Figure 5.

(A): The energy of the radial interaction $\mathcal{U}\left(\overline{R}\right)$ (black triangles) between the boundaries of a symmetric catenoid (we have taken the experimental reference $\lambda =-1/0.7$). Some catenoidal points of reference along the path: $\mathbf{a}$ ($\overline{R}=1.2$), $\mathbf{b}$ ($\overline{R}=1.7$), $\mathbf{c}$ ($\overline{R}=1.9$), and $\mathbf{d}$ ($\overline{R}=3$). The first two points belong to the subcritical regime, and the last two points are in the supercritical sector. The critical point is at ${\overline{R}}^{*}\approx 1.81$. (B): The radial force $F_{\rho }$, on the lower border (right), as a function of $\overline{h}$ (the separation distance between the borders). The inset panel outline the radial force as a function of the area of the catenoid. (C): The axial force $F_z\equiv -\overline{\eta }$ as a function of $\overline{h}$ (the distance of separation between the borders). The inset panel shows the axial force as a function of the area $\overline{A}$.