[hal-00627948, v1] Weak solutions to a thin film model with capillary effects and insoluble surfactant

Weak solutions to a thin film model with capillary effects and insoluble surfactant

Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant

It is a widely used approach in the study of the dynamical behavior of viscous thin films to approximate the full fluid mechanical system by simpler model equations, using e.g. lubrication theory and cross-sectional averaging. In most of such models surface tension effects may then become significant, or even dominant. Therefore, also the influence of surfactant, i.e. surface active agents on t...

Evaporation of Sessile Droplets Laden with Particles and Insoluble Surfactants.

We consider the flow dynamics of a thin evaporating droplet in the presence of an insoluble surfactant and noninteracting particles in the bulk. On the basis of lubrication theory, we derive a set of evolution equations for the film height, the interfacial surfactant, and bulk particle concentrations, taking into account the dependence of liquid viscosity on the local particle concentration. An...

Thin Films and Fingering Problems in Complex Flows

We consider two problems in complex fluids: (i) thickening of thin films in the Landau-Levich problem [1] of dip coating and in motion of long bubbles in capillary tubes [2]. In both of these problems, thickening of thin films is observed experimentally in the presence of interfacial surfactants which has been confirmed experimentally. Considering small concentration of insoluble surfactants at...

[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 ...