Materials Science and Engineering Laboratory FY 2004 ... - NIST

This rate is directly proportional to interfacial tension σ.
Specifically, the drop relaxation time τ is:
τ =
( 2ηˆ
+ 3)(
19ηˆ
+ 16)
ηca
40(
ηˆ
+ 1)
σ
where a o is the undeformed drop radius, h c is the
continuous phase viscosity, ε& is the shear rate, and
ηˆ is the relative viscosity of the drop.
Figure 2: Freeze-frame image of drops flowing left to right in an
extensional flow gradient. When the drops leave the constriction
(the channel walls appear as slanted lines in the left half of the
image), the flow decelerates in proportion to the change in
cross-sectional area. The drops, which are generated periodically
in time, therefore, become closer together. This deceleration
corresponds to a stretching in the transverse direction; note that
the drops at the left side are stretched vertically, and their
deformation decays as they pass to the right.
The current measurement rate may exceed 100 data
points/s and is dependent on drop formation and image
acquisition rates.
Figure 3: LabVIEW interface used to control the instrument
and record data.
o
Technical Highlights
Figure 4: a) Simulated and b) experimental analysis of drop
deformation upon departure from the channel constriction.
The radius a o , deformation D and velocity u of the drops are
measured directly by image analysis, at a rate of > 100 data
points/s. The extension rate ε is simply the gradient in the velocity
du/dx. When the data is plotted in this way, the slope is directly
proportional to the interfacial tension. For water in oil, the
tension is (31.8 ± 0.8) mN/m, which is in accord with pendant
drop measurement (32.0 mN/m). For the surfactant
(EO 19PO 30EO 19) aqueous solution in oil, the tension is 7.2 mN/m.
In this experiment, the interface age is approximately 1 s.
For More Information on this Topic
E.J. Amis, P.R. Start (Polymers Division, NIST);
Focus Project Members: ICI National Starch;
Procter and Gamble
J.T. Cabral, S.D. Hudson, C. Harrison, and
J.F. Douglas, “Frontal Photopolymerization for
Microfluidic Applications,” Langmuir, in press.
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