Dependence of the Superfluidity Criterion on the Capillary Radius

We replace the conditions on the capillary boundary with the Born–Karman periodic conditions, i. e., we consider a two-dimensional torus of radius $L_2$. If the velocity of a superfluid liquid exceeds $8\pi\hbar/(mL_2)$, then it brakes because of the friction against the eddy formed by pairs (similar to the pairs in the Andreev reflection).