Asymmetry in the Liquid and Vapor Density Fluctuations at the Critical Point

Recent theoretical evidence has suggested that in general the temperature derivative of the diameter of the liquid-vapor coexistence curve should diverge at the critical point at least as fast as the constant-volume specific heat. This evidence implies with equal force that the difference across the coexistence curve in the density fluctuations in the two phases, ${Δ}{({{∂}{ρ}}{{∂}{μ}})}T={({{∂}{ρ}}{{∂}{μ}})}TL{-}{({{∂}{ρ}}{{∂}{μ}})}TV$, should in general diverge at least as fast as the temperature derivative of the liquid-vapor density difference: ${Δ}{({{∂}{ρ}}{{∂}{μ}})}T{~}(d/dT){Δ}{ρ}{~}{({T}c{-}T)}^{{β}{-}1}$. Experimental estimates of this quantity would provide an alternative test of those hypotheses that currently predict a singular diameter.