Breaking the symmetry to suppress the Plateau–Rayleigh instability and optimize hydropower utilization

Droplet impact on solid surfaces is essential for natural and industrial processes. Particularly, controlling the instability after droplet impact, and avoiding the satellite drops generation, have aroused great interest for its significance in inkjet printing, pesticide spraying, and hydroelectric power collection. Herein, we found that breaking the symmetry of the droplet impact dynamics using patterned-wettability surfaces can suppress the Plateau–Rayleigh instability during the droplet rebounding and improve the energy collection efficiency. Systematic experimental investigation, together with mechanical modeling and numerical simulation, revealed that the asymmetric wettability patterns can regulate the internal liquid flow and reduce the vertical velocity gradient inside the droplet, thus suppressing the instability during droplet rebounding and eliminating the satellite drops. Accordingly, the droplet energy utilization was promoted, as demonstrated by the improved hydroelectric power generation efficiency by 36.5%. These findings deepen the understanding of the wettability-induced asymmetrical droplet dynamics during the liquid–solid interactions, and facilitate related applications such as hydroelectric power generation and materials transportation.

Breaking the symmetry: Suppressing Plateau-Rayleigh instability and optimizing hydropower utilization

Droplet impact on solid surfaces is essential for natural and industrial processes. Particularly, controlling the instability after droplet impact, and avoiding the satellite drops generation, have aroused great interest for its significance in inkjet printing, pesticide spraying, and hydroelectric power collection. Herein, we found that breaking the symmetry of the droplet impact dynamics using patterned-wettability surfaces can suppress the Plateau-Rayleigh instability during the droplet rebounding and improve the energy collection efficiency. Systematic experimental investigation, together with mechanical modeling and numerical simulation, revealed that the asymmetric wettability patterns can regulate the internal liquid flow and reduce the vertical velocity gradient inside the droplet, thus suppressing the instability during droplet rebounding and eliminating the satellite drops. Accordingly, the droplet energy utilization was promoted, as demonstrated by the improved hydroelectric power generation efficiency by 36.5%. These findings deepen the understanding of the wettability-induced asymmetrical droplet dynamics during the liquid-solid interactions, and facilitate related applications such as hydroelectric power generation and materials transportation.

Study on driving waveform design process for multi-nozzle piezoelectric printhead in material-jetting 3D printing

Purpose Material-jetting (MJ) three-dimensional (3D) printing processes are competitive due to their printing resolution and printing speed. Driving waveform design of piezoelectric printhead in MJ would affect droplet formation and performance, but there are very limited studies on it besides patents and know-hows by commercial manufacturers. Therefore, in this research, the waveform design process to efficiently attain suitable parameters for a multi-nozzle piezoelectric printhead was studied. Therefore, this research aims to study the waveform design process to efficiently attain suitable parameters for a multi-nozzle piezoelectric printhead. Design/methodology/approach Ricoh’s Gen4L printhead was adopted. A high-speed camera captured pictures of jetted droplets and droplet velocity was calculated. The waveforms included single-, double- and triple-pulse trapezoidal patterns. The effects of parameters were investigated and the suitable ones were determined based on the avoidance of satellite drops and preference of higher droplet velocity. Findings In a single-pulse waveform, an increase of fill time (Tf) decreased the droplet velocity. The maximum velocity happened at the same pulse width, the sum of fill time and hold time (Tf + Th). In double- and triple-pulse, a voltage difference (Vd) above zero in the holding stage was adopted except the last pulse to avoid satellite drops. Suitable parameters for the selected resin were obtained and the time-saving design process was established. Research limitations/implications Based on the effects of parameters and observed data trends, suggested procedures to determine suitable parameters were proposed with fewer experiments. Practical implications This study has verified the feasibility of suggested design procedures on another resin. The required number of trials was reduced significantly. Originality/value This research investigated the process of driving waveform design for the multi-nozzle piezoelectric printhead. The suggested procedures of finding suitable waveform parameters can reduce experimental trials and will be applicable to other MJ 3D printers when new materials are introduced.

Sprays from droplets impacting a mesh

In liquid spray applications, the sprays are often created by the formation and destabilization of a liquid sheet or jet. The disadvantage of such atomization processes is that the breakup is often highly irregular, causing a broad distribution of droplet sizes. As these sizes are controlled by the ligament corrugation and size, a monodisperse spray should consist of ligaments that are both smooth and of equal size. A straightforward way of creating smooth and equally sized ligaments is by droplet impact on a mesh. In this work we show that this approach does however not produce monodisperse droplets, but instead the droplet size distribution is very broad, with a large number of small satellite drops. We demonstrate that the fragmentation is controlled by a jet instability, where initial perturbations caused by the injection process result in long-wavelength disturbances that determine the final ligament breakup. During destabilization the crests of these disturbances are connected by thin ligaments which are the leading cause of the large number of small droplets. A secondary coalescence process, due to small relative velocities between droplets, partly masks this effect by reducing the amount of small droplets. Of the many parameters in this system, we describe the effect of varying the mesh size, mesh rigidity, impact velocity and wetting properties, keeping the liquid properties the same by focusing on water droplets only. We further perform lattice Boltzmann modelling of the impact process that reproduces key features seen in the experimental data.

Charged Satellite Drop Avoidance in Electrohydrodynamic Dripping

The quality of electrohydrodynamic jet (e-jet) printing is crucially influenced by the satellite drop formed when the primary drop detaches from the meniscus. If the satellite drop falls onto the substrate, the patterns on the substrate will be contaminated. The electric charge carried by the satellite drop leads to more complex satellite/meniscus interaction than that in traditional inkjet printing. Here, we numerically study the formation and flight behavior of the charged satellite drop. This paper discovered that the charge relaxation time (CRT) of the liquid determines the electric repulsion force between the satellite drop and meniscus. The satellite drop will merge with the meniscus at long CRT, and fail to merge and deteriorate the printing quality at short CRT. The simulations are adopted to discover the mechanism of generation and flight behavior of charged satellite drops. The results show that the critical CRT decreases with the dielectric constant of the liquid and the supplied flow rate. Namely, for small dielectric constant and fixed CRT, the satellite drop is less likely to merge with the meniscus, and for high flow rate, the satellite drop is prone to merge with the meniscus due to the delay of necking thread breakup. These results will help to choose appropriate parameters to avoid the satellite drop from falling onto the substrate.

Inertial settling of a sphere through an interface. Part 2. Sphere and tail dynamics

Selected situations in which a rigid sphere settles through a two-layer system obtained by superimposing two immiscible Newtonian fluids are studied using a combination of experiments and direct numerical simulations. By varying the viscosity of the two fluids and the sphere size and inertia, the flow conditions cover situations driven by capillary and viscous effects, in which case the sphere detaches slowly from the interface and may even rise for a period of time, as well as highly inertial cases where its motion is barely affected by the interface and essentially reacts to the change in the fluid viscosity and density. The evolutions of the sphere velocity, effective drag force and entrained volume of upper fluid are analysed. In most cases considered here, this entrained volume first takes the form of an axisymmetric tail which elongates as time proceeds until it pinches off at some point. We examine the post-pinch-off dynamics of this tail under various conditions. When the viscosity of the lower fluid is comparable or larger than that of the upper one, an end-pinching process initiated near the initial pinch-off position develops and propagates along the tail, gradually transforming it into a series of primary and satellite drops; the size of the former is correctly predicted by the linear stability theory. In contrast, when the lower fluid is much less viscous than the upper one, the tail recedes without pinching off again. During a certain stage of the process, the tip velocity keeps a constant value which is significantly underpredicted by the classical Taylor–Culick model. An improved theoretical prediction, shown to agree well with observations, is obtained by incorporating buoyancy effects resulting from the density difference between the two fluids. Spheres with large enough inertia settling in a low-viscosity lower fluid are found to exhibit specific tail dynamics prefiguring wake fragmentation. Indeed, an interfacial instability quickly develops near the top of the sphere, resulting in the formation of thin axisymmetric corollas surrounding the central part of the tail and propagating upwards. A simplified inviscid model considering the role of the boundary layer around the tail and including surface tension effects is found to predict correctly the characteristics of the observed instability which turns out to be governed by the Kelvin–Helmholtz mechanism.

Numerical Analysis of Liquid Breakup and Drop Generation in Low Velocity Jets

Biological sprays and aerodynamically assisted bio-jets are increasingly employed in treatment of living cells and organisms for applications in regenerative medicine, tissue repair, and advanced therapeutics. The liquid used in biological applications cover a wide range of viscosities and surface tensions. Determining conditions that achieve steady and uniform drop distribution for a range of properties of the liquid jet is critical in advancing biological applications. In this study, numerical simulations of jet breakup are carried out using a modified volume of fluid (VOF) approach to capture the interface. The interplay of viscosity and surface tension is studied by varying liquid properties. Simulations show that a high viscosity jet stretches and elongates before a liquid segment detaches. Based on the thickness of the liquid thread connecting the detaching drop to the main liquid stream, two fundamentally different modes of liquid pinch off have been predicted: thick-thin and thin-thick. In the thick-thin mode, the liquid jet has a growing drop at its edge. As this drop grows in size, the liquid stream stretches till the drop is pinched off the liquid stream. In the other mode in addition to the pinch off of drops from the jet, ligaments of liquid break off. The change in the breakup mode is primarily governed by the relative magnitude of the viscous force compared to surface tension with high viscous force leading to thin-thick liquid stretching and pinch off. Thick-thin stretching is seen to produce slow moving satellite drops that merge backwards with the oncoming drop, while thin-thick stretching is noticed to result in faster satellite drops that merge forwards. On the other hand when surface tension force dominates, non-merging satellite drops are formed that move with a speed close to the primary drops.

System Design and Process Optimization for the Inkjet Printing of PEDOT:Poly(styrenesulfonate)

A laboratory-scale inkjet printing system was designed for printing polymeric inks with the focus on PEDOT:PSS, a transparent, electrically conductive polymer. PEDOT:PSS inks with 0 and 1 wt. % Surfynol were tested rheologically in elongational and shear flows. A process model is presented and validated for the prediction of flow boundary after the ink exits the nozzle, including drop formation. Process optimization involved establishing a process window related to the voltage waveform, substrate temperature, speed and printed line-overlap, aiming at avoiding satellite drops, “coffee cup” rings, the Rayleigh instability, “stacked printed lines,” and discontinuities in the printed lines or films.

A non-linear model for the atomization of a swirling viscous liquid jet

The instability and consequent atomization of a swirling viscous liquid jet emanated into gaseous surroundings and subjected to periodical surface disturbances is modelled and investigated. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative forms. Numerical solutions of the governing equations along with appropriate initial and boundary conditions are obtained through a robust finite-difference scheme. The computations yield real-time evolution of the interfacial profile and subsequent breakup characteristics of the liquid jet. It is found that the jet disintegrates into main and satellite drops, under all the conditions considered in the present study. The swirl enhances the instability of the jet and causes radial stretching of the main drops, whereas the satellite drops exhibit axial elongation. Increasing viscosity hinders jet instability and leads to main and satellite drop deformations that are similar to those produced by the swirl. The sizes of both main and satellite drops are diminished at higher disturbance wave numbers. A greater swirl strength induces a higher dominant wave number, and hence a reduced size of resultant main and satellite drops. Larger satellite drops and smaller main drops are produced as viscous forces are increased. The present model could be used as a guide for designing swirl injectors.

Drop Formation in Non-Newtonian Jets at Low Reynolds Numbers

The objective of this study was to develop an experimentally verified computational model that accurately predicts evolution of shear-thinning liquid jets. A secondary objective was to investigate the formation of satellite drops and to determine conditions under which their diameter can be controlled. The model employs the Galerkin finite/element approach to solve the complete two-dimensional set of axisymmetric governing equations and the corresponding kinematic and dynamic boundary conditions at the free surface. The effect of shear-thinning behavior on breakup was studied in detail for the case of an infinitely long non-Newtonian jet. It was found that shear-thinning behavior may be useful in controlling satellite drop sizes. (We observe that increasing the shear-thinning behavior at Re∼5 leads to an initial increase in the satellite drop size, followed by a subsequent decrease.) Comparison of model predictions with experimental data is presented for the case of a shear-thinning non-Newtonian jet. The experimental liquid was pumped through a capillary and drop shapes obtained using a high speed camera. The experimentally obtained shapes were compared to those predicted by the model and found to be in good agreement.