We study the rising motion of small bubbles that undergo contraction, expansion, or oscillation in a shear-thinning fluid. We model the non-Newtonian response of the fluid using the Carreau-Yasuda constitutive equation, under the assumptions that the inertia of the fluid and the bubble is negligible and that the bubble remains spherical. These assumptions imply that the rising velocity of the bubble is instantaneously proportional to the buoyancy force, with the proportionality constant given by the inverse of the friction coefficient. Instead of computing the rising velocity for a particular radial dynamics of the bubble, we evaluate its friction coefficient as a function of the rheological parameters and of the instantaneous expansion/contraction rate. To compute the friction coefficient, we impose a translational motion and we linearize the governing equations around the expansion/contraction dynamics of the bubble, which we solve using a perturbation expansion along with the finite element method. Our results show that the radial motion of the bubble reduces the viscosity of the surrounding fluid and may thus markedly decrease the friction coefficient of the bubble. We use the friction coefficient to compute the average rise velocity of a bubble with periodic variations of its radius, which we find to be strongly increased by the radial pulsations. Finally, we compare our predictions with the experiments performed by Iwata et al. [“Pressure-oscillation defoaming for viscoelastic fluid,” J. Non-Newtonian Fluid Mech. 151(1-3), 30–37 (2008)], who found that the rise velocity of bubbles that undergo radial pulsations is increased by orders of magnitude compared to the case of bubbles that do not pulsate. Our results shed light on the mechanism responsible for enhanced bubble release in shear-thinning fluids, which has implications for bubble removal from complex fluids.
Skip Nav Destination
Article navigation
August 2019
Research Article|
August 20 2019
The rising velocity of a slowly pulsating bubble in a shear-thinning fluid
Special Collection:
Invited Contributions from Outstanding Early Career Researchers
Marco De Corato
;
Marco De Corato
a)
1
Department of Chemical Engineering, Imperial College London
, London, SW7 2AZ, United Kingdom
2
Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology (BIST)
, Baldiri Reixac 10-12, 08028 Barcelona, Spain
Search for other works by this author on:
Yannis Dimakopoulos
;
Yannis Dimakopoulos
3
Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras
, Patras 26500, Greece
Search for other works by this author on:
John Tsamopoulos
John Tsamopoulos
3
Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras
, Patras 26500, Greece
Search for other works by this author on:
a)
Electronic mail: mdecorato@ibecbarcelona.eu
Note: This paper is part of the special topic, Invited Contributions from Outstanding Early Career Researchers.
Physics of Fluids 31, 083103 (2019)
Article history
Received:
May 02 2019
Accepted:
July 26 2019
Connected Content
A companion article has been published:
Bubble removal is made easier as scientists identify mechanisms for bubble release in shear-thinning fluids
Citation
Marco De Corato, Yannis Dimakopoulos, John Tsamopoulos; The rising velocity of a slowly pulsating bubble in a shear-thinning fluid. Physics of Fluids 1 August 2019; 31 (8): 083103. https://doi.org/10.1063/1.5108812
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Pay-Per-View Access
$40.00
Citing articles via
Hidden turbulence in van Gogh's The Starry Night
Yinxiang Ma (马寅翔), 马寅翔, et al.
On Oreology, the fracture and flow of “milk's favorite cookie®”
Crystal E. Owens, Max R. Fan (范瑞), et al.
Fluid–structure interaction on vibrating square prisms considering interference effects
Zengshun Chen (陈增顺), 陈增顺, et al.
Related Content
Unsteady flow of a thixotropic fluid in a slowly varying pipe
Physics of Fluids (August 2017)
A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate
Physics of Fluids (May 2015)
Quantifying the destructuring of a thixotropic colloidal suspension using falling ball viscometry
Physics of Fluids (January 2021)
Non-Newtonian power-law fluid flow over obstacles embedded inside a cavity
Physics of Fluids (April 2021)
Numerical and experimental investigations of an air bubble rising in a Carreau-Yasuda shear-thinning liquid
Physics of Fluids (March 2017)