W' Drenckhan, N' Kern, S' Hutzler, D' Weaire

1
Controlling bubble flow through narrow channels
W. Drenckhan, N. Kern, S. Hutzler, D.
Weaire Trinity College Dublin
Introduction
Many questions concerning foam rheology can be
addressed in the continuous limit (bubbles
small compared to a typical length scale). We are
interested in the opposite limit. Such a
situation where surfactant bubbles flow through
narrow channels arises naturally in the context
of porous media 1. Recent experiments on
magnetic foams 2 have added another dimension
to this, showing that an applied magnetic field
provides control on the structure of bubbles
flowing through narrow pipes and junctions. In
particular the perspective of developing active
elements in order to manipulate the bubbles in
flow suggests applications in fluidic networks.

• Here we are interested in the simplest case
  allowing us to explore these possibilities
• Bubble diameter d of order of channel width D
• Surfactant films (non-magnetic)
• 2d channels (between glass plates) of different
  shapes
• We want to understand how the geometry of channel
  borders alone can be used to design functional
  elements and under what conditions they are
  reliable.

N2
Our immediate goal is to study the basic elements
of a network the channels, the junctions at
which they meet and devide, and the effects of
geometrical features such as bends.
Channel width and liquid fraction (stability
domains) First of all we need to understand
which structures are stable for which (relative)
channel width (see also 3) and for which liquid
fraction, and how we can use variations in the
width to provoke consecutive transitions between
1,2,3, rows of bubbles.We have studied this
using a wedge-shaped channel
Changing places The mechanism to make bubbles go
one way or another is based on swapping two rows
of bubbles before separating them by a junction.
Our first question here is can we design a
channel of such a shape as to make bubbles swap
sides?. Indeed, this can be done by introducing
two consecutive constrictions, producing an
S-shaped channel
Comparing convergence and divergence we can
establish a stability diagram, identifying
operational parameters for optimal reliability
Around the bend Finally, we need to understand to
what extent channels may be curved without
affecting the structure. We do so by looking at
semi-circular channels.The short answer is, of
course, that only sharp bends (on the scale of
the bubble size) lead to topological changes
This behaviour can be explained in terms of
quasistatics, i.e. it is a structural effect
only. Simulations (in the dry limit) using the
Surface Evolver 4 reproduce the sequence of
transitions.
Divide and conquer The junctions are surprisingly
straightforward An incoming double-row
structure is split up nicely into two bamboo
channels, and the same element can operate in
reverse to recombine them.
However, this effect is much more involved
depending on the flow rate we observe zero, one,
or even two consecutive transitions. This is a
dynamic effect, in which dissipation plays a
role. Indeed the quasistatic model does not
predict any transitions, and we thus need a
better model 5 to account for viscous
dissipation.
The whole process is amazingly reliable, unless
the foam is extremely dry.
Acknowledgements We would like to thank the SAP
AG (Germany), the German National Merit
Foundation and the European Union (Marie Curie
Fellowship) for their financial
support.
Bibliography 1 Q. Xu and W.R. Rossen,
Proceedings Eurofoam 2000 136-144 4
K. Brakke (1992), Exp. Math. 1 (2) 141-165 2
S. Hutzler, D. Weaire, F. Elias and E. Janiaud
(2002), Phil. Mag. Lett. 82 (5) 297-301,
5 J. A. Glazier and D. Weaire (1992), J. Phys.
Cond. Matt. 4 1867-1894 3 M. E. Rosa and M.
A. Fortes (1998), Phil. Mag. A, 77(6) 1423 -
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