The effects of entrainment on the hydraulic equivalence relationships of light and heavy minerals in sands

A semi-empirical critical velocity equation and critical suspension velocity equation have been developed to explain the settling velocity relationships and concentrations of light and heavy minerals in sands. Based on solutions to these equations and supporting experimental data, a fourfold classification of constant terminal settling velocity (CTSV) ratios of light and heavy minerals and heavy mineral concentrations has been constructed using ranges of R*, the boundary Reynolds number, and d/BKS, the ratio of grain size in question to the bottom roughness grain size. If R* is less than five and d (sub h) /BKS is about one, a heavy enriched, well size-sorted, fine to medium size sand deposit should result, with entrainment equivalent size ratios of heavy to light grains up to four times smaller than those predicted by settling laws. If R* is greater than five but less than 70 and d (sub h) /BKS is about one, a fine to medium deposit should be formed of very heavy enriched, very well size-sorted sand, whereas if R* is greater than 70 and d (sub h) /BKS is less than one, a coarse more poorly sorted light mineral deposit should result. Garnet and quartz in heavy and light layers from a Presque Isle, Lake Erie beach have equal sizes in the heavy layers and equal settling velocities in the light layers as predicted. A beach heavy and light mineral size budget is proposed which incorporates these mechanisms.