Drip, drip, drop

7th April 2015

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What happens when a drip drops? Novel experiments carried out by Wadham Fellow Alfonso Castrejón-Pita and his team, published in the leading journal PNAS show that there is more to a drip than previously thought.

Watch a drip

Dripping of a 150 cP drop recorded at 8,000 frames per second (Phantom camera). Nozzle diameter of 5.6 mm. Exposure time of 2.02 us. Field of view 1280 x 304 pix. Resolution = 22.22 um/pix.

Play Dripping of a 150 cP drop recorded @ 8,000 frames per second (Phantom camera). Nozzle diameter of 5.6 mm. Exposure time of 2.02 us. Field of view 1280 x 304 pix. Resolution = 22.22 um/pix

The publication, Plethora of transitions during breakup of liquid filaments, describes how drops are formed, down to the very last microseconds before breaking up from the main body of fluid from which they emerge – research essential to understanding the dripping of leaky taps, inkjet drop formation, and raindrop fragmentation.

Alfonso, Associate Professor, Fellow and Tutor in Engineering, explains the research: "When a drop is forming from a leaking tap, a liquid bridge joins the fluid of the would-be drop, and the main body of the fluid. Such a bridge, or liquid filament, will thin under the action of surface tension. This thinning is controlled by a balance between inertia, surface tension, and viscosity. However, the role these factors play in the dynamics depends on the length and time scales at which the filament is evolving. This has been the focus of study for over 300 years, and multiple theories exist that attempt to predict the different dynamical regimes the flow encounters as the bridge thins. Such theories often assume a set of ‘rules’ that the flow is expected to follow.”
 
The novel experiments, theory, and high resolution numerical simulation presented in this publication all demonstrate that there are, however, numerous intermediate regimes and that the violation of these set ‘rules’ is ubiquitous. As the bridge collapses the fluid accelerates, slows down, and undergoes a series of different states, unaccounted for in previous studies. Alfonso and his colleagues demonstrate that thinning filaments unexpectedly pass through a number of intermediate transient regimes, thereby delaying onset of the final regime.

“The findings raise the question of whether similar dynamical transitions arise in systems that are not necessarily hydrodynamic in nature,” added Alfonso.

Plethora of transitions during breakup of liquid filaments by José Rafael Castrejón-Pita, Alfonso Arturo Castrejón-Pita, Sumeet Suresh Thete, Krishnaraj Sambath, Ian M. Hutchings, John Hinch, John R. Lister, and Osman A. Basaran, appears in the March 30 edition of PNAS, doi: 10.1073/pnas.1418541112

Read an abstract from the publication

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.

  • Alfonso Castrejón-Pita

    Alfonso Castrejón-Pita

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