The dynamics of fluid flow on (and off) inclined fibers

The commonplace phenomenon of liquid drops falling from a surface is—perhaps surprisingly—not yet fully understood by scientists. Understanding the complex interactions between the forces involved here would be helpful in industry, where structured packings in cooling towers must be designed to encourage droplet formation in fluid flow but coatings mixed to maintain a pristine, smooth surface.

Furthermore, the design of meshes used to harvest clean water from fog or dew, where this is limited, relies on an understanding of how the water condenses on the fibers and drops into collection tanks.

Atefeh Pour Karimi, a Ph.D. student at the Institute of Heat and Mass Transfer, Aachen University, Germany, and her supervisors and collaborators have analyzed the dynamics of this type of flow in detail and published their findings in The European Physical Journal Special Topics.

“Droplet formation in a flowing film is controlled by an interplay of gravity, surface tension, inertia and viscous forces,” explains Pour Karimi. “Mathematically, this behavior can be described as chaotic, with small variations in parameters leading to unpredictable behavior.” She and her co-workers studied the process using oil flowing down inclined fibers under the influence of gravity, and varying the film thickness and angle of inclination.

The oil flows down the fibers as a flat film before collecting into beads or droplets. These will either remain stable on the fibers, collide and coalesce or simply grow until they are large enough to detach and drop off.

Pour Karimi and her colleagues defined a new angle ratio, Φ, to characterize the droplet shape and used this to predict accurately how each would behave.

“We suggest that the value of Φ, and therefore the behavior of each droplet, is determined by the dominant force influencing its formation,” she adds. “We now hope to confirm this speculation by using mathematical models derived from theory.”