilitates the bubble translation. At a critical volume, the shear strain developed at the front region of the bubble sharply decreases the shear viscosity. This change results in a decrease of the resistance to fluid displacement, allowing the developed shear stresses to act more effectively on bubble motion. These coupled effects are the reason for the abrupt increase of the rise velocity. The flow field for stationary solutions after the velocity jump changes drastically and intense recirculation downstream of the bubble is developed. Our predictions are in quantitative agreement with published experimental results by Pilz & Brenn (J. Non-Newtonian Fluid Mech., vol. 145, 2007, pp. 124–138) on the velocity jump in fluids with well-characterized rheology. Additionally, we predict shapes of larger bubbles when both inertia and elasticity are present and obtain qualitative agreement with experiments by Astarita & Apuzzo (AIChE J., vol. 11, 1965, pp. 815–820).

JFM classification

Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface) Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 310 - 346
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Copyright
© 2016 Cambridge University Press 

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