Experimental images for 3D initial perturbation. Image: Arindam Banerjee.
Experimental images for 3D initial perturbation. Image: Arindam Banerjee.

A team of engineers at Lehigh University has succeeded in characterizing the interface between an elastic-plastic material and a light material under acceleration. They discovered that the onset of instability – or the ‘instability threshold’ – was related to the size of the applied amplitude (perturbation) and wavelength (distance between crests of a wave).

Their results show that for both two-dimensional and three-dimensional perturbations (or motions), a decrease in initial amplitude and wavelength produced a more stable interface, thereby increasing the acceleration required for instability. This finding, reported in a paper in Physical Review E, could help advance our understanding of the huge forces involved in nuclear fusion.

"There has been an ongoing debate in the scientific community about whether instability growth is a function of the initial conditions or a more local catastrophic process," says team leader Arindam Banerjee, an associate professor of mechanical engineering and mechanics at Lehigh University. "Our experiments confirm the former conclusion: that interface growth is strongly dependent on the choice of initial conditions, such as amplitude and wavelength."

Rather bizarrely, these experiments involved pouring Hellman's Real Mayonnaise into a Plexiglass container. Banerjee and his team formed different wave-like perturbations on the mayonnaise and then accelerated the sample on a rotating wheel, tracking the growth of the material with a high-speed camera (500 fps). They then applied an image processing algorithm, written in Matlab, to compute various parameters associated with the instability.

To study the effect of amplitude, the initial conditions were ranged from w/60 to w/10, where ‘w’ represents the size of the width of the container, while the wavelength was varied from w/4 to w to study the effect of wavelength. Experimental growth rates for various wavelength and amplitude combinations were then compared to existing analytical models for such flows.

In this way, the researchers were able to visualize both the elastic-plastic and instability evolution of the material while providing a useful database for development, validation and verification of models of such flows, says Banerjee.

He adds that the new understanding of the ‘instability threshold’ of an elastic-plastic material under acceleration could be of value in helping to solve challenges in geophysics, astrophysics and industrial processes such as explosive welding, as well as high-energy density physics problems related to inertial confinement fusion.

Banerjee works on one of the most promising methods for achieving nuclear fusion, called inertial confinement. In the US, the two major labs for 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 US – and the Los Alamos National Laboratory in New Mexico. Banerjee works with both. He and his team are trying to understand the fundamental hydrodynamics of the fusion reaction, as well as the physics.

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

The massive transfer of heat, which happens in nanoseconds, melts the metal. Under massive compression, the gas inside wants to burst out, causing the capsule to explode before fusion can be reached. One way to understand this dynamic, explains Banerjee, is to imagine a balloon being squeezed.

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

In order to prevent the mixing, adds Banerjee, you have to understand how the molten metal and heated gas mix in the first place. To do this, his group runs experiments that mimic the conditions of inertial confinement, isolating the physics by removing the temperature gradient and the nuclear reactions.

Banerjee and his team have spent more than four years building a device specifically for these experiments. Housed on the first floor of Lehigh's Packard Laboratory, the experiment is the only one of its kind in the world, as it can study two-fluid mixing at conditions relevant to those in inertial confinement fusion. State-of-the-art equipment is also available for diagnosing the flow. The projects are funded by the US Department of Energy, Los Alamos National Laboratory and the US National Science Foundation.

One of the ways that researchers like Banerjee mimic the molten metal is by using mayonnaise. The material properties and dynamics of the metal at a high temperature are much like those of mayonnaise at low temperatures, he says.

The team's device re-creates the incredible speed at which the gas and molten metal are mixing. They gather data from the experiments they run and then feed them into a model being developed at Los Alamos National Laboratory.

"They have taken a very complicated problem and isolated it into six or seven smaller problems," explains Banerjee. "There are materials scientists working on certain aspects of the problem; there are researchers like me who are focused on the fluid mechanics – all feeding into different models that will be combined in the future."

This story is adapted from material from Lehigh University, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.