• Corpus ID: 119642544

Phase transitions in filtration of real gases.

@article{Lychagin2019PhaseTI,
  title={Phase transitions in filtration of real gases.},
  author={Valentin V. Lychagin and Mikhail Roop},
  journal={arXiv: Mathematical Physics},
  year={2019}
}
Steady adiabatic filtration of real gases is studied. Thermodynamical states of real gases are presented by Legendrian surfaces in 5-dimensional thermodynamical contact space. The relation between phase transitions and singularities of projection of the Legendrian surfaces on the plane of intensive variables is shown. The constructive method of finding solutions of the Dirichlet filtration problem together with analysis of critical phenomena is presented. Cases of van der Waals and Peng… 
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8 Citations
Background Citations
3
Methods Citations
1

8 Citations

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  • Physics
    2019 Twelfth International Conference "Management of large-scale system development" (MLSD)
  • 2019
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In this paper, we study non-stationary filtration of real gases in porous media. Thermodynamic state of the medium is given by van der Waals state equations. Solutions for non-stationary filtration…

References

SHOWING 1-10 OF 18 REFERENCES

Gas Flow with Phase Transitions: Thermodynamics and the Navier–Stokes Equations

In this paper we study one-dimensional viscous gas flows described by the Navier–Stokes equations. Thermodynamics of the gas obeys the van der Waals law. This implies that phase transitions can occur…

Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena

The purpose of this paper is to use the geometrical theory of nonlinear partial differential equations and the theory of singularities of maps in order to obtain the general scheme for constructing…

Introduction to Phase Transitions and Critical Phenomena

H E Stanley Oxford: University Press 1971 pp xx + 308 price ?5 In the past fifteen years or so there has been a lot of experimental and theoretical work on the nature of critical phenomena in the…

A New Two-Constant Equation of State

The development of a new two-constant equation of state in which the attractive pressure term of the semiempirical van der Waals equation has been modified is outlined. Examples of the use of the…

Contact geometry and nonlinear differential equations (Cambridge

  • 2007

The Flow of Homogeneous Fluids through Porous Media

Classification of equations of state for viscous fluids

This paper presents a classification of equations of state for viscous fluids (or gases) whose motion is governed by the Navier–Stokes equations. The classification is based on an analysis of…

The physics of flow through porous media

Physics of Flow through Porous Media

Phase Transitions and Critical Phenomena