Sahraoui Chaieb
   Assistant Professor of Theoretical and Applied Mechanics
   University of Illinois at Urbana-Champaign (web page)

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: