Breakup of a liquid rivulet falling over an inclined plate: Identification of a critical Weber number

Abstract

We have numerically investigated the breakup of a rivulet falling over a smooth inclined plate using the volume of fluid method. Rivulet breakup is a complex phenomenon dictated by many factors, such as physical properties (viscosity and surface tension), contact angle, inertia, and plate inclination. An extensive simulation was conducted wherein these factors were systematically investigated. Regimes for a stable rivulet and an unstable rivulet that leads to breakup are examined in terms of a critical value of the Weber number (Wecr) that delineates these regimes. A higher Wecr implies that a higher flow rate is required to maintain a stable rivulet. The impact of liquid properties is characterized by the Kapitza number (Ka). Variation of Wecr with Ka shows two trends depending on the Ka value of the liquid. Liquids with lower Ka values, corresponding to high viscosities and/or low surface tensions, show linear variation and smaller value of the critical Weber number. In other words, the lower the liquid Ka value, the more stable the rivulet will tend to be with changes in liquid inertia. A liquid having higher Ka value exhibits larger value of Wecr and quadratic variation of Wecr with Ka. This behavior is more pronounced with increasing contact angle (γ). Higher contact angles promote rivulet breakup so that inertia must be higher to suppress breakup, consequently Wecr increases with increasing γ. The effect of plate inclination on breakup shows that Wecr decreases with increased inclination angle (θ) owing to higher effective liquid inertia. However, the effect is negligible beyond θ> 60°. The effect of the inlet size reveals that Wecr decreases with inlet cross-sectional area, but the corresponding solvent flow rate for rivulet breakup remains unchanged. A phenomenological scaling for the critical Weber number with the Kapitza number and contact angle is presented, which may offer insight into rivulet breakup.