On buoyancy in dispersion

The relevant density of dispersion depends on the dimensionless size r of the submerged body. It is the fluid density (oi)f, when r<1. It is the mixture density (pi)m, when r>R, about 10, say. It lies somewhere between (pi)f and (pi)m, when 1 depends on the body size r. Based on the data taken from literature, it is found: f(r) =0.1635(r^-1), which gives R=7.116. When we apply the mixture density concept to a submerged body of size r, we can expect errors of order~(1+1/r)^3, as the very upper bound.