Almost Cylindrical Isorotating Liquid Bridges for small Bond Numbers

Abstract

In the absence of gravity, a cylindrical-shaped liquid bridge becomes unstable as the slenderness of the bridge A exceeds a critical value Ac, which depends on the rotational Weber number W. The unstable mode is either axisymmetric (amphora-mode) or non axisyrnmetric (C-mode) depending on whether W is smaller or bigger than 1/3. Almost cylindrical bifurcating stationary shapes, with a cylindrical volume, are calculated for |A-AC|<<1. It is seen that the bifurcation is always subcritical, i.e., the bifurcating non-cylindrical shapes appeal1 for A < Ac. The effect of a small axial gravity, i.e., a small gravitational Bond number B is also considered. It is seen that Ac(0,A) - AC(B,A) is of the order of g2/3 for amphora modes, and of the order of fi2 for C-modes. finally, a comparison is made with numerical and experimental results available in the Literature, and some comments on the dynamical behaviour of the liquid bridge are given.