On buoyancy in dispersion

The relevant density of dispersion depends on the dimensionless size r of the submerged body. It is the fluid density ρf, when r<1. It is the mixture density ρm, when r>R, about 10, say. It lies somewhere between ρf and ρm, when 1⩽r⩽R. Within this intermediate range, it can be expressed as a weighted sum (1-f)ρf+fρm of the fluid and mixture densities. The weight function f∈〈0,1〉 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.