How can you tell from Stokes’ law (Box 9.5) that grain size is more important than density in determining settling rates?

Transcribed Image Text:

Box 9.5 Crystal Settling and Stokes' Law The terminal velocity of a spherical particle sinking (or floating) through a liquid is given by Stokes' law: Terminal velocity = gravitational acceleration X density contrast (grain diameter) 18x viscosity The equation is valid as long as the flow of liquid around the particle is laminar (not turbulent), which is the case for slowly sinking crystals in viscous magma, and the liquid does not have a yield strength. From inspection of the equation we see the following: The sinking velocity is proportional to the acceleration of gravity. Thus, sinking would be six times slower on the Moon than on Earth, because the Moon's gravitational acceleration is one-sixth that of the Earth's (1.62 versus 9.8 m s). The sinking velocity is proportional to the density contrast between the solid and the liquid. Thus, denser minerals sink faster than less dense ones. The sinking velocity is inversely proportional to the viscosity. Thus, a crystal would sink faster in basaltic magma than it would in more viscous granitic magma. The sinking velocity is proportional to the square of the diameter of the grain. Thus, if a grain's diameter doubles, it sinks four times as fast. Stokes' law shows that grain size plays a very important role in crystal settling. In Section 12.6.2 we see that it plays an equally important role in determining what grain-size material can be carried in suspension in rivers.