  We investigate electrostatic stability of charged droplets, modeled as
permeable, charged spheres, and their encapsidation in thin, arbitrarily
charged nano-shells, immersed in a neutralizing asymmetric electrolyte
background. The latter consists of a small concentration of mobile multivalent
counterions in a bathing solution of monovalent (positive and negative) ions.
We use extensive Monte-Carlo simulations to investigate the spatial
distribution of multivalent counterions and the electrostatic component of
their osmotic pressure on the bounding surface of the spherical nano-shell. The
osmotic pressure can be negative (inward pressure), positive (outward pressure)
or zero, depending on the system parameters such as the charge density of the
droplet, the charge density of the shell, and the electrolyte screening, which
thus determine the stability of the nano-container. The counter-intuitive
effects of multivalent counterions comprise the increased stability of the
charged droplet with larger charge density, increased stability in the case of
encapsidating shell of charge density of the same sign as the charged droplet,
as well as the possibility to dispense altogether with the encapsidating shell,
its confining effect taken over by the multivalent counterions. These dramatic
effects are in stark contrast to the conventional mean-field picture, which in
particular implies that a more highly charged spherical droplet should be
electrostatically less stable because of its larger (repulsive) self-energy.
