  Fingering instabilities akin to the Rayleigh-Taylor (RT) instability in
fluids have been observed in a binary granular system consisting of dense and
small particles layered on top of lighter and larger particles, when the system
is subjected to vertical vibration and fluidizing gas flow. Using observations
from experiments and numerical modelling we explore whether the theory
developed to describe the Rayleigh-Taylor (RT) instability in fluids is also
applicable to binary granular systems. Our results confirm the applicability of
the classic RT instability theory for binary granular systems demonstrating
that several key features are observed in both types of systems, viz: (i) The
characteristic wavenumber of the instability is constant with time, (ii) the
amplitude of the characteristic wavenumber initially grows exponentially and
(iii) the dispersion relation between the wavenumbers k of the interface
instability and the growth rates n(k) of their amplitudes holds in both
fluid-fluid and binary granular systems. Our results also demonstrate that
inter-particle friction is essential for the RT instability to occur in
granular media. For zero particle friction the interface instability bears a
greater resembles to the Richtmyer-Meshkov instability. We further define a
yield criterion Y for the interface by treating the granular medium as a
viscoplastic material; only for Y > 15 fingering occurs. Interestingly,
previous work has shown that instabilities in the Earth's lower mantle, another
viscoplastic material, also occur for similar values of Y.
