# Poynting effect

The Poynting effect may refer to two unrelated physical phenomena. Neither should be confused with the Poynting–Robertson effect. All of these effects are named after John Henry Poynting, an English physicist.

## Solid mechanics

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] The Poynting phenomenon in torsion was noticed experimentally by J. H. Poynting.[5][6][7]

## Chemistry and thermodynamics

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.

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

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:[8]

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

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
2
O
and O
2
at high pressure while remaining in the gaseous form is due to the Poynting effect.

## References

1. C. A. Truesdell, A programme of physical research in classical mechanics, Zeitschrift f¨ur Angewandte Mathematik und Physik 3 (1952) 79-95.
2. P. A. Janmey, M. E. McCormick, S. Rammensee, J. L. Leight, P. C. Georges, and F. C. MacKintosh, Negative normal stress in semiflexible biopolymer gels, Nature Materials 6 (2006) 48-51.
3. L. A. Mihai and A. Goriely, Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials, Proceedings of the Royal Society A 467 (2011) 3633-3646.
4. L. A. Mihai and A. Goriely, Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in nonlinear elasticity, International Journal of Non-Linear Mechanics 49 (2013) 1-14.
5. J. H. Poynting, Radiation-pressure, Philosophical Magazine 9 (1905) 393-406.
6. J. H. Poynting, On pressure perpendicular to the shear-planes in finite pure shears, and on the lengthening of loaded wires when twisted, Proceedings of the Royal Society A 82 (1909) 546-559.
7. J. H. Poynting, The changes in length and volume of an Indian-rubber cord when twisted, India-Rubber Journal, October 4 (1913) p. 6.
8. Wark, Kenneth Advanced Thermodynamics for Engineers. New York: McGraw-Hill, 1995