Strange–Rahman–Smith equation

The Strange–Rahman–Smith equation is used in the cryoporometry method of measuring porosity. NMR cryoporometry ^[1][2][3] is a recent technique for measuring total porosity and pore size distributions. NMRC is based on two equations: the Gibbs–Thomson equation, which maps the melting point depression to pore size, and the Strange–Rahman–Smith equation, ^[1] which maps the melted signal amplitude at a particular temperature to pore volume.

Equation

If the pores of the porous material are filled with a liquid, then the incremental volume of the pores ${\displaystyle \Delta v}$ with pore diameter between ${\displaystyle x}$ and ${\displaystyle x+\Delta \,x}$ may be obtained from the increase in melted liquid volume for an increase of temperature between ${\displaystyle T}$ and ${\displaystyle T+\Delta T}$ by:^[1]

${\displaystyle {\frac {dv}{dx}}={\frac {dv}{d\,T}}{\frac {k_{GT}}{x^{2}}}}$

Where: ${\displaystyle k_{GT}}$ is the Gibbs–Thomson coefficient for the liquid in the pores.