Influence of a Pair of Unequal Rotational Fluxes on Entrained Gaseous Filament

Efforts are made to elucidate a comprehensive analysis of entrainment dynamics triggered by a couple of unequal rotational fluxes within a viscous pool. Cylindrical rollers are employed to establish the rotational field. The top drum is equally submerged in both phases and also it provides a constant rotational inertia. Concomitantly, the bottom roller is completely submerged in the viscous bath, and it provides an unequal rotational strength in reference to top roller. The average rotational strength of both rollers is measured using average Capillary number $(Caavg)$⁠. The entrainment phenomenon is strongly influenced by both $Caavg$ and gap between the rollers $(W/D)$⁠. Characterization of entrained filament is elucidated by predicting the horizontal distance $(L*)$⁠, radial distance $(r*)$⁠, temporal vertical displacement $(Y*)$⁠, maximum vertical displacement $(Ymax*)$⁠, width $(H*)$⁠, and location of V-shaped diversion $(Øs*)$⁠. Characterization of liquid tip is performed by measuring the travel rate $(γ*)$ along periphery of drum from receding to advancing junction. Air mass ejection from filament tip is analyzed by estimating the first bubble ejection time $(t1st*)$⁠, volume of accumulated of ejected gaseous masses $(v*)$⁠, and ejection frequency $(f)$⁠. Furthermore, the effect of gravitational pull (specified by Archimedes number, $Ar$⁠) and viscous drag (measured by Morton number, $Mo$⁠) on the pattern of entrained air filament is described. Lastly, an analytical framework is established to determine the width of the V-junction by balancing the important influencing forces, which are strongly affecting the filament. Analytical observations show a satisfactory agreement with numerical findings.