Mathematical modeling and simulation of substrate-flow interaction using generalized gradient flows

• Applicant: Dr. Dirk Peschka
• Subject Area: Theoretical Condensed Matter Physics ; Mathematics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 422792530

The goal of the project "Mathematical modeling and simulation of substrate-flow interaction using generalized gradient flows" is the thermodynamically consistent description of dewetting phenomena by gradient structures and corresponding generalizations, so that numerical stability is guaranteed by implementing appropriate models. In particular, phenomena at moving contact lines with dynamic contact angles on corresponding complex substrates (adaptive, flexible, switchable) shall be understood in detail. For this purpose, phase-field models and sharp-interface models for viscoelastic substrates with finite strain and also phase separation in the vicinity of contact lines are now being considered in this follow-up proposal. As a prerequisite, in the first funding period, both abstract fundamental work on the structure of equations and discretization methods were developed [1,2], but also work on spinodal dewetting on fluid substrates [3], comparison with molecular dynamics [4], hierarchies of models with dynamic contact angles [5], and numerical methods for phase-field models were implemented [6].Based on this, the work in this project divides into three parts:WP1 "Wetting hydrodynamics on flexible substrates with sharp interfaces and contact angles" : Based on the work in [1,2,4], models and discretization methods for moving contact lines with sharp interfaces and contact lines are investigated, where domains and grids are aligned to the interfaces, thus ensuring high control over the accuracy of the numerical methods.WP2 "Extension of long-wave approximation with sharp-interfaces to flexible substrates": Based on abstract model reduction approaches from [2], the project explores different ideas for model reduction to thin-films on viscoelastic substrates. Similar to the Galerkin ROM methods, a systematic and extensible reduction of the full continuum equations is anticipated here, also aiming at the possibility of sharp contact lines and their dynamics.WP3 "Phase separation and cloaking at solid/fluid interfaces and contact lines": In order to investigate effects such as dynamics of phase separation and cloaking in the vicinity of contact lines, the equations from [6] coupled to elasticity are systematically extended to effective interfacial thermodynamics and compared with corresponding experiments.Results are compared with experiments and other theoretical approaches in SPP.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2171: Dynamic wetting of flexible, adaptive and switchable surfaces