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Poynting effect
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<h2 id="solid-mechanics">Solid mechanics</h2> <p>In solid mechanics, the Poynting effect is a <a href="/facts/Finite_strain_theory/rEjpC9oD">finite strain theory</a> 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.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a><a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> The Poynting phenomenon in torsion was noticed experimentally by <a href="/facts/John_Henry_Poynting/EFGQqo61">J. H. Poynting</a>.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a><a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> </p> <h2 id="chemistry-and-thermodynamics">Chemistry and thermodynamics</h2> <p>In thermodynamics, the Poynting effect generally refers to the change in the <a href="/facts/Vapor_pressure/whrEr96T">vapor pressure</a> 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. </p><p>In 1881<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> Poynting generalized the <a href="/facts/Kelvin_equation/wFxkLC2e">Kelvin equation</a> pointing out that vapor pressure was not only modified by <a href="/facts/Laplace_pressure/7vv2t2LN">Laplace pressure</a> of curved surfaces, but in fact changes the same way due to any pressure source.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> In modern hermodynamics, this is understood as coming from the <a href="/facts/Maxwell_relation/1xS42h81">Maxwell relation</a> for the <a href="/facts/Chemical_potential/IaMIgg2Q">chemical potential</a> shift due to pressure: ( ∂ μ / ∂ P ) T , N = ( ∂ V / ∂ N ) T {\displaystyle (\partial \mu /\partial P)_{T,N}=(\partial V/\partial N)_{T}} , i.e. d μ = v liq d P liq {\displaystyle \mathrm {d} \mu =v_{\text{liq}}\mathrm {d} P_{\text{liq}}} at constant temperature.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> </p><p>The <a href="/facts/Fugacity/C2gdkThT">fugacity</a> shift from pressure is thus:<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a><a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> </p> f ( T , P ) f sat ( T ) = exp ( 1 R T ∫ P sat ( T ) P v liq d p ) {\displaystyle {\frac {f(T,P)}{f_{\text{sat}}(T)}}=\exp \left({\frac {1}{RT}}\int _{P^{\text{sat}}(T)}^{P}v_{\text{liq}}\,dp\right)} <p>where the exponential on the right is known as the Poynting factor.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> </p><p>If one assumes that the vapor is an ideal gas (fugacity = vapor pressure), and that the liquid is incompressible ( v liq {\displaystyle v_{\text{liq}}} constant), then: </p> p p s a t = exp ( v liq R T ( P − p s a t ) ) {\displaystyle {\frac {p}{p_{\rm {sat}}}}=\exp \left({\frac {v_{\text{liq}}}{RT}}(P-p_{\rm {sat}})\right)} <p>where </p> p {\textstyle p} is the modified vapor pressure p s a t {\textstyle p_{\rm {sat}}} is the vapor pressure as it would be with no other pressure sources applied v l i q {\textstyle v_{liq}} is the liquid molar volume R {\textstyle R} is the molar gas constant T {\textstyle T} is the temperature P {\textstyle P} is the total pressure, i.e. the pressure of the liquid <p>For a 1 atmosphere pressure, room temperature, and typical liquid densities, the vapor pressure change from Poynting effect is less than 1%.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> </p><p>A common example is the production of the medicine <a href="/facts/Entonox/SH91pGDd">Entonox</a>, a high-pressure mixture of <a href="/facts/Nitrous_oxide/Jvys91lI">nitrous oxide</a> and <a href="/facts/Oxygen/acyn6o8r">oxygen</a>. The ability to combine N2O and O2 at high <a href="/facts/Pressure/eyc37GRG">pressure</a> while remaining in the gaseous form is due to the oxygen exerting a Poynting effect on the nitrous oxide. </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>C. A. Truesdell, A programme of physical research in classical mechanics, Zeitschrift f¨ur Angewandte Mathematik und Physik 3 (1952) 79-95. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>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. <a href="http://www.nat.vu.nl/~fcm/Papers/NatMatSub2.pdf" target="_blank">http://www.nat.vu.nl/~fcm/Papers/NatMatSub2.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>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. <a href="http://rspa.royalsocietypublishing.org/content/467/2136/3633" target="_blank">http://rspa.royalsocietypublishing.org/content/467/2136/3633</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>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. <a href="http://www.sciencedirect.com/science/article/pii/S0020746212001400" target="_blank">http://www.sciencedirect.com/science/article/pii/S0020746212001400</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>C.O. Horgan and J. G. Murphy, Poynting and reverse Poynting effects in soft materials, Soft Matter, 13, 2017, 4916-4923. <a href="https://pubs.rsc.org/en/content/articlelanding/2017/sm/c7sm00992e" target="_blank">https://pubs.rsc.org/en/content/articlelanding/2017/sm/c7sm00992e</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>J. H. Poynting, Radiation-pressure, Philosophical Magazine 9 (1905) 393-406. <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>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. <a href="http://rspa.royalsocietypublishing.org/content/82/557/546.full.pdf+html" target="_blank">http://rspa.royalsocietypublishing.org/content/82/557/546.full.pdf+html</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>J. H. Poynting, The changes in length and volume of an Indian-rubber cord when twisted, India-Rubber Journal, October 4 (1913) p. 6. <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Poynting, J. H., Change of State: Solid-Liquid, Phil. Mag., 12, 32-48, 232, 1881 <a href="https://archive.org/details/londonedinburg5121881lond/page/32/mode/2up" target="_blank">https://archive.org/details/londonedinburg5121881lond/page/32/mode/2up</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Wisniak, Jaime. "John Henry Poynting" (PDF). Educación Química. doi:10.1016/S0187-893X(18)30154-X. <a href="https://www.sciencedirect.com/science/article/pii/S0187893X1830154X/pdfft?md5=19ae3933cc05e58fdc04bce7b857dab3&pid=1-s2.0-S0187893X1830154X-main.pdf" target="_blank">https://www.sciencedirect.com/science/article/pii/S0187893X1830154X/pdfft?md5=19ae3933cc05e58fdc04bce7b857dab3&pid=1-s2.0-S0187893X1830154X-main.pdf</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Devoe "THERMODYNAMICS AND CHEMISTRY" - https://www2.chem.umd.edu/thermobook/ section 12.8 <a href="https://www2.chem.umd.edu/thermobook/" target="_blank">https://www2.chem.umd.edu/thermobook/</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Wisniak, Jaime. "John Henry Poynting" (PDF). Educación Química. doi:10.1016/S0187-893X(18)30154-X. <a href="https://www.sciencedirect.com/science/article/pii/S0187893X1830154X/pdfft?md5=19ae3933cc05e58fdc04bce7b857dab3&pid=1-s2.0-S0187893X1830154X-main.pdf" target="_blank">https://www.sciencedirect.com/science/article/pii/S0187893X1830154X/pdfft?md5=19ae3933cc05e58fdc04bce7b857dab3&pid=1-s2.0-S0187893X1830154X-main.pdf</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Devoe "THERMODYNAMICS AND CHEMISTRY" - https://www2.chem.umd.edu/thermobook/ section 12.8 <a href="https://www2.chem.umd.edu/thermobook/" target="_blank">https://www2.chem.umd.edu/thermobook/</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Devoe "THERMODYNAMICS AND CHEMISTRY" - https://www2.chem.umd.edu/thermobook/ section 12.8 <a href="https://www2.chem.umd.edu/thermobook/" target="_blank">https://www2.chem.umd.edu/thermobook/</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Devoe "THERMODYNAMICS AND CHEMISTRY" - https://www2.chem.umd.edu/thermobook/ section 12.8 <a href="https://www2.chem.umd.edu/thermobook/" target="_blank">https://www2.chem.umd.edu/thermobook/</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> </ol>