Curvature-corrected sloshing spectra for cylindrical tanks in microgravity

Abstract

In microgravity, a partially filled cylindrical tank is generally bounded by a curved equilibrium meniscus rather than by an almost flat free surface. This modifies both the bulk liquid inertia and the capillary restoring force, so flat-interface sloshing frequencies can become inaccurate even in the linear regime. This effect matters once the Bond number is of order unity or smaller, precisely the regime relevant to capillarity-dominated propellant management. This study revisits the classical cylindrical curved-meniscus eigenvalue problem for capillary-gravity sloshing about axisymmetric Young-Laplace equilibria. A semi-analytical boundary-operator formulation is derived that preserves the cylindrical Bessel structure and recovers the flat-interface limit exactly. Its main advantage lies in treating the bulk Dirichlet-Neumann operator and the linearised curvature operator as distinct components, thereby making the physical origin of curvature-induced frequency shifts explicit. The results show that equilibrium curvature couples radial modes and alters the low-order spectrum once $Bo \lesssim 1$. Concave menisci lower the fundamental frequency, whereas convex menisci raise it while often lowering higher branches. The asymmetry between wetting and non-wetting configurations is found to be predominantly kinetic, being carried mainly by the Dirichlet-Neumann operator rather than by the capillary term. Curved menisci should therefore be treated as part of the leading-order model of cylindrical microgravity sloshing, not as a secondary correction, if reduced-order predictions are to capture the relevant dynamical scales for spacecraft applications.