Finite-time singularities in the dynamical evolution of contact lines
Analysis of PDEs
2013-02-07 v1 Fluid Dynamics
Abstract
We study finite-time singularities in the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact angle. Using apriori energy estimates, we derive conditions on variable speed that guarantee that a sufficiently smooth solution of the linear advection--diffusion equation blows up in a finite time. Using the class of self-similar solutions to the linear advection-diffusion equation, we find the blow-up rate of singularity formation. This blow-up rate does not agree with previous numerical simulations of the model problem.
Keywords
Cite
@article{arxiv.1302.1218,
title = {Finite-time singularities in the dynamical evolution of contact lines},
author = {D. E. Pelinovsky and A. R. Giniyatullin},
journal= {arXiv preprint arXiv:1302.1218},
year = {2013}
}
Comments
9 pages, 2 figures