Behavior of Gas Entrainment Inside Viscous Pool Due to Combined Influence of Symmetric Rotational Field and Freestream Flow of Air

The present investigation elucidates the interfacial characterization caused by the simultaneous effect of a symmetric converging rotational field and continuous air stream flow above the free surface. The converging rotational field is developed by a couple of counter and equal rotating rollers fully immersed inside the viscous liquid medium and their centers are aligned along a horizontal line. Such phenomenon is abundantly encountered in various engineering devices, where the interactions and transfer of mass, momentum, and energy are quite important through gas–liquid interfaces. Behavior of entrainment profile is observed due to the influence of various relevant pertinent parameters, namely, rotational of speed (measured by Ca), submersion depth (b*), the gap between the rollers (2a*), and strength of air stream flow (measured by Re_flow). An upper rounded structured interfacial configuration is obtained for all cases of Ca when the rollers are located very close to each other. The length of the entrainment of cusp decreases with the rise of Re_flow for the same value of Ca. The value of $Cac$ increases continuously with the increase of $Reflow$ for a particular of 2a* and b*. Bubble ejection from filament tip and subsequent accumulation increases significantly with the rise of Ca for a particular case of Re_flow. The cusp tip progressively traverses in upward direction with the continuous increase of gravitational pull for a particular value of Ca and $Reflow$⁠. Entrainment length progressively grows with the continuous rise of viscous drag for a particular value of Ca and $Reflow$⁠. Finally, an analytical formulation is proposed to analyze the structure of entrainment and this model reports an excellent match with the numerical findings.