Stability Conditions for the Stern Layer of Bulk Nanobubbles in Water

When analyzing the conditions for the formation of the stable Stern layer of bulk nanobubbles, the dependence of the relative permittivity of water on the electric field strength and accordingly, on the size of the bubbles has been taken into account. The formation of a layered structure of water dipoles near the charged bubble surface, which corresponds to the well-known experimental data, is theoretically explained. The stability conditions for the Stern layer of the nanobubbles with different radii are considered. The dependence of the nanobubble charges and the relative permittivity of water at the boundary of the stable Stern layer on its radius have been found.