Prof. Dr. Uwe Thiele
Dept. of Mathematics
University of Loughborough, UK

Title:

Thin film evolution equations for complex fluids - extensions based on a gradient dynamics formulation

Abstract:

After reviewing a number of recent experiments [1] on evaporating and dewetting thin films of suspensions and solutions, we propose a way to construct dynamical models for liquid films of suspensions and solutions, as well as for films covered by insoluble surfactants. First, however, we review film thickness evolution equations for single layers of fluid in their gradient dynamics form, mentioning in passing that such a form is valuable to detect problems in the derivation of thin film equations as in the case of nematic liquid crystals [2]. Subsequently the first example for coupled evolution equations is given using a two-layer film as example.

Then we briefly review the `classical' hydrodynamic form of the coupled evolution equations for the film height and (solute or surfactant) concentration that are well established for small concentrations; and mention recent results on line deposition from evaporating suspensions [3]. We re-formulate both basic hydrodynamic models as a gradient dynamics based on an underlying free energy functional that accounts for wettability and capillarity of the solvent. Based on this mere re-formulation in the framework of nonequilibrium thermodynamics, we propose extensions of the basic hydrodynamic models that may account for (i) surfactant- or solute-dependent wettability, and (ii) surfactant or solute phase transitions [4,5]. Other possibilities are mentioned and examples are sketched for (i) and (ii).

[1] for a small review see: U. Thiele et al., J. Phys.-Cond. Mat. 21, 264016 (2009).
[2] T.-S. Lin et al., submitted (2013).
[3] L. Frastia, A. J. Archer, U. Thiele, Phys. Rev. Lett. 106, 077801 (2011); Soft Matter 8, 11363-11386 (2012).
[4] U. Thiele, Eur. Phys. J. Special Topics, 197, 213-220 (2011).
[5] U. Thiele, A. J. Archer and M. Plapp, Phys. Fluids 24, 102107 (2012).