Drop-off characteristics of film flow on inclined fibers

Abstract This paper presents an empirical analysis of a film flow dropping-off from an inclined fiber substrate, where the fiber diameter is on the order of the capillary length. The investigation aims to elucidate the dynamics of beads traveling down the inclined fibers. We explore the parameters influencing the bead’s final shape and their stability on the substrate (in terms of detaching or not detaching) in a flow driven by gravity and affected by surface tension and inertia. Three different growth modes and their connection to the two main existing drop-off mechanisms of beads on inclined fibers, namely drop-off due to unsaturated growth and drop-off due to coalescence events, are established and demonstrated. A new parameter, $$\Phi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Φ</mml:mi> </mml:math> , is introduced, which includes information about the shape of the beads and its connection to the flow conditions. If $$\Phi &gt;1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Φ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the bead exhibits a rather sinusoidal shape, indicating that its formation is predominantly influenced by surface tension. If $$\Phi &lt; 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Φ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the bead is subjected to front-steepening due to an inertia-dominated flow. If $$\Phi =1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Φ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the bead’s tail aligns with the direction of gravity, experiencing unsaturated growth until it drops off, which indicates a flow condition driven primarily by gravitational forces. Furthermore, this study offers a quantitative experimental basis for flow parameters on inclined fibers, including Nusselt film thickness, healing length within the unperturbed film and rate of growth of beads at the end of healing length, beads crest height, beads velocity, and parameter $$\Phi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Φ</mml:mi> </mml:math> for future comparison to theoretical and numerical modelling.