Sahraoui Chaieb
Assistant
Professor of Theoretical and Applied Mechanics
University of
Illinois at Urbana-Champaign (web
page)
sch@uiuc.edu
Phase Shifted Feedback Interference Microscope (Application to Contact
Line Dynamics in Spreading)
Contrary to other techniques used in thin liquid film characterization,
this instrument is capable of achieving high temporal resolution and high
spatial resolution. We use this instrument to study the shape of a
thin liquid film in the vicinity of a moving contact line.
Laser Feedback Interferometer:
The beam emitted from the front of the laser is sent through and
electro-optic modulator (EOM), a linear polarizer with a fixed orientation
parallel to the polarization of the laser, and then focused onto a sample
using a 20 / 0.40 N.A. long working distance microscope objective .
Fluctuations in the laser's steady-state power were determined by monitoring
the light transmitted through the laser's rear mirror using a photodetector.
The voltage signal from the photodetector is digitized with a 100 kHz,
16-bit analog-to-digital board on a computer bus; This board is also used to
send voltage steps to a high-voltage operational amplifier and then to the
EOM. The process is automated with labview. To avoid thermal
perturbations that affect the polarization of the laser beam a box to
enclose the interferometer from the surrounding air. Also in order to
minimize beam distortion we installed a cylinder at the output of the EOM
cell. TTo increase the resolution, we use instead of the 0.40 NA standard
objective a higher NA objective (0.80 N.A.). The inconvenience of this
objective is that the working field is much smaller than the working field
of a standard objective
We have performed preliminary experiments and we obtained promising results.
Buckling and rippling in thin viscous fluid sheets
As a result of a competition between in-plane compression and out of
plane bending, thin sheets are known to undergo buckling instabilities. We
have noticed that not only solid sheets suffer such instabilities but
viscous sheets with slender geometry also suffer such instabilities. In the
purpose to study such instabilities we have investigated two different set
up:
Rippling Instabilities in a collapsing bubble:
We inject an air bubble into a container filled with a very viscous silicon
oil (Viscosities range from 100 Pa.s to 1000 Pa.s ). When the bubble reaches
the free surface, it becomes hemispherical and has an initial thickness of
one or two millimeters. We let the bubble drain and its thickness decreases
and we poke it with a syringe at its apex. At the beginning, the hole
expands very fast (exponentially) and the air escape from the bubble. Since
the bubble is thicker at its base, the hole is slowed down since he meets a
thicker film. During this slowing down process, the crown collapses under
its own weight. To preserve surface and minimize stretching, the film
buckles and fold in a wavy structure that looks like an eye iris. We
measured the number of ripples at onset as a function of the original bubble
size and we also measured the hole size as a function of the original size.
We fitted our experimental results with a theory similar to the elasticity
of shells.
Bubble Drop Quicktime Video (1.4MB)
Buckling of sheared viscous sheets:
To study "viscous buckling" in a more controlled fashion, we submit thin
viscous sheet to shearing. The set up resembles the one used for Couette-Taylor
flows. Instead of one liquid, a thin layer of a highly viscous liquid (PB)
is sustained on a denser and much less viscous one (water). The layer is
pinned to an inner rotating cylinder. The layer being attached to both the
inner and outer cylinders is buckled under the action of shear. The
resulting pattern has a spiral shape expanding from the inner to the outer
cylinder. We are studying this pattern by quantifying the wavelength and the
criticality of the onset of the instability..
Cusp Formation in a draining viscous fluid
We have observed that when a highly viscous liquid drains from a container
through a hole of a given size but much smaller that the container's size, a
cusp appears first closer to the interface at short times than becomes
closer to the hole at later times. The cusp moves towards the hole and
penetrates it at the late stage of drainage. The cusp then stretches
vertically over a distance of more than three centimeters for a 1000 Pa.s
PDMS "gel". This phenomena is considered among the most challenging problem
in interfacial fluid mechanics and it become one of the most interesting
subject in fluid mechanics in the last five years. We are studying the
dynamics of this cusp and its geometry in terms of stokes flow formulation
using stokeslets and green functions. We noticed that this problem is
similar to the viscous pinch-off problem of a viscous droplet. In our case,
the velocity field away from the singularity is horizontal and become
slowly central, whereas near the hole, the velocity field becomes mainly
vertical. We propose an analytical solution where the stokeslet is modified
to account for the right velocity field. A numerical simulation to fit our
experimental results will be presented as well.
Peer-reviewed
publications list: |