查看“︁分离压”︁的源代码

'''分离压'''是薄液膜中由于分子作用力产生的额外的压力<ref>[http://goldbook.iupac.org/goldbook/D01790.html "Disjoining pressure". Entry in the IUPAC Compendium of Chemical Terminology ("The Gold Book"), the International Union of Pure and Applied Chemistry, 2nd edition, 1997]{{Dead link|date=2019年10月 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>。分离压的物理定义为是单位面积[[吉布斯能]]关于距离的导数。

分离压的概念最早由[[Derjaguin]]引入。在薄膜蒸发中，分离压的概念得到广泛应用。

== 定义 ==
分离压可表示为:<ref name="Butt">Hans-Jürgen Butt, Karlheinz Graf, Michael Kappl,"Physics and chemistry of interfaces", John Wiley & Sons Canada, Ltd., 1 edition, 2003, page 95 [http://books.google.ca/books?id=r-IpcdGJMJEC&pg=PA95&lpg=PA95&dq=%22Disjoining+pressure%22&source=bl&ots=0DXcKQSLCS&sig=ZJmRRnMUld3DQq4WYI_tNjkWrC4&hl=en&ei=tS3uSvC3HoHJlAeOkNX_BA&sa=X&oi=book_result&ct=result&resnum=5&ved=0CB0Q6AEwBDgU#v=onepage&q=%22Disjoining%20pressure%22&f=false (Google books)] {{Wayback|url=http://books.google.ca/books?id=r-IpcdGJMJEC&pg=PA95&lpg=PA95&dq=%22Disjoining+pressure%22&source=bl&ots=0DXcKQSLCS&sig=ZJmRRnMUld3DQq4WYI_tNjkWrC4&hl=en&ei=tS3uSvC3HoHJlAeOkNX_BA&sa=X&oi=book_result&ct=result&resnum=5&ved=0CB0Q6AEwBDgU#v=onepage&q=%22Disjoining%20pressure%22&f=false |date=20141205163944 }}</ref>

:<math>\Pi_D = - {1 \over A} \left( \frac{\partial G}{\partial x} \right)_{T,V, A} </math>

* ''Π<sub>d</sub>'' - 分离压, N/m<sup>2</sup>
* ''A'' - 界面面积, m<sup>2</sup>
* ''G'' - 吉布斯能, J
* ''x'' - 具体, m
*  ''T'', ''V'' and ''A'' 表示在求导中，温度，体积和界面面积保持常数.

经典理论([[Hamaker theory]])可以用来计算薄液膜在平滑表面的分离压,<ref name="Israelachvili">Jacob N. Israelachvili,"Intermolecular and Surface Forces", Academic Press, Revised Third edition, 2011, page 267-268 [https://books.google.com/books?id=vgyBJbtNOcoC&printsec=frontcover&dq=Intermolecular+and+Surface+Forces+3rd+edition&hl=en&sa=X&ei=2ksfVcrlJsHCsAXBhIOwAQ&ved=0CB4Q6AEwAA#v=onepage&q=Intermolecular%20and%20Surface%20Forces%203rd%20edition&f=false (Google books)] {{Wayback|url=https://books.google.com/books?id=vgyBJbtNOcoC&printsec=frontcover&dq=Intermolecular+and+Surface+Forces+3rd+edition&hl=en&sa=X&ei=2ksfVcrlJsHCsAXBhIOwAQ&ved=0CB4Q6AEwAA#v=onepage&q=Intermolecular%20and%20Surface%20Forces%203rd%20edition&f=false |date=20200710030938 }}</ref>
:<math>\Pi_D = - {{ A_H }\over {6 \pi \delta_0^3}}  </math>

where:
* ''A<sub>H</sub>'' - Hamaker常数 J
* ''δ<sub>0</sub>'' - 薄液膜厚度, m

对于非平滑表面，分离压会受到固体表面, ''ζ''<sub>S</sub> , 和液体表面, ''ζ''<sub>L</sub> 的影响。<ref name = "Robbins">{{Cite web |url=http://journals.aps.org/pra/abstract/10.1103/PhysRevA.43.4344 |title=Mark O. Robbins, David, Andelman, and Jean-François Joanny, Phys. Rev. A 43, 4344, (1991) |accessdate=2015-07-14 |archive-date=2020-07-10 |archive-url=https://web.archive.org/web/20200710030924/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.43.4344 |dead-url=no }}</ref>
:<math>{\Pi_D (x,{{\zeta}_{\text{L}}(x)})}= \int d^2 \rho {\int_{\zeta_\text{L} (x) - \zeta_\text{S} (x+\rho)}^{+\infty}} dz \omega(\rho,z) </math>

where:
* ''ω(ρ,z)'' - 固液相互作用势能, J/m<sup>6</sup>
液体表现形状可以用能量最小原理求出。<ref>{{Cite web |url=http://pubs.acs.org/doi/abs/10.1021/nl5037066 |title=Han Hu, Christopher R. Weinberger, and Ying Sun Nano Lett., 14 (12), pp 7131–7137 (2014) |accessdate=2015-07-14 |archive-date=2020-07-10 |archive-url=https://web.archive.org/web/20200710030943/https://pubs.acs.org/doi/abs/10.1021/nl5037066 |dead-url=no }}</ref>
:<math> {\delta W_{\text{total}}} = {{\partial W_{\text{total}}} \over {\partial {\zeta_\text{L}}}} \delta \zeta_\text{L} + {{\partial W_{\text{total}}} \over {\partial \zeta_\text{L}^'}} \delta \zeta_\text{L}^'= 0 </math>

where:
* ''W''<sub>total</sub> - , 系统总能，包括表面能和固液相互作用势能, J/m<sup>2</sup>
* ''ζ''<sub>L</sub> - 液体表面形状, m
* ''ζ'''<sub>L</sub> - 液体表面斜率, 1

== 相关 ==
*[[表面张力]]

== 参考文献 ==
<references/>

[[Category:热力学]]