The breakup of liquid grids towards a regular pattern of drops

A. G. GONZÁLEZ

Banff

Workshop; Modelling of Thin Liquid Films-Asymptotic Approach vs. Gradient Dynamics; 2019

Banff International Research Station for Mathematical Innovation and Discovery

The rupture of a thin film leads to a drop pattern that is somewhat coarser than that predicted by linear theory. The unstable evolution of a film implies the formation of a mesh of connected bridges as a consequence of the growth of the initial holes in it. This late stage of hole expansion is an important intermediate stage in the further evolution of the system to the final drop pattern. Simulations show that the mesh is broken into disconnected short filaments that evolve to drops. However, the analysis of this late stage requires some additional considerations not taken into account in the linear theory of thin films or infinite filaments. Therefore, a simple experiment consisting of a controlled regular grid of filaments is considered to give insight into the physics involved in this final stage. The experiments were performed both at millimetric (with PDMS oil) and nanometric (with liquid nickel) scales. After separation from the nodes each resulting short filament has a contraction in length and afterwards the bulges formed at their extremes break up leading to new drops. The iteration of this process leads to the final pattern. The retraction is modeled using a matching between Cox-Voinov and Blake models for the dewetting. On the other side, the breakup analysis considers a perturbed quasi equilibrium that leads to a Stokes flow at the necks. As a consequence, there are two characteristic distances from the breakup point to the unperturbed regions in the filament. They can be combined to determine whether or not there is coalescence of the retracting tips. The theory yields the number of drops as a function of the height and aspect ratio of the filaments. The observed data are compared with the predictions and show a good agreement.