Two-Phase Flow with Surfactants: Diffuse Interface Models and Their Analysis

Abels, H., Garcke, H., Grün, G.: Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flow with different densities. Math. Models Methods Appl. Sci. 22(3), 1150013, 40 pp. (2012)Google Scholar

Abels, H., Garcke, H., Grün, G., Metzger, S.: Diffuse interface models for incompressible two-phase flows with different densities. In: Bothe, D., Reusken, A. (eds.) Transport Processes at Fludic Interfaces. Advances in Mathematical Fluid Mechanics. Springer International Publishing AG, Cham (to appear)Google Scholar

Abels, H., Garcke, H., Weber, J.: Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants (in preparation)Google Scholar

Abels, H., Lam, K.F., Stinner, B.: Analysis of the diffuse domain approach for a bulk-surface coupled PDE system. SIAM J. Math. Anal. 47(5), 3687–3725 (2015)MathSciNetCrossRefMATHGoogle Scholar

Aland, S., Hahn, A., Kahle, C., Nürnberg, R.: Comparative simulations of Taylor-flow with surfactants based on sharp- and diffuse-interface methods. In: Bothe, D., Reusken, A. (eds.) Transport Processes at Fludic Interfaces. Advances in Mathematical Fluid Mechanics. Springer International Publishing AG, Cham (to appear)Google Scholar

Alt, H.W.: The entropy principle for interfaces. Fluids and solids. Adv. Math. Sci. Appl. 19(2), 585–663 (2009)MathSciNetMATHGoogle Scholar

Barrett, J.W., Garcke, H., Nürnberg, R.: On the stable numerical approximation of two-phase flow with insoluble surfactant. ESAIM: M2AN 49(2), 421–458 (2015)Google Scholar

Barrett, J.W., Garcke, H., Nürnberg, R.: Stable finite element approximations of two-phase flow with soluble surfactant. J. Comput. Phys. 297, 530–564 (2015)MathSciNetCrossRefMATHGoogle Scholar

Bedeaux, D.: Nonequilibrium thermodynamics and statistical physics of surfaces. In: Prigogine, I., Rice, S.A. (eds.) Advances in Chemical Physics, vol. 64, pp. 47–109. Wiley, Hoboken, NJ (1986)CrossRefGoogle Scholar

Bothe, D., Prüss, J., Simonett, G.: Well-posedness of a two-phase flow with soluble surfactant. In: Brezis, H., Chipot, M., Escher, J. (eds.) Nonlinear Elliptic and Parabolic problems, Progress in Nonlinear Differential Equations and Their Applications, vol. 64, pp. 37–61. Springer, New York (2005)CrossRefGoogle Scholar

Burger, M., Elvetun, O.L., Schlottbom, M.: Analysis of the diffuse domain method for second order elliptic boundary value problems. Found. Comput. Math. 1–48 (2015). doi:10.1007/s10208-015-9292-6Google Scholar

Diamant, H., Andelman, D.: Kinetics of surfactant adsorption at fluid–fluid interfaces. J. Phys. Chem. 100, 13732–13742 (1996)CrossRefGoogle Scholar

Eastoe, J., Dalton, J.S.: Dynamic surface tension and adsorption mechanisms of surfactants at the air–water interface. Adv. Colloid Interface Sci. 85, 103–144 (2000)CrossRefGoogle Scholar

Garcke, H., Stinner, B.: Second order phase field asymptotics for multi-component systems. Interfaces Free Bound. 8(2), 131–157 (2006)MathSciNetCrossRefMATHGoogle Scholar

Garcke, H., Wieland, S.: Surfactant spreading on thin viscous films: Nonnegative solutions of a coupled degenerate system. SIAM J. Math. Anal. 37(6), 2025–2048 (2006)MathSciNetCrossRefMATHGoogle Scholar

Garcke, H., Nestler, B., Stoth, B.: On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Phys. D 115(1–2), 87–108 (1998)MathSciNetCrossRefMATHGoogle Scholar

Garcke, H., Lam, K.F., Stinner, B.: Diffuse interface modelling of soluble surfactants in two-phase flow. Commun. Math. Sci. 12(8), 1475–1522 (2014)MathSciNetCrossRefMATHGoogle Scholar

Kralchevsky, P.A., Danov, K.D., Denkov, N.D.: Chemical physics of colloid systems and interfaces. In: Birdi, K.S. (ed.) Handbook of Surface and Colloid Chemistry, 3rd edn., pp. 199–355. CRC Press, Boca Raton, FL (2008)Google Scholar

Lam, K.F.: Diffuse interface models of soluble surfactants in two-phase fluid flows. PhD thesis, University of Warwick (2014)Google Scholar

Li, X., Lowengrub, J., Rätz, A., Voigt, A.: Solving PDEs in complex geometries: a diffuse domain approach. Commun. Math. Sci. 7(1), 81–107 (2009)MathSciNetCrossRefMATHGoogle Scholar

Modica, L.: The gradient theory of phase transitions and the minimal interface criterion. Arch. Ration. Mech. Anal. 98(2), 123–142 (1987)MathSciNetCrossRefMATHGoogle Scholar

Simon, J.: Compact sets in space L ^p(0, T; B). Ann. Mat. Pura Appl. 146(1), 65–96 (1986)CrossRefGoogle Scholar

Slattery, J.C., Sagis, L., Oh, E.-S.: Interfacial Transport Phenomena, 2nd edn. Springer, New York (2007)MATHGoogle Scholar

Teigen, K.E., Li, X., Lowengrub, J., Wang, F., Voigt, A.: A diffuse-interface approach for modeling transport, diffusion and adsorption/desorption of material quantities on a deformable interface. Commun. Math. Sci. 7(4), 1009–1037 (2009)MathSciNetCrossRefMATHGoogle Scholar

Teigen, K.E., Song, P., Lowengrub, J., Voigt, A.: A diffuse-interface method for two-phase flows with soluble surfactants. J. Comput. Phys. 230, 375–393 (2011)MathSciNetCrossRefMATHGoogle Scholar

Wang, Y., Oberlack, M.: A thermodynamic model of multiphase flows with moving interfaces and contact line. Continuum Mech. Thermodyn. 23, 409–433 (2011)MathSciNetCrossRefMATHGoogle Scholar

Ward, A.F.H., Tordai, L.: Time dependence of boundary tensions of solutions I. The role of diffusion in time effects. J. Chem. Phys. 14(7), 453–461 (1946)Google Scholar

Weber, J.T.: Analysis of diffuse interface models for two-phase flows with and without surfactants. PhD thesis, Universität Regensburg (2016)Google Scholar