Advances in Phase Field Modeling of Multiphase Flow

Dear Colleagues,

The aim of this Special Issue is to review the theory and describe some relevant applications of the phase field, actually known as the interface diffuse, model for one-component, two-phase fluids and for liquid binary mixtures to model multiphase flows in confined geometries.

In classical models, multiphase flows are described, assuming that the different phases are separated by a sharp interface, with appropriate boundary conditions. Imposing that the condition of local equilibrium is satisfied, physical properties such as density and composition are allowed to change discontinuously across the interface, and, in fact, one of the main difficulties of this approach consists of solving the free boundary problem and determining the position of the interface in time. Clearly, interface tracking breaks down whenever the real interface thickness is comparable with the length scale of the phenomenon that is being studied as it happens, naturally, in micro-devices. This problem arises elsewhere as well, such as in modeling drop coalescence and break up and in describing the wetting and de-wetting of solid surfaces. In these cases, it is more reasonable to use a different approach, as was proposed at the end of the 19th century by Van der Waals, where interfaces have a non-zero thickness, i.e., they are diffuse, so that all quantities can vary continuously. In particular, additional stresses, the so called Korteweg stresses, arise naturally as reversible body forces that tend to minimize the free energy of the system, acting exclusively in the interface region. The diffuse interface approach can also be extended to cases in which the phase field cannot be identified (as in the diffuse interface approach) with a physical quantity (coarse-grained on a mesoscopic scale), and instead can only be interpreted as a smoothed indicator function.

In this Special Issue, the foundations of the phase field approach are analyzed, together with relevant examples of applications, showing the ability of this method to model a wide variety of multiphase problems.

Prof. Dr. Roberto Mauri
Guest Editor

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