Eur. Phys. J. E 16, 29-35 (2005)
DOI: 10.1140/epje/e2005-00004-3

An analytical approach to the rise velocity of periodic bubble trains in non-Newtonian fluids

X. Frank, H.Z. Li and D. Funfschilling

Laboratoire des Sciences du Génie Chimique (CNRS, UPR 6811), ENSIC-INPL, 1, rue Grandville, BP 451, 54001 Nancy Cedex, France

li@ensic.inpl-nancy.fr

(Received 23 April 2004 / Received in final form 5 October 2004 / Published online 31 January 2005)

Abstract
The present study aims at providing insight into the acceleration mechanism of a bubble chain rising in shear-thinning viscoelastic fluids. The experimental investigation by the Particle Image Velocimetry (PIV), birefringence visualisation and rheological simulation shows that two aspects are central to bubble interactions in such media: the stress creation by the passage of bubbles, and their relaxation due to the fluid's memory forming an evanescent corridor of reduced viscosity. Interactions between bubbles were taken into account mainly through a linear superposition of the stress evolution behind each bubble. An analytical approach together with the rheological consideration was developed to compute the rise velocity of a bubble chain in function of the injection period and bubble volume. The model predictions compare satisfactorily with the experimental investigation.

PACS
47.55.Dz - Drops and bubbles.
47.50.+d - Non-Newtonian fluid flows.
83.60.Fg - Shear rate dependent viscosity.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2005