  We study the Plateau-Rayleigh instability of a viscoelastic soft solid layer
coated on a rigid cylinder i.e., a soft fibre with a rigid core. The onset of
instability is examined using a linear stability analysis. We find that
increasing the rigid cylinder radius reduce the growth rate of the fastest
growing mode. For each rigid cylinder radius, a critical elastocapillary number
is found below which all wavelengths of disturbances are stable. The critical
value for a soft fibre with a thick rigid cylindrical core can be several
orders of magnitudes larger than that for a totally soft fibre (no rigid core),
which highlights the strong stabilizing effect of the rigid core on the system.
Increasing the relaxation timescale of the viscoelastic material also slows
down the growth of disturbance, but has no effect on the critical
elastocapillary number. Interestingly, the wavelength of the fastest growing
mode is independent of the rigid cylinder radius for the purely elastic case.
