A review on physics of familiar geoscientific phenomena: Why are fine grains deposited slowly?

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In order to understand the reason why fine grains are deposited slowly, which is a familiar geoscientific phenomenon, we must consider the drag caused by viscosity besides the gravity and buoyancy as a force acting on falling grains in fluid such as water or air. When the grains may be as the first approximation regarded as spheres, the drag acting on the grains is in proportion to the diameter of grains, the viscosity of fluid and the falling velocity, as shown by Stokes’ law.The drag increases with increasing the falling velocity, and then each grain is deposited with a constant velocity called the terminal velocity, which is achieved when the three forces of the gravity, buoyancy and drag balance with each other. The terminal velocity of grains in fluid is proportional to the square of grain size and the difference between the densities of fluid and grains and is inversely proportional to viscosity. Therefore, when the density of grains is constant, the finer the grain size is, the smaller the terminal velocity is. This is the reason why the fine grains are deposited slowly. This phenomenon universally occurs irrespective to kinds of fluid. However,the effect of drag hardly emerges in air because the viscosity of air is about one hundredth of that of water. Unless there is an extreme difference between the body sizes or the falling length is so long, the terminal velocities are almost same. On the other hand, when balloons fall in air,the larger the size of balloon is, the more slowly the balloon falls, because the density of a bigger balloon is close to that of air and then the terminal velocity becomes smaller. In case of balloons,the effect of the difference between the densities of the balloon and air on the terminal velocity is much larger than the effect of the size.