Project Details
Projekt
Mathematical modeling, analysis, numerical simulation of thin films and droplets on rigid and visoelastic substrates, emphasizing the role of slippage
Applicant
Professorin Barbara Agnes Wagner, Ph.D.
Subject Area
Theoretical Condensed Matter Physics
Term
from 2006 to 2011
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 23855696
As fluid dynamical models are being considered on nano- and microscopic scales, an old and sometimes controversial topic has been taken up again, which is the validity of the no-slip condition. This is a central theme of this proposal.In order to capture the effects of slippage on the larger-scale, long-time dynamics of liquids near a solid interface, efficient continuum descriptions are needed. Progress depends strongly on the ability to achieve model reductions by using asymptotic techniques that address the presence of highly separated sales. Our recently developed models for nanoscopically thin dewetting films on hydrophobized substrates correctly predict experimentally observed morphological changes that depend on effects of slippage. We will explore their range of validity and make quantitative comparisons with experiments, also where intertial effects play a role.A major portion of the proposed research will be concerned with the largely unexplored effect of slippage and a soft, viscoelastic substrate on the liquid motion. A model for the dynamics of the liquid on a soft layer will be developed and used to investigate the q liquid droplet or a thin film moving on substrates such as silicon-rubber as well as substrates grafted with a soft layer of polymer brushes. A boundary integral method will be implemented to numerically capture the 2D dynamics and lubrication-type equations will be derived from the general 3D problem. The results will be compared to experimental investigations as part of ¿lab-on-a-chip¿ designs, and used to extrapolate results from Molecular Dynamics simulations for liquid droplets on brush layers, thereby making the connection to microscopic theory.
DFG Programme
Priority Programmes
