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In this paper we review the Dynamic Van der Waals theory, which is a recent developed method to study phase separation and transition process in multiphase flow. Gradient contributions are included in the entropy and energy functions, and it’s particularly useful and non-trivial if we consider problems with temperature change. Using this theory, we can simulate that, a droplet in an equilibrium liquid will be attracted to the heated wall(s) which was initially wetted, which is the main cause of the famous hydrodynamic phenomena-Leidonfrost Phenomena. After more than ten years development, this theory has been widely used to study the fluid flow in vaporing and boiling process, e.g., droplet motion. Furthermore, this theory has been combined with phase field model, which could be extended to solid-liquid phase transition. There has also been researches about constructing LBM scheme to extend to the Dynamic Van der Waals theory, using Chapman-Enskog analyze. In all, due to its rigorous thermodynamic derivation, this theory has now become the fundamental theoretical basis in the heated multiphase flow.


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Review on Dynamic Van der Waals Theory in two-phase flow

Show Author's information Tao Zhang1( )Jisheng Kou2Shuyu Sun1
Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia
School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, P. R. China

Abstract

In this paper we review the Dynamic Van der Waals theory, which is a recent developed method to study phase separation and transition process in multiphase flow. Gradient contributions are included in the entropy and energy functions, and it’s particularly useful and non-trivial if we consider problems with temperature change. Using this theory, we can simulate that, a droplet in an equilibrium liquid will be attracted to the heated wall(s) which was initially wetted, which is the main cause of the famous hydrodynamic phenomena-Leidonfrost Phenomena. After more than ten years development, this theory has been widely used to study the fluid flow in vaporing and boiling process, e.g., droplet motion. Furthermore, this theory has been combined with phase field model, which could be extended to solid-liquid phase transition. There has also been researches about constructing LBM scheme to extend to the Dynamic Van der Waals theory, using Chapman-Enskog analyze. In all, due to its rigorous thermodynamic derivation, this theory has now become the fundamental theoretical basis in the heated multiphase flow.

Keywords: phase transition, Van der Waals Theory, vaporing and boiling.

References(42)

Anderson, J.C., Gerbing, D.W. Structural equation modeling in practice: A review and recommended two-step approach. Psychol. Bull. 1988, 103(3): 411-423.
Armijo, J., Barnard, J.J. Droplet Evolution in Warm Dense Matter Expanding Flow. Livermore, CA, Lawrence Livermore National Laboratory (LLNL), 2010.
Barbante, P., Frezzotti, A. Simulations of condensation flows induced by reflection of weak shocks from liquid surfaces. Paper 110004 Presented at 30th International Symposium on Rarefied Gas Dynamics, 2016.
DOI
Charles, A. Smoothed Particle Modelling of Liquid-Vapour Phase Transitions. Melbourne, Australia, RMIT University, 2014.
Charles, A., Daivis, P. Smooth particle methods for vapour liquid coexistence. Paper Presented at 18th World IMACS / MODSIM Congress, Cairns, Australia, 13-17 July, 2009.
Chaudhri, A., Bell, J.B., Garcia, A.L., et al. Modeling multiphase flow using fluctuating hydrodynamics. Phys. Rev. E 2014, 90(3): 033014.
Chen, C.Y., Meiburg, E. Miscible displacements in capillary tubes: Influence of Korteweg stresses and divergence effects. Phys. Fluids 2002, 14(7): 2052-2058.
Chen, C.Y., Wang, L., Meiburg, E. Miscible droplets in a porous medium and the effects of Korteweg stresses. Phys. Fluids 2001, 13(9): 2447-2456.
Felderhof, B.U. Hydrodynamic interaction between two spheres. Phys. A 1977, 89(2): 373-384.
Gan, Y.B., Xu, A.G., Zhang, G.C., et al. Physical modeling of multiphase flow via lattice Boltzmann method: Numerical effects, equation of state and boundary conditions. Front. Phys. 2012, 7(4): 481-490.
Garrabos. Y., Lecoutre-Chabot, C., Hegseth, J., et al. Gas spreading on a heated wall wetted by liquid. Phys. Rev. E 2001, 64(5): 051602.
Gonnella, G., Lamura, A., Sofonea, V. Lattice Boltzmann simulation of thermal nonideal fluids. Phys. Rev. E 2007, 76(3): 036703.
Găƒrăƒjeu, M., Gouin, H., Saccomandi, G. Scaling Navier-Stokes equation in nanotubes. Phys. Fluids 2013, 25(8): 082003.
Korteweg, D.J. Sur la forme que prennent les equations du mouvements des fluides si l’on tient compte des forces capillaires causees par des variations de densite considerables mais connues et sur la theorie de la capillarite dans l’hypothese d’une variation continue de la densite. Archives Neerlandaises des Sciences Exactes et Naturelles 1901, 6: 1-24.
Kou, J., Sun, S. Convergence of discontinuous Galerkin methods for incompressible two-phase flow in heterogeneous media. SIAM J. Numer. Anal. 2013, 51(6): 3280-3306.
Kou, J., Sun, S. Numerical methods for a multi-component two-phase interface model with geometric mean influence parameters. SIAM J. Sci. Comput. 2015, 37(4): B543-B569.
Kou, J., Sun, S. Thermodynamically consistent modeling and simulation of multi-component two-phase flow model with partial miscibility. arXiv preprint arXiv:1611.08622. 2016a, 1-29.
Kou, J., Sun, S. Unconditionally stable methods for simulating multi-component two-phase interface models with Peng-Robinson equation of state and various boundary conditions. J. Comput. Appl. Math. 2016b, 291: 158-182.
Kou, J., Sun, S. Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility. J. Comput. Phys. 2016c, 318: 349-372.
Kou, J., Sun, S., Wang, X. Efficient numerical methods for simulating surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Comput. Methods Appl. Mech. Eng. 2015, 292: 92-106.
Kou, J., Sun, S., Wang, X. An energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles, volume and temperature. Comput. Geosci. 2016, 20(1): 283-295.
Lamorgese, A., Mauri, R., Sagis, L.M.C. Modeling soft interface dominated systems: A comparison of phase field and Gibbs dividing surface models. Phys. Rep. 2017, 675: 1-54.
Li, Q., Luo, K.H., Kang, Q.J., et al. Lattice Boltzmann methods for multiphase flow and phase-change heat transfer. Prog. Energy Combust. Sci. 2016, 52: 62-105.
Liu, J., Amberg, G., Do-Quang, M. Diffuse interface method for a compressible binary fluid. Phys. Rev. E 2016, 93(1): 013121.
Liu, J., Landis, C.M., Gomez, H., et al. Liquid-vapor phase transition: thermomechanical theory, entropy stable numerical formulation, and boiling simulations. Comput. Methods Appl. Mech. Eng. 2015, 297: 476-553.
Nikolayev, V.S., Beysens, D.A. Boiling crisis and non-equilibrium drying transition. Europhys. Lett. 1999, 47(3): 345-351.
Nikolayev, V.S., Garrabos, Y., Lecoutre, C., et al. Evaporation condensation-induced bubble motion after temperature gradient set-up. C.R. Mec. 2017, 345(1): 35-46.
Nold, A. From the Nano-to the Macroscale-Bridging Scales for the Moving Contact Line Problem. London, UK, Imperial College London, 2016.
Onuki, A. Dynamic van der Waals theory of two-phase fluids in heat flow. Phys. Rev. Lett. 2005, 94(5): 054501.
Onuki, A. Dynamic van der Waals theory. Phys. Rev. E 2007, 75(3): 036304.
Pecenko, A., Van Deurzen, L.G.M., Kuerten, J.G., et al. Non-isothermal two-phase flow with a diffuse-interface model. Int. J. Multiph. Flow 2011, 37(2): 149-165.
Rowlinson, J.S. Translation of JD van der Waals’ The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density. J. Stat. Phys. 1979, 20(2): 197-200.
Shen, J., Yang, X. Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. SIAM J. Numer. Anal. 2015, 53(1): 279-296.
Sofonea, V., Lamura, A., Gonnella, G., et al. Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems. Phys. Rev. E 2004, 70(4): 046702.
Takae, K., Onuki, A. Phase field model of solid-liquid and liquid-liquid phase transitions in flow and elastic fields in one-component systems. arXiv preprint arXiv 1003.4376. 2010, 1-6.
Taylor, M.T., Qian, T. Thermal singularity and contact line motion in pool boiling: Effects of substrate wettability. Phys. Rev. E 2016, 93(3): 033105.
Teshigawara, R., Onuki, A. Droplet evaporation in one-component fluids: Dynamic van der Waals theory. Europhys. Lett. 2008, 84(3): 36003.
Tryggvason, G., Scardovelli, R., Zaleski, S., et al. Direct numerical simulations of gas-liquid multiphase flows. New York, USA, Cambridge University Press, 2011.
Widom, B., Rowlinson, J.S. New model for the study of liquid-vapor phase transitions. J. Chem. Phys. 1970, 52(4): 1670-1684.
Xie, C., Liu, G., Wang, M. Evaporation flux distribution of drops on a hydrophilic or hydrophobic flat surface by molecular simulations. Langmuir 2016, 32(32): 8255-8264.
Xu, X., Liu, C., Qian, T. Hydrodynamic boundary conditions for one-component liquid-gas flows on non-isothermal solid substrates. Commun. Math. Sci. 2012, 10: 1027-1053.
Xu, X., Qian, T. Thermal singularity and droplet motion in one-component fluids on solid substrates with thermal gradients. Phys. Rev. E 2012, 85(6): 061603.
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Publication history

Received: 10 August 2017
Revised: 16 September 2017
Accepted: 19 September 2017
Published: 25 September 2017
Issue date: September 2017

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© The Author(s) 2017

Acknowledgements

The authors would like to express their gratitude to the anonymous referees for their efforts in providing valuable comments.

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Published with open access at Ausasia Science and Technology Press on behalf of the Division of Porous Flow, Hubei Province Society of Rock Mechanics and Engineering.

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