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{{Distinguish|Poynting–Robertson 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.<ref>C. A. Truesdell, A programme of physical research in classical mechanics, Zeitschrift f¨ur Angewandte Mathematik und Physik 3 (1952) 79-95.</ref><ref>P. A. Janmey, M. E. McCormick, S. Rammensee, J. L. Leight, P. C. Georges, and F. C. MacKintosh, [http://www.nat.vu.nl/~fcm/Papers/NatMatSub2.pdf Negative normal stress in semiflexible biopolymer gels], Nature Materials 6 (2006) 48-51.</ref><ref>L. A. Mihai and A. Goriely, [http://rspa.royalsocietypublishing.org/content/467/2136/3633 Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials], Proceedings of the Royal Society A 467 (2011) 3633-3646.</ref><ref>L. A. Mihai and A. Goriely,  [http://www.sciencedirect.com/science/article/pii/S0020746212001400 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.</ref><ref>C.O. Horgan and J. G. Murphy, [https://pubs.rsc.org/en/content/articlelanding/2017/sm/c7sm00992e Poynting and reverse Poynting effects in soft materials], Soft Matter, 13, 2017, 4916-4923.</ref> The Poynting phenomenon in torsion was noticed experimentally by [[John Henry Poynting|J. H. Poynting]].<ref>J. H. Poynting, Radiation-pressure, ''Philosophical Magazine'' 9 (1905) 393-406.</ref><ref>J. H. Poynting, [http://rspa.royalsocietypublishing.org/content/82/557/546.full.pdf+html 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.</ref><ref>J. H. Poynting, The changes in length and volume of an Indian-rubber cord when twisted, ''India-Rubber Journal'', October 4 (1913) p. 6.</ref>

== Chemistry and thermodynamics ==
In thermodynamics, the Poynting effect generally refers to the change in the [[vapor pressure]] of a liquid substance when the total pressure of the liquid is varied. In particular this occurs when the vessel containing the vapor and liquid is pressurized by a non-condensable and non-soluble gas.

In 1881<ref>[https://archive.org/details/londonedinburg5121881lond/page/32/mode/2up Poynting, J. H., Change of State: Solid-Liquid, Phil. Mag., 12, 32-48, 232, 1881]</ref> Poynting generalized the [[Kelvin equation]] pointing out that vapor pressure was not only modified by [[Laplace pressure]] of curved surfaces, but in fact changes the same way due to any pressure source.<ref name=Wisniak>{{cite journal|title=John Henry Poynting|first=Jaime|journal=Educación Química|last=Wisniak|date=2011 |volume=22 |issue=4 |pages=340–348 |doi=10.1016/S0187-893X(18)30154-X|url=https://www.sciencedirect.com/science/article/pii/S0187893X1830154X/pdfft?md5=19ae3933cc05e58fdc04bce7b857dab3&pid=1-s2.0-S0187893X1830154X-main.pdf}}</ref> In modern thermodynamics, this is understood as coming from the [[Maxwell relation]] for the [[chemical potential]] increase (of the liquid phase) due to pressure: <math>(\partial \mu/\partial P)_{T,N} = (\partial V/\partial N)_{T} </math>, i.e. <math>\mathrm d\mu = v_\text{liq} \mathrm dP_\text{liq}</math> at constant temperature.<ref name="devoe">Devoe "THERMODYNAMICS AND CHEMISTRY" - https://www2.chem.umd.edu/thermobook/ section 12.8</ref>

The [[Fugacity#Condensed phase|fugacity]] shift from pressure is thus:<ref name=Wisniak/><ref name="devoe"/>

:<math> \frac{ f (T, P) }{f_\text{sat} (T)}  = \exp\left(\frac{ 1 }{ R T } \int_{P^\text{sat} (T)}^{P} v_\text{liq} \, dp \right) </math>

where the exponential on the right is known as the '''Poynting factor'''.<ref name="devoe"/> 

If one assumes that the vapor is an [[ideal gas]] (fugacity = vapor pressure), and that the liquid is incompressible (<math>v_\text{liq}</math> constant), then:

:<math> \frac{ p}{p_{\rm sat}}  = \exp\left(\frac{ v_\text{liq} }{ R T } ( P - p_{\rm sat} ) \right)</math>

where
:<math display="inline">p</math> is the modified vapor pressure
:<math display="inline">p_{\rm sat}</math> is the vapor pressure as it would be with no other pressure sources applied
:<math display="inline">v_{liq}</math> is the liquid molar volume
:<math display="inline">R</math> is the molar gas constant
:<math display="inline">T</math> is the temperature
:<math display="inline">P</math> is the total pressure, i.e. the pressure of the liquid

For a 1 atmosphere pressure, [[room temperature]], and typical liquid densities, the vapor pressure change from Poynting effect is less than 1%.<ref name="devoe"/>

The Poynting effect assumes that the background pressure is supplied by an insoluble gas. If the gas is soluble, then it will also cause a ''decrease'' of the vapor pressure, a form of [[Colligative properties|colligative]] effect that is caused by all solutes (and mathematically resembles the Poynting effect except with a negative 'pressure' equal to the [[osmotic pressure]]). This decrease may cancel or even overwhelm the small increase from the Poynting effect, depending on the solubility.

A commonly cited example is the production of the medicine [[Entonox]], a high-pressure mixture of [[nitrous oxide]] and [[oxygen]]. The ability to combine {{chem|N|2|O}} and {{chem|O|2}} at high [[pressure]] while remaining in the gaseous form is attributed to the oxygen exerting a Poynting effect on the nitrous oxide,<ref>{{cite journal|last1=Tunstall |first1=M.E. |title=Obstetric Analgesia |journal=The Lancet |date=1961 |volume=278 |issue=7209 |page=964 |doi=10.1016/S0140-6736(61)90799-1}}</ref> though in fact the effect at play is slightly distinct and involves a shift in the [[critical point (thermodynamics)|critical point]] (also called Poynting effect).<ref>{{cite journal|last1=Litwin |first1=Patrick D. |title=The effects of temperature on nitrous oxide and oxygen mixture homogeneity and stability |journal=BMC Anesthesiology |date=2010 |volume=10 |article-number=19 |doi=10.1186/1471-2253-10-19 |pmid=20950473 |pmc=2967548 |doi-access=free }}</ref>

== References ==
{{Reflist}}

{{DEFAULTSORT:Poynting Effect}}
[[Category:Elasticity (physics)]]
[[Category:Rubber properties]]
[[Category:Gases]]


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