Rayleigh-Taylor stability boundary at solid-liquid interfaces

Linear analysis of Rayleigh-Taylor instability in viscoelastic materials

Rayleigh-Taylor instability (RTI) has become a powerful tool for determining the mechanical properties of materials under extreme conditions. In this paper, we first present the exact and approximate linear dispersion relations for RTI in viscoelastic materials based on the Maxwell and Kelvin-Voigt models. The approximate dispersion relation produces good predictions of growth rates in comparison with the exact one. The motion of the interface in Maxwell flow is mainly controlled by viscosity and elasticity dominates this behavior in Kelvin-Voigt flow. Since elasticity plays a distinct role from viscosity, cutoff wavelengths arise only in Kelvin-Voigt flow. The variation of the maximum growth rates and their corresponding wave numbers are also carefully studied. For both types of materials, viscosity suppresses the growth of instability, while elasticity speeds it up. This is at odds with the well-known understanding that elasticity suppresses hydrodynamic instabilities. The dependence of the maximum growth rate on slab thickness is also investigated for RTI in both types of flow, since the metal slab as a pusher has been extensively employed in high-energy-density physics. The model presented here allows study of more realistic situations by considering convergent effects and shock wave interactions, for the traditional potential flow theory is not suitable. To summary, it is able to provide guidances for future experimental designs for studies of materials under high strain and high strain rate conditions, as well as allow us to study RTI theoretically in more complicated conditions.

Studies of equation of state properties of high-energy-density matter generated by intense ion beams at the facility for antiprotons and ion research

The work presented in this paper shows with the help of two-dimensional hydrodynamic simulations that intense heavy-ion beams are a very efficient tool to induce high energy density (HED) states in solid matter. These simulations have been carried out using a computer code BIG2 that is based on a Godunov-type numerical algorithm. This code includes ion beam energy deposition using the cold stopping model, which is a valid approximation for the temperature range accessed in these simulations. Different phases of matter achieved due to the beam heating are treated using a semiempirical equation-of-state (EOS) model. To take care of the solid material properties, the Prandl-Reuss model is used. The high specific power deposited by the projectile particles in the target leads to phase transitions on a timescale of the order of tens of nanosecond, which means that the sample material achieves thermodynamic equilibrium during the heating process. In these calculations we use Pb as the sample material that is irradiated by an intense uranium beam. The beam parameters including particle energy, focal spot size, bunch length, and bunch intensity are considered to be the same as the design parameters of the ion beam to be generated by the SIS100 heavy-ion synchrotron at the Facility for Antiprotons and Ion Research (FAIR), at Darmstadt. The purpose of this work is to propose experiments to measure the EOS properties of HED matter including studies of the processes of phase transitions at the FAIR facility. Our simulations have shown that depending on the specific energy deposition, solid lead will undergo phase transitions leading to an expanded hot liquid state, two-phase liquid-gas state, or the critical parameter regime. In a similar manner, other materials can be studied in such experiments, which will be a very useful addition to the knowledge in this important field of research.

Stability boundaries for the Rayleigh-Taylor instability in accelerated elastic-plastic solid slabs

The linear theory of the incompressible Rayleigh-Taylor instability in elastic-plastic solid slabs is developed on the basis of the simplest constitutive model consisting in a linear elastic (Hookean) initial stage followed by a rigid-plastic phase. The slab is under the action of a constant acceleration, and it overlays a very thick ideal fluid. The boundaries of stability and plastic flow are obtained by assuming that the instability is dominated by the average growth of the perturbation amplitude and neglecting the effects of the higher oscillation frequencies during the stable elastic phase. The theory yields complete analytical expressions for such boundaries for arbitrary Atwood numbers and thickness of the solid slabs.

Effects of the Atwood number on the Richtmyer-Meshkov instability in elastic-plastic media

The Richtmyer-Meshkov instability of small perturbed single-mode interfaces between an elastic-plastic solid and an inviscid liquid is investigated by theoretical analysis and numerical simulation in this work. A modified model including the Atwood number effect is proposed to describe the long-term behaviors of small perturbations at the solid-liquid interface. In contrast to an effective theoretical model at the solid-vacuum interface, this model is appropriate at different Atwood numbers. Owing to the effect of elastic-plastic characteristics and the density ratio, the evolution of the spike amplitude exhibits nonlinear mechanical behavior. As the absolute value of the Atwood number decreases, the maximum spike amplitude also decreases. To validate this model, an Eulerian finite-difference multicomponent code is adopted to study the time evolution of the spike amplitude at different Atwood numbers. The model coefficients are obtained by analyzing the relevant characteristic statistics collected from the numerical results. Under different initial conditions such as Atwood number and shock strength, the applicability of this modified model is verified by comparing the numerical results with the model profile. The consistency in results signifies that the modified model is not only suitable for specific shock intensity and Atwood number, but also adaptable within a certain range.

Unified decomposition method to study Rayleigh-Taylor instability in liquids and solids

In the previous studies of Rayleigh-Taylor instability, different methods were used to consider the effects of elasticity, viscosity, and magnetic fields. In this paper, a unified method, which was first used for fluids, is validated for different physical models, where the unstable mode is decomposed into an irrotational part and a rotational part, and the latter one includes the effects of nonconservative forces and constitutive relations. Previous results of solid and liquid with or without the effects of magnetic fields and finite thickness can be easily recovered after applying the corresponding interface boundary conditions. In addition, new approximate but analytical solutions of the growth rates for a semi-infinite solid-solid interface and solid-fluid interface are obtained with substantially improved accuracy in comparison with the previous ones.

Rayleigh-Taylor instability in accelerated elastic-solid slabs

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ_{2}, shear modulus G, and thickness h, placed over a semi-infinite ideal fluid of density ρ_{1}<ρ_{2}. It extends previous results for Atwood number A_{T}=1 [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998)ZAMPA80044-227510.1007/s000330050121] to arbitrary values of A_{T} and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ_{2}gh/G≤2(1-A_{T})/A_{T}.

Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number A_{T}=1, the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

Rayleigh-Taylor Instability in Elastoplastic Solids: A Local Catastrophic Process

We show that the Rayleigh-Taylor instability in elastoplastic solids takes the form of local perturbations penetrating the material independently of the interface size, in contrast with the theory for simple elastic materials. Then, even just beyond the stable domain, the instability abruptly develops as bursts rapidly moving through the other medium. We show that this is due to the resistance to penetration of a finger which is minimal for a specific finger size and drops to a much lower value beyond a small depth (a few millimeters).

Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration

A model is presented for the linear Rayleigh-Taylor instability taking place at the early stage of acceleration of an elastic-plastic solid, when the shock wave is still running into the solid and is driven by a time varying pressure on the interface. When the the shock is formed sufficiently close to the interface, this stage is considered to follow a previous initial phase controlled by the Ritchmyer-Meshkov instability that settles new initial conditions. The model reproduces the behavior of the instability observed in former numerical simulation results and provides a relatively simpler physical picture than the currently existing one for this stage of the instability evolution.

Rayleigh-Taylor linear growth at an interface between an elastoplastic solid and a viscous liquid

A previously developed model for the Rayleigh-Taylor instability at an interface between an elastoplastic solid and a viscous fluid [Piriz, Sun, and Tahir, Phys. Rev. E 88, 023026 (2013)] has been used for calculating the time evolution of the perturbations in terms of the mechanical properties of the solid and the liquid, as well as of the initial amplitude ξ_{0} and the wavelength λ of the perturbation. Four kinds of possible evolution are found: two stable and two unstable, depending on their positions in the space of parameters (ξ_{0},λ). All of them present some features that are independent of the solid properties and that are determined only by the liquid viscosity.