Poynting effect

In solid mechanics, the Poynting effect is a Finite strain theory effect observed when an elastic cube is sheared between two plates and stress is developed in the direction normal to the sheared faces, or when a cylinder is subjected to torsion and the axial length changes.[1][2][3][4][5] The Poynting phenomenon in torsion was noticed experimentally by J. H. Poynting.[6][7][8]

In thermodynamics, the Poynting effect generally refers to the change in the fugacity of a liquid when a non-condensable gas is mixed with the vapor at saturated conditions.

${\displaystyle \ln {\frac {f^{L}(T,P)}{f_{\text{sat}}(T)}}={\frac {1}{RT}}\int _{P^{\text{sat}}(T)}^{P}v_{\text{liq}}\,dp}$

Equivalently in terms of vapor pressure, if one assumes that the vapor and the non-condensable gas behave as ideal gases and an ideal mixture, it can be shown that:[9]

${\displaystyle \ln {\frac {p_{v}}{p_{v,o}}}={\frac {v_{\text{liq}}}{RT}}(P-p_{v,o})\!}$

where

${\textstyle p_{v}}$ is the modified vapor pressure

${\textstyle p_{v,o}}$ is the unmodified vapor pressure

${\textstyle v_{liq}}$ is the liquid molar volume

${\textstyle R}$ is the liquid/vapor's gas constant

${\textstyle T}$ is the temperature

${\textstyle P}$ is the total pressure (vapor pressure + non-condensable gas)

A common example is the production of the medicine Entonox, a high-pressure mixture of nitrous oxide and oxygen. The ability to combine N
₂O and O
₂ at high pressure while remaining in the gaseous form is due to the Poynting effect.