Dynamics of fixed-volume pinned films – dealing with a non-self-adjoint thin-film problem

The use of thin liquid films has expanded beyond lubrication and coatings, into applications in actuators adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite or periodic films, these are characterized a finite amount an impermeable domain. global mass conservation constraint, together with common boundary conditions (e.g. pinning), create quantitatively qualitatively different than those films. Mathematically, this manifests itself as non-self-adjoint problem. This work presents combined theoretical experimental study for We provide time-dependent closed-form analytical solution the linearized system that arises from conditions. highlight that, self-adjoint problems, here, special care should given deriving adjoint problem reconstruct based on eigenfunctions properly. compare solutions obtained permeable conditions, representing models thin-film problems. show while initial is nearly identical, eventually affect film deformation well its response time. To experimentally illustrate validate model, we fabricated set-up subjects prescribed normal force distribution through dielectrophoresis, used high-frame-rate digital holography measure real experiments agree model confirm confined exhibit behaviour which could not predicted existing models.