  We review some geometric criteria and prove a refined version, that yield
existence of capillary surfaces in tubes $\Omega\times \mathbb{R}$ in a gravity
free environment, in the case of physical interest, that is, for bounded, open,
and simply connected $\Omega \subset \mathbb{R}^2$. These criteria rely on
suitable weak one-sided bounds on the curvature of the boundary of the
cross-section $\Omega$.
