Drainagedriven instabilities in foams

1
Drainage-driven instabilities in foams

• M.D. Alonso,
• S. Hutzler,
• S.J. Cox and
• D. Weaire

Motivation A foam subject to forced drainage at
high flow rates can become unstable. In this
poster we describe different instability modes
for 2D and 3D foams and give some ideas about the
conditions that trigger different instabilities.

Vertical tube
Roll type I
Roughly half of the bubbles move upwards while
the other half move downwards in a convective
pattern.(1,2)
0 s.
2 s.
4 s.
Roll type II
All the bubbles on the surface of the cylinder
move downwards. We infer that the bubbles in the
centre of the tube move upwards (3)..
0 s.
2 s.
4 s.
Comparative ranges of domain of the rolls in a
vertical tube. The length of the roll type I
increases when the input is off-centered.
The liquid fraction at the onset of the motion
depends on the bubble size but it is fairly
independent of the tube diameter, as we can see
in the graph.
Tilted tube
2D instabilities
By tilting the tube we impose different local
liquid fraction below and above the axis of the
tube, forcing a convective roll.
Roll type I and roll type II are both observed in
2D experiments under different conditions. Roll
type I is associated with an imbalance in the
wetting input. Roll type II seems to be limited
to the layer of bubbles at the walls (4).
The graph shows the velocity of the bubbles that
move upwards in relation to the angle of tilt.
Each curve is labeled with the fixed flow rate at
which it was taken. Data are fitted to curves a
tanh(bq -c) where q is the tilt angle. The
parameter a is the maximal velocity reached by
the bubbles and the angle at the onset of the
motion is c/b.
0 s.
3 s.
6 s.
This graph shows a fitting of the onset angle,
c/b, to a theoretical formula (3).
0 s.
3 s.
6 s.

• References
• Hutzler S., Weaire D. and Crawford R. (Europhys.
  Lett.,41,461-465(1998) )
• Vera M.U., Saint-Jalmes A. and Durian D, J.
  (Phys. Rev. Lett. ,84,3001-3004(2000))
• Alonso M.D. et al. (in preparation)
• Alonso M.D. et al. (in preparation)

Acknowledgments Research supported by ESA-Prodex,
as a contribution to ESA contract
C14308/AO-075-99, and the Irish HEA (PRTL199).