Experiments reveal a "threshold of instability" of an elastic plastic material

Arindam Banerjee, associate professor of mechanical engineering and mechanics at the University of Lehigh, studies the dynamics of materials in extreme environments. He and his team built several devices to effectively study the dynamics of fluids and other materials under the influence of strong acceleration and centrifugal force.

One of the areas of interest is Rayleigh-Taylor instability, which occurs between materials of different densities when the density and pressure gradients are in opposite directions, creating unstable lamination.

"In the presence of gravity, or any field of acceleration, the two materials penetrate as" fingers, "says Banerjee.

According to Banerjee, the understanding of instability is mainly limited to fluids (liquids or gases). Little is known about the evolution of instability in accelerated solids. The short time scales and the large measurement uncertainties of the accelerated solids make the search for this type of material very difficult.

Banerjee and his team have successfully characterized the interface between an elastoplastic material and a light material in acceleration. They discovered that the appearance of instability – or "threshold of instability" – was related to the size of the amplitude (perturbation) and the wavelength ( distance between the peaks of a wave) applied. Their results showed that for two-dimensional and three-dimensional perturbations (or motions), a decrease in initial amplitude and wavelength produced a more stable interface, thus increasing the acceleration required for l & # 39; instability.

These results are described in an article published today in Physical examination E called "Rayleigh-Taylor-instability experiments with elastic-plastic materials." In addition to Banerjee, co-authors include Rinosh Polavarapu (currently a PhD student) and Pamela Roach (a former Master's student) from the Banerjee Group.

"The scientific community is questioning whether the growth of instability is a function of initial conditions or a more local catastrophic process," Banerjee said. "Our experiments confirm the previous conclusion: the growth of the interface strongly depends on the choice of initial conditions, such as amplitude and wavelength."

In the experiments. The real Hellman mayonnaise has been poured into a Plexiglas container. Different wave type disturbances were formed on the mayonnaise and the sample was then accelerated as part of an experiment with a rotating wheel. The growth of the material was followed with the help of a high speed camera (500 fps). An image processing algorithm, written in Matlab, was then applied to compute various parameters associated with instability. For the effect of amplitude, the initial conditions were between w / 60 and w / 10, while the wavelength ranged from w / 4 to w in order to study the Effect of the wavelength ("w" represents the size of the width of the container). . Experimental growth rates for various combinations of wavelengths and amplitudes were then compared to existing analytical models for such fluxes.

This work allows researchers to visualize the evolution of both elastic plastic and material instability while providing a useful database for developing, validating and verifying patterns of such flows, says Banerjee.

He adds that the new understanding of the "threshold of instability" of elastic-plastic materials in acceleration could prove useful for solving the problems of geophysics, astrophysics, industrial processes such as explosive welding. and the high energy density physical problems associated with inertia. containment fusion.

Understand the hydrodynamics of inertial confinement

Banerjee is working on one of the most promising methods to achieve nuclear fusion called inertial containment. In the United States, the two main laboratories in this research are the National Ignition Facility at the Lawrence Livermore National Laboratory in Livermore, California – the largest operational inertial confinement fusion experiment in the United States – and the Los Alamos National Laboratory in New York. -Mexico. Banerjee works with both. He and his team are trying to understand the fundamental hydrodynamics of the fusion reaction, as well as physics.

In inertial confinement experiments, the gas (isotopes of hydrogen, as in magnetic fusion) is frozen in metal pellets the size of a pea. The pellets are placed in a chamber and then struck with high-powered lasers that compress the gas and heat it to a few million Kelvin – about 400 million degrees Fahrenheit – creating the conditions for fusion.

The massive heat transfer, which occurs in nanoseconds, melts the metal. Under massive compression, the gas in the interior wants to explode, causing an undesirable result: the capsule explodes before fusion can be achieved. One way to understand this dynamic, says Banerjee, is to imagine a balloon being pressed.

"As the balloon compresses, the air inside pushes against the material confining it, trying to get out," says Banerjee. "At one point, the balloon will burst under pressure, the same thing happens in a fusion capsule, and the mixture of gas and molten metal causes an explosion."

To avoid mixing, Banerjee adds, you need to understand how molten metal and heated gas mix in the first place.

To do this, his group conducts experiments that mimic the conditions of inertial confinement, isolating physics by suppressing the temperature gradient and nuclear reactions.

Banerjee and his team spent more than four years building a device specifically for these experiments. Installed on the first floor of the Lehigh Packard Laboratory, this experiment is unique in the world, as it allows the study of the mixing of two fluids under conditions corresponding to those of inertial confinement fusion. State-of-the-art equipment is also available to diagnose the flow. The projects are funded by the Ministry of Energy, the Los Alamos National Laboratory and the National Science Foundation.

Researchers like Banerjee mimic molten metal, including mayonnaise. The properties of the materials and the dynamics of the metal at high temperatures are very similar to those of low temperature mayonnaise, he says.

The team's device recreates the incredible speed at which gas and molten metal mix together. They collect data on their experiences and then incorporate them into a model under development at the Los Alamos National Laboratory.

"They took a very complicated problem and isolated it in six or seven smaller problems," says Banerjee. "Some material scientists are working on some aspects of the problem, and some researchers, like me, are focusing on fluid mechanics – all fueling different models that will be combined in the future."