A thin film approximation of the Muskat problem with gravity and capillary forces

A gradient flow approach to a thin film approximation of the Muskat problem

[hal-00636647, v1] A gradient flow approach to a thin film approximation of the Muskat problem

Abstract. A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two ...

Invasion Percolation in Presence of Gravity

Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displaceme...

Capillary buckling of a thin film adhering to a sphere

We present a combined theoretical and experimental study of the buckling of a thin film wrapped around a sphere under the action of capillary forces. A rigid sphere is coated with a wetting liquid, and then wrapped by a thin film into an initially cylindrical shape. The equilibrium of this cylindrical shape is governed by the competing effects of elasticity and capillarity: elasticity tends to ...

Investigation of extinction spectra of THTS Mn thin films and comparsion with discrete dipole approximation simulation results

In this work, the extinction spectra of the nano-structure of the Tilt Helical and Stair-like Towers of Mn thin films were obtained using discrete dipole approximation (DDA) simulation for both s-and p-polarization at two incident light angles of 10°, and 60° at different azimuthal angles for the there samples with different tilt. Obtained results are compared with the experimental optical exti...