English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
Add to Basket
  Local TagsRelease HistoryDetailsSummary

Released
Journal Article

Capillary-driven flow induced by a stepped perturbation atop a viscous film

MPS-Authors
/persons/resource/persons187626

Bäumchen,  Oliver
Group Dynamics of fluid and biological interfaces, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Salez, T., McGraw, J. D., Bäumchen, O., Dalnoki-Veress, K., & Raphael, E. (2012). Capillary-driven flow induced by a stepped perturbation atop a viscous film. Physics of Fluids, 24(10): 102111. doi:10.1063/1.4763569.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-7693-9
Abstract
Thin viscous liquid films driven by capillarity arewell described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a particular initial profile: a stepped perturbation. This initial condition allows a linearization of the problem making it amenable to Fourier analysis. The solution is obtained and characterized. As for a temperature step in the heat equation, self-similarity of the first kind of the full evolution is demonstrated and a long-term expression for the excess free energy is derived. In addition, hydrodynamical fields are described. The solution is then compared to experimental profiles from a model system: a polystyrene nanostep above the glass transition temperature which flows due to capillarity. The excellent agreement enables a precise measurement of the capillary velocity for this polymeric liquid, without involving any numerical simulation. More generally, as these results hold for any viscous system driven by capillarity, the present solution may provide a useful tool in hydrodynamics of thin viscous films.