Micro-patterning of coatings on a fiber surface exploiting the contact instabilities of thin viscoelastic films

Abstract

Contact instabilities of a thin viscoelastic film on a curved surface have been explored with the help of linear and nonlinear analyses. The governing equations and boundary conditions for a thin deforming zero-frequency linear viscoelastic solid film are linearized to predict the time and length scales. A long-wave analysis corroborates the accuracy of the eigenvalues obtained from the general analysis. While the adhesive interaction between the film surface and contactor stimulates contact instability by subduing the restoring elastic and surface tension forces, the forces due to radial curvature instigate the capillary instability. Importantly, unlike the unconditionally unstable viscous films, this instability manifests beyond a critical destabilizing force due to the elastic stiffness of viscoelastic film. The destabilizing intermolecular and radial curvature forces are tuned by controlling the film-contactor gap and radius of fiber to engender the formation of drops, columns, or mixed morphologies. The nonlinear simulations demonstrate the conditions to decorate columns, droplets, and hybrid morphologies on the fiber surface. For example, when the contactor-film gap is higher and the radius of the fiber and the film thickness are lower, the dominant force due to radial curvature can break the film into droplets, whereas a smaller contactor-film separation distance on a fiber of large radius instigates contact instability to develop columnar structures. Otherwise, the formation of a mixed morphology composed of droplets and columns is expected. Furthermore, surface patterns having length scales of few micrometers to hundreds of nanometers can be obtained by tuning film-contactor gap, fiber-radius, and stabilizing-destabilizing forces.