Abstract:
We develop the kinetic theory of critical phenomena in the Van der Waals model. Our approach is considerably different from the traditional phenomenological approach based on the scaling invariance hypothesis and the renormalization group method. From the analysis of the kinetic equation, we can calculate the dynamic and fluctuation characteristics and thus explain a number of experimental observations. The dynamic processes are investigated using self-consistent equations for the first and second moments of the distribution function. We use the corresponding Langevin equation to describe the fluctuation processes. The structure of the dissipative terms in the kinetic equation determines the source intensities. Analysis of experimental data for the temperature dependence of the heat capacity and for the molecular scattering spectra confirms the conclusions derived from the kinetic theory.
Citation:
Yu. L. Klimontovich, “Vapor–liquid phase transition: The Van der Waals model”, TMF, 115:3 (1998), 437–458; Theoret. and Math. Phys., 115:3 (1998), 707–722
\Bibitem{Kli98}
\by Yu.~L.~Klimontovich
\paper Vapor--liquid phase transition: The Van der Waals model
\jour TMF
\yr 1998
\vol 115
\issue 3
\pages 437--458
\mathnet{http://mi.mathnet.ru/tmf885}
\crossref{https://doi.org/10.4213/tmf885}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1692390}
\zmath{https://zbmath.org/?q=an:0941.82023}
\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 115
\issue 3
\pages 707--722
\crossref{https://doi.org/10.1007/BF02575494}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000075883900009}
Linking options:
https://www.mathnet.ru/eng/tmf885
https://doi.org/10.4213/tmf885
https://www.mathnet.ru/eng/tmf/v115/i3/p437
This publication is cited in the following 3 articles:
I. R. Yukhnovskii, “Phase space of collective variables and the Zubarev transition
function”, Theoret. and Math. Phys., 194:2 (2018), 189–219
Hlushak P. Tokarchuk M., “Chain of Kinetic Equations For the Distribution Functions of Particles in Simple Liquid Taking Into Account Nonlinear Hydrodynamic Fluctuations”, Physica A, 443 (2016), 231–245
Yukhnovskii I.R. Hlushak P.A. Tokarchuk M.V., “BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids”, Condens. Matter Phys., 19:4 (2016), 43705