Wetting of quantum fluids: a route to free-standing shell-shaped quantum droplets

We investigate wetting phenomena between self-bound quantum fluids in a three-component Bose mixture of $^{23}$Na, $^{39}$K, and $^{41}$K atoms. Within a density-functional approach including mean-field interactions and Lee-Huang-Yang quantum-fluctuation corrections, we consider two binary quantum liquids, formed by components $(1,2)$ and $(2,3)$, and study the adsorption of the softer $(1,2)$ liquid on a stiffer $(2,3)$ substrate. By tuning the interspecies scattering length $a_{12}$, we show that the surface tension of the $(1,2)$ liquid can be strongly varied, driving a transition from partial wetting to complete wetting of the $(2,3)$ phase. The contact angle extracted from cylindrical-cap geometries decreases continuously with increasing $a_{12}$ and vanishes near a critical value $a_{12}^{c}= -42\,a_0$. In the complete-wetting regime, a finite amount of $(1,2)$ liquid wraps around a spherical $(2,3)$ droplet, producing a self-bound core-shell droplet without external confinement, whose component-1 density has a shell-like, hollow projection. We further show that such shell-shaped quantum droplets can sustain quantized vortical excitations. These results identify wetting as a route to engineering free-standing shell-shaped quantum liquids and suggest new possibilities for studying capillarity, topology, and superfluidity in multicomponent quantum droplets.