Microfluidic Membrane Networks - Towards Autonomous Soft Matter Systems - page 16

within the channel mainly due to their hydrodynamic drag in the surrounding oil
phase. Contact between adjacent droplets was not desired, in an effort to keep droplet
coalescence and other cross-talk effects to a minimum.
The situation becomes completely different if the volume fraction of the oil phase
is reduced such that droplets maintain mutual contact throughout. The transport of
the droplets in the device is then not anymore determined by the streamlines of the
oil phase, but by the (dynamically varying) geometry of optimum packing of the
droplets within the channel geometry [ 12 , 16 ]. In fact, the arrangement of spherical
droplets has been reported to change from random to crystalline as their volume
fraction becomes large. In a square channel with a lateral dimension of about four
droplet diameters, a volume fraction of 0.75 shows a crystalline order, while a random
arrangement is observed at 0.55 [ 12 ].
It is clear that this opens up qualitatively new possibilities of droplet manipulation.
In particular, the existence of several meta-stable configurations gives rise to strong
hysteresis effects in the droplet geometry. Droplet motion may thus not be reversible,
and become strongly history dependent. If the droplets are all of the same size, i.e.,
if a mono-disperse gel emulsion is used, these effects can in principle be exploited
to dynamically access a large variety of droplet configurations in the device [ 10 , 11 ,
17 , 18 ]. Furthermore, these configurations are geometrically rather stable, because
the wetting forces determining the angles of contact of the oil lamellae spanning
between the droplets, give rise to substantial energy barriers for any spontaneous
rearrangement.
A simple example is displayed in Fig. 2.3 , which shows regular configurations of
droplets with different content. We used squalane with 15mg/ml of 1,2-diphytanoyl-
sn-glycero-3-phosphocholine (DPhyPC, Avanti Polar Lipids) plus 15mg/ml of
cholesterol as the oil phase, which enters the emulsification unit [ 13 ] from the left.

Fig. 2.3 Gel emulsions of water in oil generated by step emulsification, forming rafts in a wider
channel. The channel width is 500 m, the volume fraction of the aqueous phase is 0.75. The elemen-

tary cells of such rafts can be quite complex, as the lower example shows. Controlled rearrangement
of these configurations are possible by appropriately chosen channel geometries [ 12 , 18 , 20 ]

µ