Efforts are made to delineate the dynamics of entrained gaseous cusps and flow of liquid films wrapped around a horizontal partially submerged rotating roller numerically. The solid roller is allowed to rotate across the gas–liquid interface with a fixed submergence ratio of 0.5 (equally immersed in both gaseous and liquid phases) and the gaseous phase is subjected to horizontal crossflow. The finite volume-based solver Gerris has been employed to track the interfacial configuration by using the volume of fluid (VOF) method. The combined influence of roller rotation (ω) and strength of crossflow (Reflow) on the wrapped film thickness and the structure of entrained cusp is demonstrated thoroughly for different gas–liquid pairs in order to understand the underlying physics. This study also includes the transient dynamics of liquid tip movement from the receding to advancing junction for various Reflow and gas–liquid pairs. Subsequently, the structure and rate of entrainment are also estimated, where the collapsible gaseous jet breaks into circular gaseous bubbles. Predictions are also made in order to establish the dependence of interfacial configuration on the Archimedes number (Ar). Finally, a theoretical model has been developed to elucidate both entrainment and wrapped film dynamics, which shows excellent agreement with the numerical results.

A thorough physical understanding of gas entrainment within a liquid pool is established using a pair of fully submerged cylinders with an opposite but symmetric rotational field. An asymmetric version of such entrainment of gaseous filaments inside a liquid has been demonstrated in our earlier work [P. Kumar, A. K. Das and S. K. Mitra, Phys. Fluids 29, 022101 (2017)]. Here, our efforts focus on revealing the governing factors and understanding the stages of alteration from a stratified to an undulating interface for a wide range of symmetric cylinder rotations. Interfacial configurations such as an upper rounded crest, a bubble-ejecting jet, and a non-collapsible jet with an air pocket in the stagnant zone are obtained as the cylinder rotation increases. Near the critical capillary number, air pinch-off into a filament and subsequent stable collapse of this filament into bubbles were observed. As the rotation-driven capillary number increased, we noted the formation of an entrained jet of gaseous-phase forming air pockets in the region, which resulted in a diverging rotational field. Our analysis of the fluid stream explains the interfacial configurations and corresponding entrainment patterns based on fundamental physics. The power-law fit (Y = KXm) of the cusp profiles revealed close agreement with numerically obtained interfaces. We propose correlation coefficients as a function of the capillary number. We also assess the dependence of the entrainment pattern on cylinder submergence and spacing.

Transformation from annular to droplet flow is investigated for co-current, upward gas-liquid flow through a cylindrical tube using grid based volume of fluid framework. Three transitional routes, namely, orificing, rolling, and undercutting are observed for flow transformation at different range of relative velocities between the fluids. Physics behind these three exclusive phenomena is described using circulation patterns of gaseous phase in the vicinity of a liquid film which subsequently sheds drop leading towards transition. Orifice amplitude is found to grow exponentially towards the core whereas it propagates in axial direction in a parabolic path. Efforts have been made to fit the sinusoidal profile of wave structure with the numerical interface contour at early stages of orificing. Domination of gas inertia over liquid flow has been studied in detail at the later stages to understand the asymmetric shape of orifice, leading towards lamella formation and droplet generation. Away from comparative velocities, circulations in the dominant phase dislodge the drop by forming either a ligament (rolling) or a bag (undercut) like protrusion in liquid. Study of velocity patterns in the plane of droplet dislodge reveals the underlying physics behind the disintegration and its dynamics at the later stages. Using numerical phase distributions, rejoining of dislodged droplet with liquid film as post-rolling consequences has been also proposed. A flow pattern map showing the transitional boundaries based on the physical mechanism is constructed for air-water combination.

Here we have proposed the increase of the entrainment rate by extruding an air filament under the action of convergent but asymmetric rotational field. By varying the source speed and the diameter of rotational fields, we showed the bending of an air filament towards the higher strength direction of the asymmetric inertia. Interfacial profiles like bubble ejection from the air filament and non-collapsible entrainment with air accumulation in a stagnant zone are obtained in finite volume based numerical simulations, on gradual increase of average rotational fields. Physical understanding of bent interface profile reveals the presence of multiple stages in filament growth depending upon the inertia of surrounding medium. Accumulation of air in the stagnant zone is found to be more prominent in case of rotational speed based asymmetry in contrast to its counterpart having diametric asymmetry of imposing sources. Relative comparison between these two methods of producing asymmetric field showed faster growth of filament upon varying the source diameter, while keeping the speed same. In case of extreme retardation and enhancement of rotational asymmetry, film pinch off and formation of bubble train have been reported. The shape of ejected bubbles is governed by the inertia of the surrounding medium, and bubbles have taken elliptical shapes with their major axis aligned parallel to the adjacent velocity field.

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