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A R Piriz1, Y B Sun2, N A Tahir3

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The Rayleigh-Taylor instability model reveals four evolution types for elastoplastic solids and viscous fluids. Liquid viscosity significantly influences perturbation behavior, independent of solid properties.

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Area of Science:

  • Fluid Dynamics
  • Solid Mechanics
  • Instability Phenomena

Background:

  • The Rayleigh-Taylor instability occurs at the interface between two fluids of different densities accelerated against each other.
  • Understanding this instability is crucial in fields ranging from astrophysics to inertial confinement fusion.
  • Previous models have focused on fluid-fluid interfaces, with limited exploration of solid-fluid interactions.

Purpose of the Study:

  • To analyze the time evolution of perturbations at an elastoplastic solid-viscous fluid interface.
  • To investigate the influence of mechanical properties, initial amplitude (ξ₀), and wavelength (λ) on instability dynamics.
  • To identify distinct stable and unstable evolution regimes.

Main Methods:

  • Utilized a previously developed model for Rayleigh-Taylor instability at solid-fluid interfaces.
  • Calculated the time evolution of perturbations based on material properties and initial perturbation parameters (ξ₀, λ).
  • Analyzed parameter space (ξ₀, λ) to categorize different evolutionary behaviors.

Main Results:

  • Identified four distinct types of perturbation evolution: two stable and two unstable.
  • Demonstrated that the evolution depends on the position within the parameter space (ξ₀, λ).
  • Observed that certain evolutionary features are independent of the solid's mechanical properties and are solely determined by the fluid's viscosity.

Conclusions:

  • The study categorizes Rayleigh-Taylor instability dynamics at solid-fluid interfaces into distinct stable and unstable regimes.
  • Liquid viscosity plays a critical role in shaping the instability's evolution, irrespective of the solid's characteristics.
  • The findings provide a more comprehensive understanding of interfacial instabilities involving complex material behaviors.