Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

The variability of bird beak morphology reflects diverse foraging strategies. One such feeding mechanism in shorebirds involves surface tension-induced transport of prey in millimetric droplets: By repeatedly opening and closing its beak in a tweezering motion, the bird moves the drop from the tip of its beak to its mouth in a stepwise ratcheting fashion. We have analyzed the subtle physical mechanism responsible for drop transport and demonstrated experimentally that the beak geometry and the dynamics of tweezering may be tuned to optimize transport efficiency. We also highlight the critical dependence of the capillary ratchet on the beak's wetting properties, thus making clear the vulnerability of capillary feeders to surface pollutants.

https://science.sciencemag.org/content/sci/320/5878/931.full.pdf

Surface Tension Transport of Prey by Feeding Shorebirds: The Capillary Ratchet

A capillary surface is an interface between two fluids whose shape is determined primarily by surface tension. Sessile drops, liquid bridges, rivulets, and liquid drops on fibers are all examples of capillary shapes influenced by contact with a solid. Capillary shapes can reconfigure spontaneously or exhibit natural oscillations, reflecting static or dynamic instabilities, respectively. Both instabilities are related, and a review of static stability precedes the dynamic case. The focus of the dynamic case here is the hydrodynamic stability of capillary surfaces subject to constraints of (a) volume conservation, (b) contact-line boundary conditions, and (c) the geometry of the supporting surface.

Stability of Constrained Capillary Surfaces

A method for determining the stability of general static capillary surfaces is illustrated by application to the liquid bridge. Axisymmetric bridges with fixed contact lines under gravity are parametrized by three quantities: bridge length L, bridge volume V, and Bond number B. The method delivers i) stability envelopes in the {L,V,B,} parameter space for constant pressure and constant volume disturbances (recovering classical and generating new results), ii) the number of unstable modes for any equilibrium (state of instability) once the stability of one equilibrium state is known, based on, iii) a demonstration that all known families of equilibria are ultimately connected. The state of instability of an equilibrium shape relative to its neighbors is immediate from a plot of volume V versus pressure p, a "preferred" bifurcation diagram. The preferred diagram method gives stronger results than classical bifurcation theory based on properties of eigenvalues of the Jacobi equation for problems with a variational formulation. Application to other capillary surfaces including drops and nonaxisymmetric shapes is discussed. In addition, motivated by general tangency considerations, an invariant wavenumber classification is introduced and used to label the numerous families of liquid bridge equilibria.

Capillary Surfaces: Stability from Families of Equilibria with Application to the Liquid Bridge

Conditions are summarized for manipulating and stabilizing fluid objects based on the acoustic radiation pressure of standing waves. Examples include (but are not limited to) liquid drops, gas bubbles in liquids, and cylindrical liquid bridges. The emphasis is on situations where the characteristic wavelength of the acoustic field is large in comparison to the relevant dimension of the fluid object. Tables are presented for ease of comparing the signs of qualitatively different radiation force parameters for a variety of fluid objects.

Manipulation of fluid objects with acoustic radiation pressure.

Flow-Influenced Stabilization of Liquid Columns

Experiments document the influence of flow on the Plateau-Rayleigh (PR) instability of a near-cylindrical liquid bridge. The slightly heavy bridge is subjected to a surrounding pipe flow from bottom to top. Linear and nonlinear regimes of response are reported. Islands of stability in flow rate are observed; that is, there are bridges that are stable with flow but otherwise not. Density imbalance and flow each, on its own, is destabilizing but together they are stabilizing as recorded by a variety of measures. This nonlinear stabilization is explained in terms of the codimension-2 nature of the pitchfork bifurcation of the 'perfect' Plateau-Rayleigh instability.

Brian J. Lowry

Papers

Capillary Surfaces: Stability from Families of Equilibria with Application to the Liquid Bridge

Flow-Influenced Stabilization of Liquid Columns

Stability of slender liquid bridges subjected to axial flows

Stabilization of an axisymmetric liquid bridge by viscous flow

On the density matching of liquids using Plateau's method