Where does flotation collide?

The physical support that keeps a body afloat in a fluid, and the geometry of where it sits: a body floats when the weight of the fluid it pushes aside equals its own weight. Archimedes set this out in On Floating Bodies in the third century BCE (in the standard edition of Heath, 1897), establishing that a floating body displaces a volume of fluid equal in weight to the body. Modern ship hydrostatics sharpens the term into the centre of flotation, the centroid of the waterplane area about which a hull trims (Biran and López-Pulido, 2013). In this meaning flotation is a fact of fluid mechanics and hull geometry, described by displaced volume and waterplane position, not a way of separating crushed rock or a way of selling company shares.[1][2]

Unit

One floating body in equilibrium, set by the weight of fluid it displaces

Recovery means

When tilted, the buoyant support shifts relative to the weight and pushes the body back toward its floating position

Measured by

Computed from hull geometry as displaced volume, waterplane area, and the position of the centre of flotation

A method of separating valuable minerals from crushed ore by differences in how their surfaces attract or repel water. First patented by the Bessel brothers in 1877 in Dresden for cleaning graphite, and traced as the root of the froth process by Kitchener (1984), it conditions a slurry with chemicals so that target grains cling to air bubbles and rise into a froth while the rest sinks. Mondal, Acharjee, Mandal, and Saha (2021) review how surface wettability, collector chemicals, and frothers are tuned to float one mineral and hold another down. Here flotation is a physical and chemical concentration step, judged by the grade and yield of the floated product, and it has nothing to do with buoyant support of a hull or the issue of company securities.[3][4]

Unit

One separation of a target mineral into a froth, per batch or continuous cell

Recovery means

The fraction of the valuable mineral captured in the froth is itself called recovery in this field

Measured by

Assessed by the grade and recovery of the floated concentrate and by contact angle and zeta potential of the mineral surfaces

The act of offering a company's securities to investors, especially for the first time, together with the costs of doing so. Lee, Lochhead, Ritter, and Zhao (1996) measured these flotation costs across thousands of United States equity and bond issues, separating the underwriter's fee from other direct expenses and from underpricing. The word carries the older business image of floating a company onto the market, but the priced construct is the cost of raising external capital. Here flotation names a capital-raising transaction and its expense, stated in cents on each dollar raised, and it is unrelated to a body resting in water or to bubbles carrying rock to the surface.[5]

Unit

One securities issue, with its cost stated as a share of the amount raised

Recovery means

Not applicable

Measured by

Measured as the underwriter fee plus other issuing expenses divided by gross proceeds