Droplets spreading under contact line friction: scaling laws and existence result

Date

May 15, 2014

Time

2:00 PM - 3:00 PM

Speaker

Dr. Maria Chiricotto

Affiliation

TU Dresden, Institut für Analysis

Series

TUD Mathematik AG Analysis & Stochastik

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. Peter Hornung

Description

This talk is concerned with the spreading of a liquid droplet on a plane solid surface in the regime of lubrication approximation. The focus is on effective conditions which relate the speed of the contact line (where liquid, solid and vapor meet) to the microscopic contact angle. One such condition has been recently proposed by Weiqing Ren and Weinan E [Phys. Fluids 19(2007)]: it includes into the model the effect of frictional forces which arise at the contact line from unbalanced components of the Young's stress, leading to an additional dissipation term in the energy balance. In lubrication approximation, the spreading of thin droplets may be modeled by a class of free boundary problems for fourth order nonlinear degenerate parabolic equations. We provide the analysis of the well-posedness, regularity, and qualitative properties of weak solutions. For speed-dependent contact angle conditions of rather general form, a matched asymptotic study is worked out, relating the macroscopic contact angle to the speed of the contact line. Here, well-posedness for a class of traveling-wave solutions is proved and used. The results have been obtained jointly with Lorenzo Giacomelli (La Sapienza - University of Rome).

Links

• Webseite der AG Analysis & Stochastik

Last modified: Apr 28, 2014, 6:26:06 PM