Hydrostatic density distribution of fluids in steep field gradients and near critical points

A new perturbation expansion for the hydrostatic density distribution of a fluid in a steep field gradient is presented. It is a power series in the scale γ of an external potential ψ (γx), and is asymptotically valid as γ→0, although convergence is not proved. Significant corrections to the conventional hydrostatic equations are found near the critical point of a fluid, even in the gravitational field.