Reversibility of droplet trains
in microfluidic networks
Piotr Garstecki1, Michael J. Fuerstman2,
George M. Whitesides2
1 Institute
of Physical Chemistry, PAS, Warsaw, Poland
2 Department of Chemistry and Chemical Biology, Harvard University
Kenis, Science (1999)
the simplest network – a single loop
amplification and feedback:
• drop flows into the arm characterized by lower resistance
(higher pressure gradient)
• once the drop enters a channel it increases its resistance
the simplest network – a single loop
period-1
period-2
ffeed / fflow
period-3
irregular
Phys. Rev. E (2006)
nonlinear dynamics embedded in a linear flow
invariant under: x  - x,
(or, equivalently V  - V, and p  -p)
period 1
period N
??? period 1
period N
The “operation” of the system
is stable against small differences
in the incoming signal
Science (2007)
there is amplification and feedback, but:
• the nonlinear events are isolated (very short)
• the long-range interactions are instantaneous (information is
transmitted much faster than the flow proceeds)
• it is all embedded in a linear, dissipative flow
formation of bubbles – a single nozzle
water
gas
water
height = 30 mm
1 mm
Appl. Phys. Lett. 85, 2649 (2004)
formation of bubbles – a single nozzle
water
gas
water
height = 30 mm
Appl. Phys. Lett. 85, 2649 (2004)
fraction of the area of the orifice occupied by gas
1
fraction
1 mm
0.8
0.6
0.4
0.2
0
0
5
10
15
20
time [ms]
nitrogen (p=8 psi) / 2% Tween20 in water (Q=3 mL/h), orifice width/length/height: 60/150/30 mm.
liquid
gas
liquid
50 mm
end of the gas
Inlet channel
equilibrium shape
for a given volume
enclosed by the
gas-liquid interface
end of the orifice
surface evolver
• rate of collapse linear in the of inflow of the
continuous phase
• only the very last (and short) stage is driven
by interfacial tension
Phys. Rev. Lett. 94, 164501 (2005)
coupled flow-focusing oscillators
information
(fast)
final break-up takes ‘no’ time
evolution
(slow)
+ dissipative dynamics (low to mod Re)
coupled flow-focusing oscillators
period-29
Nature Phys. 1, 168 (2005)
coupled flow-focusing oscillators
Nature Phys. 1, 168 (2005)
160 kfps –
– 6.25 ms
The observed dynamics is (again) stable.
Nature Phys. 1, 168 (2005)
dynamics of flow through networks:
• complicated (complex)
 it is possible to design complex,
automated protocols
• stable
 the protocols can be executed in practice