Droplets engulfing on a filament

Two immiscible droplets wetting on a filament may assume engulfing, partial-engulfing, or non-engulfing morphology that depends on the wetting behavior and geometries of the resulting droplet-on-filament system. This paper studies the wetting behavior of two immiscible droplets contacting and sitting symmetrically on a straight filament. A set of ordinary differential equations (ODEs) is formulated for determining the wetting morphology of the droplet-on-filament system. In the limiting case of engulfing or non-engulfing, the morphology of the droplet-on-filament system is determined in explicit form. In the case of partial-engulfing, surface finite element method is further employed for determining the wetting morphology, surface energy, and internal pressures of droplets of the system. Numerical scaling study is performed to explore their dependencies upon the wetting properties and geometries of the system. The study can be applicable for analysis and design of textiles with tailorable wetting properties and development of novel multifunctional fibrous materials for environmental protection such as oil-spill sorption, etc.