Objective Richtmyer-Meshkov instability arises when a shock wave encounters an interface between two materials of different densities. As instability develops through linear regime to nonlinear regime, mixing between two materials occurs and grows. The study of interface instability and mixing is relevant and of significant interest due to its promising application in many studies and engineering fields, such as phase transformations, multi-phase flow, and dynamic damage. Generally, hydrodynamic instabilities are studied under liquid conditions in which the materials have been shocked to liquid. Meanwhile, instability in solids is governed by their elastic and plastic properties (strength), and this area is attracting much interest presently due to its promising applications in investigating the constitutive properties of matter. Usually, a laser pulse ablation produces an unsupported shock in a material, and Rayleigh-Taylor instability (RTI) is induced due to the interface deceleration after the shock transit. In this study, we investigate the instability and mixing between the tin and polymer foam under unsupported shock loading via nanosecond laser ablation. The loading pressure is changed to evaluate the influence of strength on the instability growth and mixing characteristic via high-energy radiography. We hope the experimental results can improve the understanding of the issue and provide help for further studies.
Methods Tin and polymer foam with initial single-mode sinusoidal interface perturbation (Atwood number A=-0.87, kAη0=0.82) are employed in this study. A nanosecond laser pulse after the continuum phase plate of 2 mm diameter is focused on the tin surface, and an unsupported shock is produced at the tin-polymer foam interface. Another picosecond laser ablates the golden wire and produces several high-energy X-ray images, which are used to diagnose the instability and mixing via side-on radiography. The radiographs are recorded by the image plate fixed on the rear side of the high-energy X-ray camera. The evolution images of interface instability and mixing are obtained by changing the radiography time related to the nanosecond laser.
Results and Discussions Since the Atwood number, A, is negative, the interface experiences a phase inversion at the beginning. As instability comes into a nonlinear regime, the radiographs of interface instability and mixing under different loading pressure become quite different. When the tin is shocked into liquid, the spike evolves into a mushroom tip, just like wearing a thin “hat”, which has a sharp crest and two long braids around two sides (Fig. 4). Afterward, secondary spikes emerge at the center of the original spikes due to the second shock loading within the tin. However, when the loading pressure is lower, the tin has not melted or only melted partially upon release. In this case, the growth of the spike and bubble is suppressed by the strength and the spike evolves into a different appearance (Fig. 6). The spikes consist of one thin tip and one thick root. Later, the tip becomes thicker and the it is different from the root shrinks. In the end, the mixing between the tin and polymer foam becomes acute, leading to curve and fragmentation of spike tip. Besides, the spike root has totally deviated from the initial interface and broken up into debris. Assuming that the spikes have achieved their maximum height before fragmentation, then the yield strength of tin can be determined. Moreover, the contribution of RTI is evaluated according to the interface deceleration process (Fig. 8).
Conclusions In this study, the interface instability and mixing between the tin and polymer foam with initial single-mode sinusoidal interface perturbation driven by unsupported shock is studied via high-energy side-on X-ray radiography for the SG-Ⅱ upgraded laser facility. Radiographs of instability and mixing at different delay times are obtained at two typical loading pressures. One is at the shock melting point and the other is around the melting point upon release. When the tin is shocked into liquid, the spikes evolve into a mushroom tip. However, when the loading pressure is lower, the tin has not melted or only melted partially upon release, the growth of spike and bubble is suppressed by residual strength of the tin, and the interface evolves into another pattern. The spikes consist of one thin tip and one thick root. In the end, severe mixing between tin and polymer foam results in the curve and fragmentation of spike tip. Besides, the spike root has totally deviated from the initial interface and broken up into debris. Assuming that the spikes have achieved their maximum height before fragmentation, the yield strength of tin is determined, which is consistent with the reported value. Moreover, the contribution of RTI is evaluated due to interface deceleration and the results show that its contribution is negligible. Overall, this study improves the understanding of the interface instability and mixing driven by unsupported shock; in addition, it will serve as a useful reference for future studies.
