# Does buoyancy change on smaller scales?

For baseball size objects on the order of centimeters across we have experience with what floats and what doesn't. A stick will float and a rock will not. But what if the rock were a grain of sand? What if it were a thousand times smaller still? Would it's small size allow it to float because of surface tension?

You're confusing buoyancy with surface tension. The former applies to (macroscopic) objects which are (at least partly) immersed, while the latter applies to inter-fluid surfaces.

Thus, a sufficiently small grain of rock (sand) may stay on the water surface owing to its tension, but will sink if submerged (say by a breaking wave). If you make it very small, however, it will undergo Brownian motion (when submerged) and the fluid model (which describes buoyancy) is no longer applicable.

In answer to the comment: if submerged, it's (by definition) underneath the surface: surface tension is out of the equation and buoyancy rules. In addition, there is of course a frictional drag force between fluid and object (which depends on the size, shape, and speed of the object, as well as the viscosity and density of the fluid). After some initial transient period, the drag force, gravity, and buoyancy become balanced and the object sinks at a constant rate, which does depend on the object's mass, size, and shape.

• Won't the rate at which it sinks be different if it sinks at all. Assuming it isn't heavy enough to break the surface tension underneath it even when submerged.
– Alex
Jul 29 '15 at 16:48
• @Alex velocity is a different question and I suspect there is a terminal velocity in water question on this site. Jul 29 '15 at 17:16
• It's not just velocity, theoretically a grain of sand loses potential energy as it breaks the bonds between water molecules. It would be interesting to know what height you can drop it from without sinking and so on. I would like someone to discuss these forces and how they behave at smaller scales.
– Alex
Jul 29 '15 at 17:24
• @Alex And now that is a third question. This answers the stated question. Jul 29 '15 at 18:08
• Terminal velocity does increase with size. Mass is r cubed and area is r squared. Jul 29 '15 at 18:13