Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms, and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of traveling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the traveling wave solution of the model.

Growing concern over the scarcity of freshwater motivates the development of compact and economic vapor capture methods for distributed thermal desalination or harvesting of water. We report a study of water vapor condensation on cold liquid beads traveling down a massive array of vertical cotton threads that act as pseudo-superhydrophilic surfaces. These liquid beads form through intrinsic flow instability and offer localized high-curvature surfaces that enhance vapor diffusion toward the liquid surface, a critical rate-limiting step. As the liquid flow rate increases, the bead spacing decreases, whereas the bead size and speed stay nearly constant. The resulting increase in the spatial bead density leads to mass transfer conductances and hence condensation rates per volume that are almost three times higher than the best reported values. Parallel and contiguous gas flow paths also result in a substantial reduction in gas pressure drop and hence electric fan power consumption.

Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with evaporative e↵ects. The governing lubrication model is a fourth-order nonlinear parabolic partial di↵erential equation with a non-conservative loss term due to evaporation. Several di↵erent types of finite-time singularities are observed due to balances between evaporation and surface tension or intermolecular forces. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.

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