The fluid mechanics of floating and sinking

Abstract

This thesis is concerned with the fluid mechanics of floating and sinking. More specifically, the majority of this thesis considers the role played by surface tension in allowing dense objects to float. We first derive the conditions under which objects can float at an interface between two fluids. We obtain the conditions on density and size for various objects to float and show that being ‘super-hydrophobic’ does not generally help small, dense objects to float. Super-hydrophobicity does, however, dramatically reduce the energy required to remove an object from the interface. We then show that two floating objects can sink if they come into close proximity with one another. We extend this to show that a raft consisting of many interfacial objects can become arbitrarily large without sinking, providing that its density is below a critical value. Above this critical value, there is a threshold size at which sinking occurs. We then consider the surface tension dominated impact of an object onto a liquid–gas interface. We determine a similarity solution, valid shortly after impact, for the shape of the interface and study the asymptotic properties of the capillary waves generated by impact. We also show how the interfacial deformation slows down the impacting body. We use a boundary integral simulation to study the motion at later times and determine the conditions under which the object either sinks or is trapped by the surface. We find that for an object of a given weight there is a threshold impact speed above which it sinks. We study the waterlogging of a floating porous body as a model for the waterlogging of the pumice ‘rafts’ that often form on bodies of open water after a volcanic eruption. We study the inflow of water that is driven by capillary suction and hydrostatic pressure imbalances, and determine the time taken for this inflow to cause the object to sink. Finally, we study the effects of a natural slope on the spreading of carbon dioxide sequestered into aquifers. We use laboratory models and numerical techniques to study the spreading of the resulting gravity current. Initially the current spreads axisymmetrically, while at later times it spreads predominantly along any slope in the overlying cap rock. We show that in industrial settings the time scale over which this asymmetry develops is typically a few years. This effect may have important practical implications since the current propagates faster in the asymmetric state.