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.rop formation is ubiquitous in daily life, industry, and nature (1-3). The phenomenon is central to inkjet printing (4, 5), dripping from leaky faucets (6, 7), measurement of equilibrium and dynamic surface tension (8, 9), DNA arraying and printing of cells (10, 11), chemical separations and analysis (12, 13), production of particles and capsules (14, 15), printing of wires and transistors (16,17), and mist formation in waterfalls and fragmentation of raindrops (18,19). Fig. 1A shows an experimental setup for studying the dynamics of a drop of an incompressible Newtonian fluid of density ρ, viscosity μ, and surface tension σ forming from a tube of radius R (Fig. 1B and Drop Formation from a Tube and Filament Thinning). A salient feature of, and key to understanding, drop formation is the occurrence of a thin filament that connects an about-to-form primary drop to the rest of the fluid that is attached to the tube ( Fig. 1 B and C). Thus, it often proves convenient to study filament thinning in the idealized setup depicted in Fig. 1D (Drop Formation from a Tube and Filament Thinning). As time t advances and the filament radius decreases, curvature and capillary pressure, both of which are at leading order inversely proportional to radius, increase and fluid is expelled with increasing velocity from the neck. At the instant t = t b when the neck radius vanishes, a finite time singularity occurs and the filament breaks. When the filament breaks, one or more satellite droplets may also...

Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity, and air pressure. By imaging ethanol drops impacting silicone gels of different stiffnesses, we show that substrate stiffness also affects the splashing threshold. Splashing is reduced or even eliminated: droplets on the softest substrates need over 70% more kinetic energy to splash than they do on rigid substrates. We show that this is due to energy losses caused by deformations of soft substrates during the first few microseconds of impact. We find that solids with Young's moduli ≲100  kPa reduce splashing, in agreement with simple scaling arguments. Thus, materials like soft gels and elastomers can be used as simple coatings for effective splash prevention. Soft substrates also serve as a useful system for testing splash-formation theories and sheet-ejection mechanisms, as they allow the characteristics of ejection sheets to be controlled independently of the bulk impact dynamics of droplets.

Whether a thin filament of liquid separates into two or more droplets or eventually condenses lengthwise to form a single larger drop depends on the liquid's density, viscosity, and surface tension and on the initial dimensions of the filament. Surface tension drives two competing processes, pinching-off and shortening, and the relative time scales of these, controlled by the balance between capillary and viscous forces, determine the final outcome. Here we provide experimental evidence for the conditions under which a liquid filament will break up into drops, in terms of a wide range of two dimensionless quantities: the aspect ratio of the filament and the Ohnesorge number. Filaments which do not break up into multiple droplets demand a high liquid viscosity or a small aspect ratio.

Inkjet printing relies on the formation of small liquid droplets to deliver precise amounts of material to a substrate under digital control. Inkjet technology is becoming relatively mature and is of great industrial interest thanks to its flexibility for graphical printing and its potential use in less conventional applications such as additive manufacturing and the production of printed electronics and other functional devices. Its advantages over traditional methods of printing include the following: it produces little or no waste, it is versatile because several different methods exist, it is non-contact and does not require a master template so that printed patterns can be readily modified on demand. However, the technology is in need of further development to become mainstream in emerging applications such as additive manufacturing (3D printing). This review contains a description of conventional and less common inkjet methods and surveys the current applications of inkjet in industry. This is followed by specific examples of the barriers, limitations and challenges faced by inkjet in both graphical printing and manufacturing.

Effective integration of molecular self‐assembly and additive manufacturing would provide a technological leap in bioprinting. This article reports on a biofabrication system based on the hydrodynamically guided co‐assembly of peptide amphiphiles (PAs) with naturally occurring biomolecules and proteins to generate hierarchical constructs with tuneable molecular composition and structural control. The system takes advantage of droplet‐on‐demand inkjet printing to exploit interfacial fluid forces and guide molecular self‐assembly into aligned or disordered nanofibers, hydrogel structures of different geometries and sizes, surface topographies, and higher‐ordered constructs bound by molecular diffusion. PAs are designed to co‐assemble during printing in cell diluent conditions with a range of extracellular matrix (ECM) proteins and biomolecules including fibronectin, collagen, keratin, elastin‐like proteins, and hyaluronic acid. Using combinations of these molecules, NIH‐3T3 and adipose derived stem cells are bioprinted within complex structures while exhibiting high cell viability (>88%). By integrating self‐assembly with 3D‐bioprinting, the study introduces a novel biofabrication platform capable of encapsulating and spatially distributing multiple cell types within tuneable pericellular environments. In this way, the work demonstrates the potential of the approach to generate complex bioactive scaffolds for applications such as tissue engineering, in vitro models, and drug screening.

In this Letter, we study the splashing behavior of droplets upon impact onto a variety of substrates with different wetting properties, ranging from hydrophilic to superhydrophobic surfaces. In particular, we study the effects of the dynamic contact angle on splashing. The experimental approach uses high-speed imaging and image analysis to recover the apparent contact angle as a function of the spreading speed. Our results show that neither the Capillary number nor the so-called splashing parameter are appropriate to characterize the splashing behavior under these circumstances. However, we show that the maximum dynamic advancing contact angle and the splashing ratio β adequately characterize the splashing behavior.

An experimental study of the dynamic response of a Newtonian fluid and a Maxwellian fluid under an oscillating pressure gradient is presented. Laser Doppler anemometry is used in order to determine the velocity of the fluid inside a cylindrical tube. In the case of the Newtonian fluid, the dissipative nature is observed. In the dynamic response of the Maxwellian fluid an enhancement at the frequencies predicted by theory is observed.

Drop penetration in textiles is determined by the pore size and the liquid properties.