P.C. Rossin College of
Engineering and Applied Science
MEM professor Arindam Banerjee’s experiments could apply to high-energy density physics problems relevant to inertial confinement fusion

Arindam Banerjee, an associate professor of mechanical engineering and mechanics, studies the dynamics of materials in extreme environments. He and his team have built several devices to effectively investigate the dynamics of fluids and other materials under the influence of high acceleration and centrifugal force.

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

“In the presence of gravity―or any accelerating field―the two materials penetrate one another like ‘fingers,’” says Banerjee.

According to Banerjee, the understanding of the instability is mostly confined to fluids (liquids or gases). Not much is known about the evolution of the instability in accelerated solids. The short time scales and large measurement uncertainties of accelerated solids make investigating this kind of material very challenging.

Banerjee and his team have succeeded in characterizing the interface between an elastic-plastic material and a light material under acceleration. They discovered that the onset of the instability―or “instability threshold”―was related to the size of the amplitude (perturbation) and wavelength (distance between crests of a wave) applied. Their results showed 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.     

These results are described in a paper published in Physical Review E called “Rayleigh-Taylor-instability experiments with elastic-plastic materials.” In addition to Banerjee, co-authors include Rinosh Polavarapu (a current Ph.D. student) and Pamela Roach (a former M.S. student) in Banerjee’s group.

“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 Banerjee. “Our experiments confirm the former conclusion: that interface growth is strongly dependent on the choice of initial conditions, such as amplitude and wavelength.”

In the experiments, Hellmann’s Real Mayonnaise was poured into a Plexiglass container. Different wave-like perturbations were formed on the mayonnaise and the sample was then accelerated on a rotating wheel experiment. The growth of the material was tracked using a high-speed camera (500 fps). An image-processing algorithm, written in Matlab, was then applied to compute various parameters associated with the instability. For the effect of amplitude, the initial conditions were ranged from w/60 to w/10, while the wavelength was varied from w/4 to w to study the effect of wavelength (“w” represents the size of the width of the container). Experimental growth rates for various wavelength and amplitude combinations were then compared to existing analytical models for such flows.
This work allows researchers 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 elastic-plastic material under acceleration could be of value in helping to solve challenges in geophysics, astrophysics, industrial processes such as explosive welding, and high-energy density physics problems related to inertial confinement fusion.
Banerjee works on one of the most promising methods to achieve nuclear fusion called inertial confinement. In the U.S., 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 U.S.—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.
Read the full story in the Lehigh University News Center
Story by Lori Friedman
Arindam Banerjee

MEM professor Arindam Banerjee is affiliated with Lehigh's IRIs: the Institute for Functional Materials & Devices (I-FMD), the Institute for Data, Intelligent Systems & Computation (I-DISC), and the Institute for Cyber Physical Infrastructure & Energy.

experimental images for 3D initial perturbation

Experimental images for 3D initial perturbation (Credit: Arindam Banerjee)