On the calculation of free fall velocity of mineral grains

Abstract

Free fall is theoretically defined as the fall of an isolated grain in an unlimited space of a surrounding medium (water or air). Practically, it is considered as the fall of a set of grains at a concentration where the movement of any grain is not significantly disturbed, either directly or through the surrounding medium, by accompanying grains. Free fall is of particular importance in the process of precise classification, where the movement of grains is considered to be uniform and occurring at a constant terminal velocity. As the grains fall through the medium, they displace the medium from the places that they successively occupy. Strictly speaking, their shapes and internal mass distributions do not remain constant during such movement, but these changes are so small that they are unconditionally neglected. In all cases of grain‑liquid interaction, we observe the same phenomenon: the flow of the medium around the grain. This flow, caused by the impermeability of the space occupied by the grain to the liquid medium, causes a change in the motion of the oncoming flow of the medium. The motion is accompanied by friction at the boundary between the grain and the medium. The question of the magnitude of the resistance experienced by a moving body is one of the oldest problems in dynamics, but to this day no final theoretical solution has been achieved, which has led to attempts to directly determine the resistance experimentally and has given rise to the successful development of experimental hydro‑ and aerodynamics.

None