Journal of Scientific Computing

, Volume 43, Issue 3, pp 471–487 | Cite as

Two-Phase Shallow Water Equations and Phase Separation in Thin Immiscible Liquid Films



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.


Phase separation Shallow flows Invariant FDM 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsJosai UniversitySakadoJapan

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