Two-Phase Shallow Water Equations and Phase Separation in Thin Immiscible Liquid Films
- 119 Downloads
Simulations of the whole course of flow-induced phase separation in thin immiscible liquid films were performed using a new invariant finite difference scheme. Equations of flow phenomena in thin immiscible liquid films were developed to resolve the interface of phase separation: two-phase shallow water equations were formulated and an invariant finite difference scheme was developed. We first constructed a one-dimensional scheme. We then extended the scheme to a two-dimensional case that has invariance under rotation by the locally one-dimensional method. Regarding phenomena of phase separation, if the volume fraction of the minor phase of the liquid is greater than a critical value, phase separation occurs. Two patterns appear: a sea-island structure and a bi-continuous structure. Different phenomena proceed in each structure, but in the late stage of the phenomena, a single circular droplet persists stably, irrespective of the intermediate state.
KeywordsPhase separation Shallow flows Invariant FDM
Unable to display preview. Download preview PDF.
- 1.Chaikin, P.M., Lubensky, T.C.: Principles of Condensed Matter Physics. Cambridge University Press, Cambridge (1995) Google Scholar
- 2.Daly, B.J., Torrey, M.D.: SOLA-PTS: a transient, three-dimensional algorithm for fluid-thermal mixing and wall heat transfer in complex geometries NUREG/CR-3822; LA-10132-MS. Technical Report of Los Alamos National Laboratory (1984) Google Scholar
- 4.Ishii, M.: Thermo-Fluid Dynamics Theory of Two-Phase Flow. Eyrolles, Paris (1975) Google Scholar
- 5.Keyfitz, B.L., Mora, C.A.: Prototype for nonstrict hyperbolicity in conservation law. In: Bona, J., Saxton, K., Saxton, R. (eds.) Contemporary Mathematics, vol. 255, pp. 125–137. AMS, Providence (2000) Google Scholar
- 6.LeVeque, R.J.: Finite Volume Method for Hyperbolic Problems. Cambridge University Press, Cambridge (2002) Google Scholar
- 8.Nose, T.: Time evolution of the structure function in the late stage of the phase separation process in polymer mixture. In: Tanaka, F., Doi, M., Ohta, T. (eds.) Springer Series in Chemical Physics, vol. 51, pp. 40–50. Springer, Berlin (1989) Google Scholar
- 13.Toro, E.F.: Shock-Capturing Methods for Free-Surface Shallow Water Flows. Wiley, New York (2001) Google Scholar
- 16.Yanenko, N.N., Shokin, Y.L.: On the group classification of the difference schemes for systems of equations of gas dynamics. In: Holt, M. (ed.) Lecture Notes in Physics, vol. 8, pp. 3–17. Springer, Berlin (1971) Google Scholar
- 17.Yanenko, N.N., Shokin, Y.L.: On group classification of difference schemes for the system of gas dynamics. Proc. Steklov Inst. Math. 122, 87–99 (1973) Google Scholar
- 18.Yanenko, N.N., Shokin, Y.L.: Schemes numerique invariants de groupe pour les equations de la dynamique de gas. In: Cabannes, H., Temam, R. (eds.) Lecture Notes in Physics, vol. 18, pp. 174–186. Springer, Berlin (1973) Google Scholar