Thermodynamically consistent evolution equations in gradient dynamics form for layers of complex fluids

Thiele, Uwe

Loughborough University, Department of Mathematical Sciences, Loughborough, UK

After reviewing a number of recent experiments 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, 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 [1]. Then 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 re-formulation within the framework of nonequilibrium thermodynamics, we extend the basic hydrodynamic models to account for (i) surfactant- or solute-dependent wettability, and (ii) surfactant or solute phase transitions [2,3]. Other possibilities are mentioned and examples are sketched for (i) and (ii). [1] L. Frastia, A. J. Archer, U. Thiele, Phys. Rev. Lett. 106, 077801 (2011); Soft Matter 8, 11363-11386 (2012). [2] U. Thiele, Eur. Phys. J. Special Topics, 197, 213-220 (2011). [3] U. Thiele, A. J. Archer and M. Plapp, Phys. Fluids 24, 102107 (2012).

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