On the validity of certain integro-differential equations for the density—orientation profile of molecular fluid interfaces

✍ Scribed by P. Tarazona; R. Evans

• Book ID: 103021209
• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 326 KB
• Volume: 97
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(83)80007-4

✦ Synopsis

The status of some recently proposed intgro-differential equations for the density-orientation profile. p@t .Ot). of non-uniform molecule fluids is es;rmined. Two of the equntions derived by Gubbins. \hich involve derivatives with resprcl to an_gular coordinates 01. are shown to be incorrect and corrected versions are proposed_ The implications of the results for p&wise correlations and for the surface tension of the liquid-gas interface sre discussed. In 1980 Gubbins [I] presented some integro-differential equations for the density-orientation profile p(l) =p(rl _ ol) in a non-unifon molecular fluid. For molecules in an external (one-body) potential u(1) F' u(rl, ml) he derived the following: Yr, In p(l) = sdrz do2 c(')(l?) Vr2p(2) -PV,,u(l), Or, In Al) = -psdr, do, P(WW)V~~@) -PV,,~W. V"r in p(l) = Jbz dy ~(~)(12)Vqp(2) -PVqW