Inertial impedance of coalescence during collision of liquid drops

The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industrial applications, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, which includes occurrence of hydrodynamic singularities, has required study of the problem at different scales – macroscopic, mesoscopic and molecular – using stochastic and deterministic methods. In this work, a multi-scale, deterministic method is adopted to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier–Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometres. This free boundary problem is solved by a Galerkin finite element-based algorithm. The interplay of inertial, viscous, capillary and van der Waals forces on the coalescence dynamics is investigated. It is shown that, in certain situations, because of inertia two drops that are driven together can first bounce before ultimately coalescing. This bounce delays coalescence and can result in the computed value of the film drainage time departing significantly from that predicted from existing scaling theories

Plethora of transitions during breakup of liquid filaments.

Thinning and breakup of liquid filaments are central to dripping of leaky faucets, inkjet drop formation, and raindrop fragmentation. As the filament radius decreases, curvature and capillary pressure, both inversely proportional to radius, increase and fluid is expelled with increasing velocity from the neck. As the neck radius vanishes, the governing equations become singular and the filament breaks. In slightly viscous liquids, thinning initially occurs in an inertial regime where inertial and capillary forces balance. By contrast, in highly viscous liquids, initial thinning occurs in a viscous regime where viscous and capillary forces balance. As the filament thins, viscous forces in the former case and inertial forces in the latter become important, and theory shows that the filament approaches breakup in the final inertial-viscous regime where all three forces balance. However, previous simulations and experiments reveal that transition from an initial to the final regime either occurs at a value of filament radius well below that predicted by theory or is not observed. Here, we perform new simulations and experiments, and show that a thinning filament unexpectedly passes through a number of intermediate transient regimes, thereby delaying onset of the inertial-viscous regime. The new findings have practical implications regarding formation of undesirable satellite droplets and also raise the question as to whether similar dynamical transitions arise in other free-surface flows such as coalescence that also exhibit singularities.The authors thank Dr. Pankaj Doshi for several insightful discussions. This work was supported by the Basic Energy Sciences program of the US Department of Energy (DE-FG02-96ER14641), Procter & Gamble USA, the Chevron Corporation, the UK Engineering and Physical Sciences Research Council (Grant EP/H018913/1), the John Fell Oxford University Press Research Fund, and the Royal Society.This is the final published version. It first appeared via PNAS at http://dx.doi.org/10.1073/pnas.141854111

Dynamics of drop disintegration and coalescence with and without electric fields

Ranging from raindrops in thunderclouds, to electrosprays in mass spectrometry to printing and coating processes of 5 microns or thinner, the scenario of liquid drops subject to strong electric fields is more common than it is perceived to be. Such drops develop sharp conical tips from which thin jets emanate which subsequently disintegrate into a fine spray of charged droplets. Despite being one of the oldest and most celebrated problems in science, there exist conflicting theories and measurement on the size and charge of these small electrospray droplets. In this work, dynamics of uncharged liquid drops subjected to an electric field is simulated by solving the Navier-Stokes equations augmented with Maxwells equations using the Galerkin finite element method. Theory and simulations are used here to show that liquid conductivity can be tuned to obtain three distinct scaling regimes for the size and charge of droplets thus formed, a finding that has been missed by previous studies and that bridges the gap between experiments and theory. It is further shown that these charged droplets are Coulombically stable, i.e., they do not explode into finer droplets, irrespective of the size and physical properties of the parent drop, making it the most fundamental law of semi-conducting liquids. Emulsion systems are common to a various industries ranging from food to pharmaceuticals to oil and gas to chemicals to cosmetics with some needing to be stabilized and others be broken. At the heart of emulsions lie liquid drops dispersed in a second liquid. Interactions and coalescence events of these individual drops is, not surprisingly, central to understanding the macro properties and behavior of emulsions. If and when these dispersed liquid drops interact and coalesce, they undergo a topological change involving finite time singularities. One of the important indicators for emulsion stability (or its instability) is the time it takes for two drops to drive away the second liquid in between and subsequently coalesce - used to estimate shelf life of bottled products, e.g., mayonnaise, or residence time of coalescer units for water-oil separations. Simulations are used here to calculate this coalescence time and, more generally, elucidate the approach and pre-contact dynamics of drops identifying conditions conducive for coalescence in terms of flow and fluid properties