Workshop

A pinned contact line

  • Jens Eggers (University of Bristol)
E1 05 (Leibniz-Saal)

Abstract

We consider the dynamics of a drop with a pinned contact line h(0,t)=0, as described by the thin film equation ht+(hnhxxx)x=0. Starting from an arbitrary initial condition at t=0, the profile relaxes toward an equilibrium parabolic profile. Our focus is on the early-time dynamics, which for n3 is described by a local similarity solution. As a result, the contact angle changes like a power law as a function of the time t. In the case n=3, which corresponds to a no slip boundary condition, the problem becomes non-local, and the change in contact angle is of the form eA/tα (with A complex). We consider the implications of this result for Huh and Scriven's contact line paradox for the case n=3. (joint work with Marco Fontelos)

Katja Heid

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Lorenzo Giacomelli

Sapienza Università di Roma

Hans Knüpfer

Ruprecht-Karls-Universität Heidelberg

Felix Otto

Max Planck Institute for Mathematics in the Sciences

Christian Seis

Universität Münster