Finite-amplitude dynamics of coupled cylindrical menisci

The cylindrical meniscus is a liquid/gas interface of circular-cap cross-section constrained along its axis and bounded by end-planes (see figure). The inviscid motions of coupled cylindrical menisci are studied here. Motions result from the competition between inertia and surface tension forces. Restriction to shapes that are of circular-cap cross-section leads to an ordinary differential equation (ode) model, with the advantage that finite-amplitude stability can be examined. The second-order nonlinear ode model has a Hamiltonian structure, showing dynamical behavior like the Duffing-oscillator. The energy landscape has either a single- or double-welled potential depending on the extent of volume overfill. Total liquid volume is a bifurcation parameter. Unlike the spherical-cap problem, however, axial disturbances can also destabilize, depending on overfill. For large volumes, previously known axial stability results are applied to find the limit at which axial symmetry is lost and comparison is made to the Plateau-Rayleigh limit. [Display omitted] ► Inviscid motion of coupled menisci exhibits Duffing-like behavior. ► Total liquid volume is the appropriate bifurcation parameter. ► Large-volume equilibrium states are analogous to constrained full-cylinder. ► Constraint results in stabilization beyond Plateau–Rayleigh limit. The cylindrical meniscus is a liquid/gas interface of circular-cap cross-section constrained along its axis and bounded by end-planes. The inviscid motions of coupled cylindrical menisci are studied here. Motions result from the competition between inertia and surface tension forces. Restriction to shapes that are of circular-cap cross-section leads to an ordinary differential equation (ode) model, with the advantage that finite-amplitude stability can be examined. The second-order nonlinear ode model has a Hamiltonian structure, showing dynamical behavior like the Duffing-oscillator. The energy landscape has either a single- or double-welled potential depending on the extent of volume overfill. Total liquid volume is a bifurcation parameter, as in the corresponding problem for coupled spherical-cap droplets [1]. Unlike the spherical-cap problem, however, axial disturbances can also destabilize, depending on overfill. For large volumes, previously known axial stability results are applied to find the limit at which axial symmetry is lost and comparison is made to the Plateau–Rayleigh limit.