A morphological model for complex fluids

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Abstract
A new model is proposed for the study of porous media and complex fluids using morphological measures to describe homogeneous spatial domains of the constituents. Under rather natural assumptions a general expression for the Hamiltonian can be given extending the model of Widom and Rowlinson for penetrable spheres. The Hamiltonian includes energy contributions related to the volume, surface area, mean curvature, and the Euler characteristic of the configuration generated by overlapping sets of arbitrary shapes. Phase diagrams of the model are calculated and discussed. In particular, we find that the Euler characteristic in the Hamiltonian stabilizes a highly connected bicontinuous structure, resembling the middle phase in oil - water microemulsions.

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