Water drops falling on a deep pool can either coalesce to form a vortex ring or splash, depending on the impact conditions. The transition between coalescence and splashing proceeds via a number of intermediate steps, such as thick and thin jet formation and gas-bubble entrapment. We perform simulations to determine the conditions under which bubble entrapment and jet formation occur. A regime map is established for Weber numbers ranging from 50 to 300 and Froude numbers from 25 to 600. Vortex ring formation is seen for all of the regimes; it is greater for the coalescence regime and less in the case of the thin jet regime.

Laminar-to-turbulent transition of pipe flows occurs, for sufficiently high Reynolds numbers, in the form of slugs. These are initiated by disturbances in the entrance region of a pipe flow, and grow in length in the axial direction as they move downstream. Sequences of slugs merge at some distance from the pipe inlet to finally form the state of fully developed turbulent pipe flow. This formation process is generally known, but the randomness in time of naturally occurring slug formation does not permit detailed study of slug flows. For this reason, a special test facility was developed and built for detailed investigation of deterministically generated slugs in pipe flows. It is also employed to generate the puff flows at lower Reynolds numbers. The results reveal a high degree of reproducibility with which the triggering device is able to produce puffs. With increasing Reynolds number, ‘puff splitting’ is observed and the split puffs develop into slugs. Thereafter, the laminar-to-turbulent transition occurs in the same way as found for slug flows. The ring-type obstacle height, h, required to trigger fully developed laminar flows to form first slugs or puffs is determined to show its dependence on the Reynolds number, Re = DU/ν (where D is the pipe diameter, U is the mean velocity in the axial direction and ν is the kinematic viscosity of the fluid). When correctly normalized, h⁺ turns out to be independent of Re_τ (where h⁺ = hU_τ/ν, Re_τ = DU_τ/ν and $U_{\tau}\,{=}\,\sqrt{\tau_{w}/ \rho}$ ; τ_w is the wall shear stress and ρ is the density of the fluid).

When a droplet of liquid 1 falls through liquid 2 to eventually hit the liquid 2–liquid 1 interface, its initial impact on the interface can produce daughter droplets of liquid 1. In some cases, a partial coalescence cascade governed by self-similar capillary-inertial dynamics is observed, where the fall of the secondary droplets in turn continues to produce further daughter droplets. Results show that inertia and interfacial surface tension forces largely govern the process of partial coalescence. The partial coalescence is suppressed by the viscous force when Ohnesorge number is below a critical value and also by gravity force when Bond number exceeds a critical value. Generation of secondary drop is observed for systems of lower Ohnesorge number for liquid 1, lower and intermediate Ohnesorge number for liquid 2 and for low and intermediate values of Bond number. Whenever the horizontal momentum in the liquid column is more than the vertical momentum, secondary drop is formed. A transition regime from partial to complete coalescence is obtained when the neck radius oscillates twice. In this regime, the main body of the column can be fitted to power-law scaling model within a specific time range. We investigated the conditions and the outcome of these coalescence events based on numerical simulations using a coupled level set and volume of fluid method (CLSVOF).

In this study, coalescence dynamics of two unequal sized drops of the same liquid have been investigated using the coupled level set and volume of fluid method. A broad range of fluid properties is considered with two orders of magnitude variation of Ohnesorge numbers and Atwood number ranging between 0.01 and 0.9976. The pinch-off process and controlling parameters that lead to satellite generation have been investigated. The capillary waves are generated as a result of the sharp curvature produced near the contact region. Here we demonstrate that the capillary waves propagating along the interface of the lower drop can affect the eventual pinch-off of the satellite. The local curvature of the neck plays a crucial role in the pinch-off process. A sharper axial curvature of the neck increases the local capillary pressure which restricts the pinch-off. The critical diameter ratio above which a satellite pinches off during the coalescence of two free-falling drops increases with increasing relative strength of the viscous force and the gravity force. The critical ratio can be as low as 1.2 at a lower relative strength of the viscous and the gravity forces. The coalescence of two unequal sized drops may produce much smaller satellite drops, on account of coalescence in successive steps, with or without intermediate detachment.

The present study focuses on the identification of the large bubble entrapment regime on the V-D map and on the We-Fr map together with the detailed analysis of the mechanism of large bubble entrapment. The sequential large and small bubble entrapment previously found by Wang, Kuan, and Tsai [“Do we understand the bubble formation by a single drop impacting upon liquid surface?,” Phys. Fluids 25, 101702 (2013)] has been observed in this investigation. Large bubble entrapment is observed only for prolate-shaped drops. Prolate shaped drops bring about deeper penetration of the vortex ring into the pool. The emergence of an ejecta sheet that leads to lamella prevents the penetration of the vortex ring and thus prevents the large bubble entrapment. The entrapment of a large bubble is always accompanied by an inward jet and an upward jet. The inward jet penetrates through the bubble and deforms the bubble shape. A thorough parametric study has been conducted numerically and experimentally on the crater dynamics and its dependence on the initial condition of the drop at the instance of impact.