Filament Breakup Research Articles

Inkjet printing of ceramic colloidal suspensions: Filament growth and breakup

Filament growth and breakup are investigated in the context of ceramic inkjet printing. Several inks were formulated and ejected on a printer dedicated to ceramic materials. They consisted of six colloidal inks, four simple fluids and two graphic inks. For each, stroboscopic snapshots were acquired and the filament shape was extracted and analysed, for different nozzle actuation pulses. The filament length and the thread minimum radius were measured during the ejection process. A scaling of the breakup time with the Rayleigh number was obtained, as well as a general behaviour for the filament growth rate during the ejection process.

TR-PIV measurements and POD analysis of the plane wall jet subjected to lateral perturbation

An experimental investigation has been carried out using time resolved particle image velocimetry (TR-PIV) to investigate the aerodynamic behavior of a wall jet subjected to external lateral stream (ELS). The experiments are performed on a reduced-scale model representing a generic configuration of a refrigerated display cabinet (RDC) by focusing on the near-field region downstream the nozzle exit (x/e<10) where strong interactions are expected between the jet core, wall boundary and external lateral stream. Comparisons of experimental data obtained with and without external perturbation make it possible to quantify the effect of the perturbation on the time-averaged wall jet characteristics such as airflow patterns, mean velocity and root mean square (RMS) of velocity fluctuations, Reynolds shear stress, space correlations and the development of primary and secondary instabilities. The vortex shedding frequency of the perturbed wall jet has been assessed through a spectral analysis. It was found that the Strouhal number decreases with an increase of lateral-flow velocity, indicating an inhibiting effect exerted by the lateral flow on the formation and the development of Kelvin–Helmholtz (K–H) vortices in the outer shear layer. This paper also gives an insight into the altered behavior of coherent structures related to perturbed jet in terms of topology, alignment, trajectory and vortex shedding frequency. The break-up of vortex filaments in the braid region and its effect on the pairing process and the mutual interaction between inner and outer layer vortices has also been discussed. A proper orthogonal decomposition (POD) analysis has been performed showing the role of the ELS in redistributing the energy content in favor of small length scales and in the emerging of less well-organized structures.

Breakup of Thin Liquid Filaments on Partially Wetting Substrates: from Micrometric to Nanometric Scales

We present theoretical and experimental results regarding the instability of a thin liquid film in the form a long filament sitted on a solid substrate. We consider this problem in two different scenarios, namely, at submillimetric and nanometric scales, and we study their free surface instability. In the first scale, we take into account the effects due to surface tension and gravity, while in the smaller scale, we add intermolecular interaction and neglect gravity. The flows are modeled within the long wave approximation, which leads to a nonlinear fourth-order differential equation for the fluid thickness. This model equation also includes the partial wetting condition between the liquid and the solid. In the theoretical models, we analyze the linear stability of the equilibrium configurations. The linear stability analyses lead to eigenvalue problems that are solved using pseudo spectral methods in the submillimetric case, and finite differences in the nanoscale. Whenever possible, the theoretical results are compared with experiments performed on a submillimetric scale (silicon oils on glass), as well as on nanometric scale (nickel films melted by laser irradiation on SiO2 substrates).

Heterogeneity in the final stage of filament breakup of silicone oil/PMMA suspensions

We investigate the filament thinning behavior of the suspensions under extensional flow in the final stage of filament breakup process. Under the extensional flow, the particles dispersed in a Newtonian medium induce complex behaviors; in particular, the particles cause non-uniform filament thinning when the minimum neck diameter (W) of the filament becomes as thin as the length scale of the particle. We suspend 20 wt% of 10 μm poly(methyl methacrylate) (PMMA) particles in a silicone oil, and compare the filament thinning of the suspension with that of silicone oil having the same viscosity and surface tension. In this way, the effect of the particles on the thinning filament can be confirmed while eliminating differences in the rheological properties of the two fluids. The particles begin to affect filament shape when the filament becomes thinner than W = 10 D (D = 10 μm; particle diameter). The filament surface is rough and the shape of the filament is random for W < 2 D, which leads to a random pinch-off of the thinning filament, because the particles confined in the filament are distributed non-uniformly. The random distribution of the particles induces heterogeneity in the final stage of the filament thinning process, when the filament becomes as thin as the length scale of the particle.

Extensional rheometry of cellulose ether solutions: flow instability

Capillary breakup extensional rheometry of semi-dilute hydroxyethyl cellulose (HEC) solutions was performed under several step-stretch conditions. The resulting parameters, i.e. terminal steady state extensional viscosity (η E ) and the timescale for viscoelastic stress growth, commonly referred to as the extensional relaxation time (λ E ) were found to be sensitive to the step-stretch conditions. The λ E decreased with increasing step-strain as opposed to the η E . Prior to the filament break-up, a ‘bead-on-string’ instability was observed close to the mid-plane. It is believed that this instability originated from the accumulation of viscoelastic stresses near the filament neck leading to the ‘elastic recoil’ of the extended polymer chains. The reasons for this belief are discussed in detail with the perspective of the past literature. Such type of flow instability has been reported for the first time for a cellulosic system. Various dimensionless numbers were plotted for the HEC solutions and compared with those obtained from past studies for various biopolymers as well as synthetic polymers.

Heterogeneous fragmentation of metallic liquid microsheet with high velocity gradient**Project supported by the Science and Technology Development Foundation of China Academy of Engineering Physics (Grant Nos. 2013A0201010 and 2015B0201039) and the National Natural Science Foundation of China (Grant No. 11402032).

Large-scale molecular dynamics simulations are performed to study the fragmentation of metallic liquid sheets with high velocity gradient. Dynamic fragmentation of the system involves the formation of a network of fragments due to the growth and coalescence of holes, decomposition of the network into filaments, and further breakup of the filaments into spherical clusters. The final size distribution of the fragmented clusters in the large volume limit is found to obey a bilinear exponential form, which is resulted from the heterogeneous breakup of quasi-cylindrical filaments. The main factors contributing to fragmentation heterogeneity are introduced, including strain rate inhomogeneity and matter distribution nonuniformity of fragments produced during decomposition of the network structure.

The dynamics of laser surface modification

The mechanisms involved in the production of surface features of protruding material formed by the interaction of a laser beam and a metallic substrate are investigated aiming to optimise the process efficiency. A relationship between laser induced surface features and filament breakup theory has been established. Results indicate that for the production of features the geometry of the protrusion with a filament critical aspect ratio over 6.0±1.0 is required. In addition results show the surface tension, viscosity and density of the molten material, and the dynamics of the process dictate the characteristics of the forming feature. Using filament breakup and spatter production equations surface feature processing parameters can be predicted as demonstrated by the three metallic materials used in this study: Aluminium 5000 series, Stainless steel 304 and Ti–6Al–4V, all of which show consistent results.

Filament thinning of silicone oil/poly(methyl methacrylate) suspensions under extensional flow

We investigate the effect of particles dispersed in a Newtonian medium on the filament breakup of suspensions under extensional flow. In particular, we focus on the final stage of the breakup process: 10 μm poly(methyl methacrylate) (PMMA) particles with 0∼20 wt% are dispersed in silicone oil and the effects of the added particles on the thinning dynamics of the filament are observed with time-dependent changes in the minimum neck diameter (W). The particles decelerate the breakup process until the minimum thickness (W) of the filament becomes 5 d (d = 10 μm: particle diameter), and then they accelerate the process rapidly until the pinch-off. When the thinning dynamics and filament shape of the 20 wt% PMMA suspension are compared with those of a silicone oil with the same viscosity and surface tension, the particles affect the thinning dynamics by changing the breakup velocity under W∼35 d compared with the viscosity-matched silicone oil. When the filament becomes thinner than W∼10 d, the particles induce different surface shapes compared with those of the viscosity-matched silicone oil. When the filament becomes thinner than W∼5 d, the roughness of the filament surface increases. Thus, the effect of the particles in the final stage of filament breakup is more complicated than that in the initial stage, and we demonstrate that the particles dispersed in a Newtonian medium induce complex behaviors in the final stage of filament breakup.

Experimental investigation of a plane wall jet subjected to an external lateral flow

The present work aims to experimentally investigate the aerodynamic behavior of a wall jet subjected to external lateral stream by means of time-resolved PIV measurement technique. The experiments are performed on a reduced-scale model representing a generic configuration of a refrigerated display cabinet by focusing on the near-field region (x/e < 10) where strong interactions are expected between the jet core, wall boundary and external lateral stream. Comparisons of experimental data obtained with and without external perturbation make it possible to quantify the effect of the perturbation on the time-averaged wall jet characteristics such as airflow patterns, velocity profiles, maximum velocity decay, half-width jet growth, jet entrainment, RMS velocities and coherent structures as well as those related to the development of instabilities. Temporal PIV visualizations have allowed gaining insight on the effect of external lateral perturbation at the outer edge of the jet on the topology of Kelvin–Helmholtz vortices that dominate the early stages of wall jet transition process and play a relevant role on the jet entrainment inwards. Special attention was paid to bring new knowledge of the flow physics related to mutual interactions between outer and inner layer of the wall jet after the break-up of vortex filaments in the braid region due to the external perturbation.

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.

An analytic solution for capillary thinning and breakup of FENE-P fluids

The FENE-P model of a fluid is particularly suitable for describing the rheology of dilute polymer solutions (Newtonian solvents containing small amounts of dissolved polymer) as a result of its ability to capture nonlinear effects arising from the finite extensibility of the polymer chains. In extensional flows, these polymer solutions exhibit dramatically different behavior from the corresponding Newtonian solvents alone, notably through the creation of persistent filaments when stretched. By using the technique of capillary thinning to study the dynamics of the thinning process of these filaments, the transient extensional rheology of the fluid can be characterized. We show that under conditions of uniaxial elongational flow, a composite analytic solution can be developed to predict the time evolution of the radius of the filament. Furthermore we derive an analytic expression for the finite time to breakup of the fluid filaments. This breakup time agrees very well with results obtained from full numerical simulations, and both numerics and theory predict an increase in the time to breakup as the finite extensibility parameter b, related to the molecular weight of the polymer, is increased. As b→∞, the results converge to an asymptotic result for the breakup time which shows that the breakup time grows as tbreak∼ln(MW), where MW is the molecular weight of the dilute polymer solution.

Filament Dynamics during Simulated Ventricular Fibrillation in a High-Resolution Rabbit Heart.

The mechanisms underlying ventricular fibrillation (VF) are not well understood. The electrical activity on the heart surface during VF has been recorded extensively in the experimental setting and in some cases clinically; however, corresponding transmural activation patterns are prohibitively difficult to measure. In this paper, we use a high-resolution biventricular heart model to study three-dimensional electrical activity during fibrillation, focusing on the driving sources of VF: “filaments,” the organising centres of unstable reentrant scroll waves. We show, for the first time, specific 3D filament dynamics during simulated VF in a whole heart geometry that includes fine-scale anatomical structures. Our results suggest that transmural activity is much more complex than what would be expected from surface observations alone. We present examples of complex intramural activity, including filament breakup and reattachment, anchoring to the thin right ventricular apex; rapid transitions among various filament shapes; and filament lengths much greater than wall thickness. We also present evidence for anatomy playing a major role in VF development and coronary vessels and trabeculae influencing filament dynamics. Overall, our results indicate that intramural activity during simulated VF is extraordinarily complex and suggest that further investigation of 3D filaments is necessary to fully comprehend recorded surface patterns.

Dispensing of rheologically complex fluids at the dripping regime

Dispensing characteristics of rheologically complex fluids are investigated experimentally at the dripping regime. Two mixtures of ethylene glycol and glycerin (50:50 and 31:69) were used as base Newtonian fluids. As the polymer solution, 1000ppm of polyacrylamide of 5–6Mg/mol was added to the 50:50 base Newtonian fluid. 2.5, 5 or 7.5vol% of polystyrene particles of 2μm in diameter were added to the liquids to prepare particle suspensions. The liquids were dispensed to the air by using a nozzle with the inner and outer diameters of 0.61 and 0.91mm, respectively. It was found that the drop size is primarily determined by the balance of drop weight and surface tension force holding the drop, and hence drop size does not depend on volume flow rate. The drop diameter is approximately 10% smaller for elastic liquids due to the severe extension of the filament before the detachment from the nozzle. The result also shows that the dripping characteristics of the fluids without the polymer are mainly determined by the balance of the gravity force, surface tension force holding the liquid volume and pressure force. The addition of less than approximately 10% of 2μm spherical particles hardly changes the dispensing characteristics of Newtonian fluids except at the final stage of detachment. For polymeric liquids, the transient extensional property drastically changes the dripping dynamics. The force balance shows that the strain hardening of the polyacrylamide solution under the extensional flow causes severe retardation of the filament breakup. The filament breakup of the polymeric suspension is further decelerated by the increase in zero shear viscosity as a result of the particle addition.

The dynamic behaviour of a micro liquid bridge of magnetic fluid in static and alternating magnetic fields

Experimental study on the dynamic behaviour of magnetic fluid micro bridges under the effect of static and alter- nating magnetic fields was conducted using a high-speed video camera system. Two needle-shaped NdFeB permanent magnets were used to generate the static magnetic field, and Helmholtz coil was used to generate alternating field. Harmonic motion of magnetic fluid bridge was observed. It was found that the amplitude in the vibration of magnetic fluid bridge depends on the strength of alternating magnetic field at the constant frequency. Phenomena of filament thinning and breakup in a capillary bridge of magnetic fluid under the alternating magnetic fields were revealed.

Effect of concentration on shear and extensional rheology of guar gum solutions

The steady shear and extensional rheology of aqueous guar gum solutions was studied for concentrations, C, ranging from 1 g/L to 20 g/L. Extensional rheometry measurements were made using the Cambridge Trimaster filament-stretching device. The steady shear tests indicated a transition between a semi-dilute regime, below 10 g/L, and an entangled regime at higher concentrations. The solutions were shear-thinning and obeyed the unmodified Cox–Merz rule in the dilute regime, but deviated from Cox–Merz and exhibited strongly viscoelastic behaviour at higher concentrations. The surface tension at higher concentration also deviated from the Szyszkowski model, exhibiting behaviour consistent with entanglement. The filament-thinning data did not fit the model for polymer solution behaviour presented by Entov and Hinch (1997), but gave a good fit to a modified form where time was normalised by the time for filament break-up. This scaling was independent of concentration effects, as reported by Chesterton, Meza, Moggridge, Sadd, and Wilson (2011) for cake batters. The modified model parameters approached asymptotic values for entangled solutions. The estimated apparent extensional viscosity exhibited a peak at unit strain followed by a constant value. The former increased as Cn, where n > 1, while the latter increased linearly with C.

The rheology and processing behavior of starch and gum-based dysphagia thickeners

The addition of a starch or gum-based thickener to patient fluids with dysphagia is commonly carried out, but the mechanism behind the efficacy of this treatment is not fully understood. This paper describes the rheological behavior of two commercially available thickening powders and an additional xanthan gum solution with a view to explaining the efficacy of thickened fluids in terms of their rheology. Both linear viscoelastic and steady shear data were obtained for the fluids together with filament extensional stretch, decay, and breakup data. In order to follow the behavior of the fluids in a processing situation, a mechanical “Cambridge Throat” was designed and tested. The action of the tongue was modeled using a constant torque cam that forced fluid contained within a flexible membrane through a model throat. Movie photography captured images of the fluid behavior and showed that for a constant tongue torque, the transit time within the model throat increased with increasing fluid viscosity, with implications for the time available for the successful function of the larynx, throat muscles, and epiglottis.

Simulations of the breakup of liquid filaments on a partially wetting solid substrate

We report direct numerical simulations of liquid filaments breaking up into droplets on partially wetting substrates. It is motivated by recent experiments, linear stability analyses, and lubrication-based calculations. The fluid flow is governed by the Stokes equations and the contact line motion is handled by a phase-field model, which also serves to capture the interfacial motion. The coupled Stokes and Cahn-Hilliard equations are solved using a finite-element algorithm in three dimensions. This avoids additional approximations of the fluid flow or contact line motion, and allows us to compute arbitrary contact angles on the substrate. We simulate both the breakup of infinite liquid filaments via growing capillary waves and that of finite liquid filaments with drops pinching off from the ends, with a focus on the effect of the wetting angle. In both cases, substrate hydrophobicity promotes breakup of the thread, and decreases the spacing of the daughter drops. The results show the differences in the two processes and in the final drop size and spacing. The development of capillary waves agrees well with prior linear analysis and the end-pinching results offer new insights into this poorly understood phenomenon.

Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids

An energy-based, phase field model is developed for the coupling of two incompressible, immiscible complex fluid phases, in particular a nematic liquid crystal phase in a viscous fluid phase. The model consists of a system of coupled nonlinear partial differential equations for conservation of mass and momentum, phase transport, and interfacial boundary conditions. An efficient and easy-to-implement numerical scheme is developed and implemented to extend two benchmark fluid mechanical problems to incorporate a liquid crystal phase: filament breakup under the influence of capillary force and the gravity-driven, dripping faucet. We explore how the distortional elasticity and nematic anchoring at the liquid crystal-air interface modify the capillary instability in both problems. For sufficiently weak distortional elasticity, the effects are perturbative of viscous fluid experiments and simulations. However, above a Frank elasticity threshold, the model predicts a transition to the beads-on-a-string phenomenon associated with polymeric fluid filaments.

Determination of axial forces during the capillary breakup of liquid filaments – the tilted CaBER method

The capillary breakup extensional rheometry (CaBER) is a versatile method to characterize the elongational behavior of low-viscosity fluids. Commonly, data evaluation is based on the assumption of zero normal stress in axial direction ( $\upsigma_{\rm zz}=0$ ). In this paper, we present a simple method to determine the axial force using a CaBER device rotated by 90° and analyzing the deflection of the filament due to gravity. Forces in the range of 0.1–1,000 μN could be assessed. Our study includes experimental investigations of Newtonian fructose solutions and silicon oil mixtures (viscosity range, 0.9–60 Pa s) and weakly viscoelastic polyethylene oxide (PEO, $M_{\rm w}=10^{6}$ g/mol) solutions covering a concentration range from c ≈ c* (critical overlap concentration) up to c > c e (entanglement concentration). Papageorgiou’s solution for the stress ratio $\upsigma_{\rm zz}/\upsigma_{\rm rr}$ in Newtonian fluids during capillary thinning is experimentally confirmed, but the widely accepted assumption of vanishing axial stress in weakly viscoelastic fluids is not fulfilled for PEO solutions, if c e is exceeded.

Breakup of Liquid Filaments

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.