Rheol Acta (2009) 48:961–970
DOI 10.1007/s00397-009-0376-6
ORIGINAL CONTRIBUTION
Sphere settling in an aging yield stress fluid: link between
the induced flows and the rheological behavior
B. Gueslin · L. Talini · Y. Peysson
Received: 27 January 2009 / Accepted: 27 June 2009 / Published online: 17 July 2009
© Springer-Verlag 2009
Abstract The flow pattern induced by the settling of a
non-Brownian sphere in a fluid depends on the rheo-
logical properties of that fluid. For instance, at small
Reynolds numbers, the pattern presents a fore–aft sym-
metry in a Newtonian fluid, whereas, in some viscoelas-
tic polymer solutions, it can exhibit a negative wake,
i.e., an upward flow in the sphere’s wake. This study is
an experimental work on the settling of a sphere in a
suspension of a synthetic colloidal clay, laponite. The
fluid is a yield stress fluid that ages, i.e., whose rheo-
logical properties evolve over time. We show that the
settling velocity of a given sphere, as well as the induced
flow pattern, are strongly modified as the fluid ages. In
particular, the flow pattern asymmetry increases with
C. Allain, passed away in October 2006, whom we keep
in our thoughts.
B. Gueslin (B ) · L. Talini
Univ Pierre et Marie Curie - Paris 6, CNRS,
Univ Paris-Sud 11. Lab FAST, Bât 502,
Campus Universitaire, Orsay 91405, France
e-mail: blandine@gueslin.org
B. Gueslin · Y. Peysson
Institut Français du Pétrole, 1 et 4 avenue de Bois Préau,
Rueil-Malmaison 92852, France
Present Address:
B. Gueslin
Institut de Physique du Globe de Paris case 89,
4 place Jussieu, Paris cedex 05 75252, France
Present Address:
L. Talini
Laboratoire de physicochimie des polymères
et des milieux dispersés ESPCI, 10 rue Vauquelin,
Paris cedex 05 75231, France
e-mail: laurence.talini@espci.fr
the age of the fluid, and a negative wake eventually
forms. We relate those modifications to rheological
measurements and suggest, in line with works dealing
with polymer solutions, that it is the increase in the fluid
viscoelasticity that is responsible for the formation of a
negative wake. The flow field measurements are also
compared with flow-induced birefringence measure-
ments, and we show that very slow relaxation processes
are involved in the sphere settling.
Keywords PIV · Yield stress · Birefringence
Introduction
The seemingly simple problem of a single non-Brownian
spherical particle settling in a non-Newtonian fluid has
been the subject of numerous numerical and exper-
imental studies (Chhabra 1993; McKinley 2001). In
the most widely studied case of low Reynolds num-
bers, the attempts to relate the sphere’s velocity to
the rheological properties of the suspending fluid have
not been completely successful. Although qualitative
features, such as the drag reduction observed in shear-
thinning fluids (Mena et al. 1987) and the drag enhance-
ment in Boger fluids (Solomon and Muller 1996), are
well understood, the agreement between rheological
measurements and settling is rarely quantitative. This
difficulty indeed results, in particular, from the local
nature of the action exerted on the fluid in a settling
experiment, opposed to the averaging over the whole
sample volume made in a rheological measurement.
To better understand the settling behavior, studies
have aimed to characterize the creeping flows induced
by the settling sphere in the fluids. In a Newtonian