Newtonian Jet Research Articles

Laminar planar jets of elastoviscoplastic fluids

We perform numerical simulations of planar jets of elastoviscoplastic (EVP) fluid (Saramito (2007) model) at low Reynolds number. Three different configurations are considered: (i) EVP jet in EVP ambient fluid, (ii) EVP jet in Newtonian ambient fluid (miscible), and (iii) EVP jet in Newtonian ambient fluid (immiscible). We investigate the effect of the Bingham number, i.e. of the dimensionless yield stress of the EVP fluid, on the jet dynamics, and find a good agreement with the scaling for laminar, Newtonian jets for the centerline velocity uc/u0∝(x/h)−1/3 and for the jet thickness δmom/h∝(x/h)2/3 at small Bingham number. This is lost once substantial regions of the fluid become unyielded, where we find that the spreading rate of the jet and the decay rate of the centerline velocity increase with the Bingham number, due to the regions of unyielded fluid inducing a blockage effect on the jet. The most striking difference among the three configurations we considered is the extent and position of the regions of unyielded fluid: large portions of ambient and jet fluids (in particular, away from the inlet) are unyielded for the EVP jet in EVP ambient fluid, whereas for the other two configurations, the regions of unyielded fluid are limited to the jet, as expected. We derive a power law scaling for the centerline yield variable and confirm it with the results from our numerical simulations. The yield variable determines the transition from the viscoelastic Oldroyd-B fluid (yielded) to the viscoelastic Kelvin–Voigt material (unyielded).

Toward large eddy simulation of shear-thinning liquid jets: A priori analysis of subgrid scale closures for multiphase flows

While direct numerical simulation (DNS) of multiphase flows has been the focus of many research investigations in recent years, large eddy simulation (LES) of multiphase flows remains a challenge. There is no standardized set of governing equations for multiphase LES. Different approaches and formulations have been discussed in the literature, each with its own advantages and disadvantages. In this paper, the conventional (non-weighted) filtering approach is compared with the density-weighted Favre filtering method by evaluating the subgrid scale (SGS) energy transfer for a simple test case of a shear-thinning droplet in air. The findings reveal that, unlike the Favre filtering approach, the conventional filtering method results in a notable amount of nonphysical backward scatter in the flow. Based on these results, the Favre filtering method appears preferable and is applied to the a priori analysis of shear-thinning liquid jets, where the viscosity has been modeled using the Carreau–Yasuda model. First, by explicitly filtering existing DNS data of shear-thinning jet breakup into stagnant air, the order of magnitude of different SGS terms is evaluated using the Favre filtering method. Consistent with earlier studies on Newtonian jets, the present study indicates that the diffusive term remains negligible, while the convective term plays a dominant role. Functional and structural models for the closure of the convective SGS term are assessed by means of a correlation analysis and an order of magnitude study. Existing structural models provide good results for both Newtonian and shear-thinning cases. Promising a posteriori model candidates are discussed.

A review on free miscible buoyant jets

Buoyant jets have been a topic of interest due to their presence in various natural and industrial phenomena, as well as in our daily lives. Covering extensive literature, our focus in this review article is on free, miscible buoyant jets with small-density differences (under the Boussinesq approximation) within uniform and stagnant environments. We examine the latest research on Newtonian jet flows and expand our scope to their viscoplastic counterparts, reflecting a burgeoning trend in contemporary literature. Our analysis covers negatively buoyant, pure, and positively buoyant jets, via delving into their dynamics. This includes regime classifications and key jet characteristics, such as laminar length, penetration length, mixing behavior, velocity profiles, and turbulence parameters. In particular, the effects of the key governing dimensionless parameters, including the Reynolds number, the Froude number, the Bingham number, the viscosity ratio, and the injection angle, on these characteristics are explored.

Coherent structures in elastic turbulent planar jets

At low Reynolds numbers, the flow of a Newtonian planar jet remains laminar, thus easy to characterize. In contrast, the presence of elasticity (e.g., attained dissolving polymers in a Newtonian solvent) enables a highly-complex turbulent-like behavior termed elastic turbulence. In this work, we run data-driven modal decomposition algorithms on high-fidelity data collected from the simulation of an elastic turbulent planar jet. The large-scale motions are expressed as a finite expansion of modes that condense the dominant dynamics. The modes associated with lower frequencies weight the most on the reconstruction of the original data, thus they are further decomposed in space to investigate their implications on the sustainment of the elastic turbulent state. Our findings suggest that slower dynamics are crucial for the sustainment of elastic turbulence, which is connected to the interaction of spanwise-coherent structures, steady in space, with spanwise-periodic traveling waves, causing the breakdown of the structures close to the inlet.

Stability and thinning of liquid jets in the presence of soluble surfactants.

The dynamics of many multiphase fluid systems involve the thinning and eventual break up of a slender fluid filament or a liquid jet. The interfacial instability that controls the rate of jet thinning depends on the relative magnitudes of capillary, viscous, and inertial stresses. Surfactants add an additional layer of physicochemical dynamics by reducing the surface tension of the interface and introducing reverse Marangoni flows in response to surface concentration gradients. Surfactants may also introduce an intrinsic surface rheology that affects jet thinning. Quantifying these effects has been a significant problem in chemical physics and a topic of key research interest. Recent studies have shown that insoluble surfactants delay thread thinning and suppress instabilities in Newtonian jets. However, the role of surfactant solubility in liquid jet stability is still unknown. In this work, we use linear stability analysis to quantitatively show the stabilizing effects of Marangoni stresses, surfactant adsorption and desorption time, and intermolecular forces upon adsorption. We highlight the seemingly indistinguishable way in which various surfactant properties result in the same outcome. We also identify a surface dissipative contribution that arises from the interplay of Marangoni flows with finite adsorption and desorption, which acts as an "apparent" surface viscosity. We verify predictions of our linear stability results against numerical simulations and conclude by noting that tuning surface activity and kinetics of adsorbed surfactants or particles can potentially suppress droplet formation, which is of significant impact in the printing industry and in the control of the spread of aerosols.

Non-Newtonian turbulent jets at low-Reynolds number

We perform direct numerical simulations of planar jets of non-Newtonian fluids at low Reynolds number, in typical laminar conditions for a Newtonian fluid. We select three different non-Newtonian fluid models mainly characterized by shear-thinning (Carreau), viscoelasticity (Oldroyd-B) and shear-thinning and viscoelasticity together (Giesekus), and perform a thorough analysis of the resulting flow statistics. We characterize the fluids using the parameter γ, defined as the ratio of the relevant non-Newtonian time scale over a flow time scale. We observe that, as γ is increased, the jet transitions from a laminar flow at low γ, to a turbulent flow at high γ. We show that the different non-Newtonian features and their combination give rise to rather different flowing regimes, originating from the competition of viscous, elastic and inertial effects. We observe that both viscoelasticity and shear-thinning can develop the instability and the consequent transition to a turbulent flowing regime; however, the purely viscoelastic Oldroyd-B fluid exhibits the onset of disordered fluid motions at a lower value of γ than what observed for the purely shear-thinning Carreau fluid. When the two effects are both present, an intermediate condition is found, suggesting that, in this case, the shear-thinning feature is acting against the fluid elasticity. Despite the qualitative differences observed in the flowing regime, the bulk statistics, namely the centerline velocity and jet thickness, follow almost the same power-law scalings obtained for laminar and turbulent Newtonian planar jets. The simulations reported here are, to the best of our knowledge, the first direct numerical simulations showing the appearance of turbulence at low Reynolds number in jets, with the turbulent motions fully induced by the non-Newtonian properties of the fluid, since the Newtonian case at the same Reynolds number is characterized by steady, laminar flow.

The viscoplastic circular hydraulic jump

We examine theoretically the spread of a jet impacting on a circular disk and the hydraulic jump of a viscoplastic fluid of the Herschel–Bulkley type. The depth-averaging approach is employed in the supercritical region, and the subcritical flow is assumed to be inertialess of the lubrication type. The jump is treated as a shock, where the balance of mass and momentum is established in the radial direction, including the effect of surface tension across the jump. We show that, in contrast to the Newtonian jet, which requires separate formulations in the developing-boundary layer and fully viscous layers, the supercritical formulation for the fully yielded and pseudo-plug layers is uniformly valid between the impingement zone and the jump. Consequently, a viscoplastic jet does not experience the discontinuity in the film height, pseudo-plug layer velocity gradient, and shear stress, exhibited by a Newtonian film at the transition location. The jump is found to occur closer to impingement, with growing height, as the yield stress increases; the subcritical region becomes invaded by the pseudo-plug layer. The viscosity does not influence sensibly the jump location and height except for small yield stress; only the yielded-layer is found to remain sensitive to the power-law rheology for any yield stress. In particular, shear thickening can cause the fully yielded layer to drop in height despite the jump in the film surface. We also find that the jump would not occur if the disk was smaller than a critical size, but the yield stress tends to enhance the formation of the jump compared to a Newtonian jet. We show that an almost constant local downstream Froude number also exists for a viscoplastic fluid. Finally, our results reduce to the limiting cases of Bingham, power-law, and Newtonian fluids.

A revisit of Rayleigh capillary jet breakup at low Ohnesorge number

The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity must be determined by the selection of normal modes with time-independent amplitude and wavelength. Invariant modes (IMs) with both positive and negative group and phase velocities exist in ample ranges of the parameter domain (Weber and Ohnesorge), which explains (i) the self-sustained average breakup length (long-term resonance) and (ii) the governing role on breakup of both spatial growth rate and wave number of the dominant positive group velocity IM. Published experimental results at low Ohnesorge numbers confirm our proposal.

Effect of velocity and radius distribution on jet breakup

The focus of this paper is on the effect of velocity and radius distribution on jet breakup. A theoretical model is established to analyze and predict the velocity distribution along the jet, which is physically and mathematically continuous. The simplified forms of the breakup time, the disturbance growth rate, and the disturbance level considering the velocity and radius distribution are presented. A series of prediction methods for predicting the jet breakup length and droplet size are developed. A Newtonian laminar jet falling vertically was experimentally observed to validate the theoretical model and prediction methods. It is shown that the relaxation of the velocity profile leads to the rapid contraction of the jet radius near the outlet, which leads to the increase in the growth rate of the instability disturbance. The surface tension prevents the growth rate of disturbance from increasing by restraining the contraction of jet radius. The final amplification of jet velocity and contraction due to gravity acceleration depend on the Froude number and breakup length. When the influence of jet radius distribution on the growth rate of disturbance is considered, the breakup time is indirectly affected by the breakup length. The experimental and predicted results show that the accelerated falling of jet lengthens the breakup length traveled by the jet in a shortened breakup time due to the contraction of jet radius. The droplet volume is proportional to the predicted jet cross-sectional area at the breakup position and the Rayleigh wavelength determined by the nozzle radius.

Rheological identification of jetted fluid using machine learning

The understanding of flowing properties of fluids and the knowledge of the related rheological properties are crucial from both a research and industrial point of view. To determine the complex rheological properties of fluids, many devices have thus been developed, the so-called rheometers. The main objective of the present paper is to identify the rheological properties of a fluid jetted using continuous inkjet (CIJ) printing process by comparing the morphology of the aforementioned jetted fluid to a dataset of known (rheologically speaking) fluid jet morphologies and properties of a fluid by the viscosity, the surface tension, and the density of fluids using large datasets and a CIJ printing process. When ejecting a fluid, the CIJ ejection process competes among several forces: inertial, viscous, surface tension, and elasticity, which affect the morphology of the resulting jet. Also, under certain conditions, the morphology of the jet is unique and directly related to the rheological properties of the fluid. We want to use this uniqueness to identify the fluid among a large dataset of known fluid jet morphologies to be compared with, to obtain its rheological properties. Using a large numerically generated dataset of Newtonian fluid jets, we show in this article that the identification of the viscosity using neural network is not only feasible but also proves to be very accurate with an average error of less than 1% for a large range of viscosities.

Temporal instability of curved viscous fibers with a radial electric field

Abstract One-dimensional equations are derived for a rotating viscous slender liquid jet in a radial electric field using asymptotic methods. The trajectory of the curved Newtonian liquid jets is found by solving the nonlinear one-dimensional equations. The temporal instability of the steady solutions is analysed. It was found that the electric force enhances the growth rate and increases its corresponding maximum wavenumber.

Viscoelastic effects probed by drop-jet collisions

We experimentally probe the stability of a continuous liquid jet deformed by successive impacts of immiscible drops. For Newtonian jets, two fragmentation thresholds are observed, which can be associated to two critical jet extensions. For viscoelastic jets, however, these fragmentations are partially or totally suppressed and cannot be correlated to any critical jet extension. We explain this dramatic change by the different drainage dynamics of the produced filaments, which we successfully model for both the Newtonian and viscoelastic jets. For the latter, long-lived filaments made of the jet liquid appear, which connect the encapsulated immiscible drops, giving rise to a new structure called Capsules On A String (COAS).

Free surface lubrication of rotating cylinders by impacting Newtonian liquid jet

AbstractFree surface lubrication of rotating cylinders by Newtonian liquid jets was investigated at different impingement positions, jet‐ and circumferential velocities. The interaction between impinging round laminar jet and rotating surface was characterised by high‐speed imaging. Compared to flat surface impingement, the liquid deposition mechanism is more complex and often accompanied by phenomena such as splashing, jet deflection and formation of radial surface stripes. Liquid splashing initially develops in direct deposition regime due to hydraulic jump‐induced droplet shedding, transitioning to lamella instability splash at higher Reynolds numbers. The critical Reynolds number for splash onset is of same order of magnitude as for flat surface impingement and fairly constant at low relative jet impingement angles, but increases exponentially when angle approaches 90°. Liquid film width and thickness were both determined proportional to the square root of the jet/surface velocity ratio, with respective power law models in good agreement with measured values.

Pinch-off of a surfactant-covered jet

Abstract

Electrohydrodynamic instability of confined viscoelastic liquid jets

Linear stability analysis is performed to study the electrohydrodynamic instability of viscoelastic jets subjected to axisymmetric (m=0) and first non-axisymmetric (m=1) perturbations in the creeping-flow limit. The viscoelastic liquid jet is under the influence of a radially applied electric field induced by a concentrically placed electrode located at a finite gap width from the jet. The leaky dielectric model is used to account for the finite conductivity of the fluid. The gap between the liquid jet and the electrode is assumed to be occupied by a hydrodynamically passive gas. The influence of the applied electric potential, electrode width, electrical properties, fluid elasticity, and solvent viscosity on the stability of the jet is analyzed comprehensively. For m=0 mode, the electric field has a dual effect on the stability of a Newtonian jet above a critical electrode width to jet radius ratio (Rcr). Here, the dual effect means that the electric field has a stabilizing effect for low wavenumbers (k) and a destabilizing effect for higher k. However, for R<Rcr, the electric field has a uniformly destabilizing effect, and the dual nature disappears. In the limit of perfectly conducting Newtonian jet, Rcr = 2.7. The maximum growth rate increases with an increase in Deborah number (De), which is a dimensionless relaxation time of the fluid, but the range of unstable wavenumbers remains unaffected due to an increase in De. For m=0 mode, there exists a critical Deborah number (Decr), for given values of other physical parameters, above which the growth rate diverges. This behavior is similar to the previous results for the planar geometry and is caused due to the neglect of inertia. As the conductivity of the liquid increases, the Decr decreases and reaches an asymptotic value in the limit of a perfect conductor. The inclusion of elasticity has no effect on the Rcr value, thus suggesting that the dual nature of the electric field is independent of fluid elasticity. The singularity in the growth rate is shown to be mitigated by introducing solvent viscous stresses into the model. Thus, the present study shows that finite electrode distance and elasticity have important consequences on the stability of the liquid jet for the axisymmetric mode. For m=1 mode, the growth rate is singular at low wavenumbers which is due to the neglect of inertia of the system. For the Newtonian case, the range of wavenumbers where the growth rates are singular increases with either increasing the electric potential or decreasing the electrode width. Inclusion of elasticity increases the range of wavenumbers where the growth rates are singular, whereas the range of unstable wavenumbers remains unchanged. Therefore, the neglect of inertia gives rise to non-physical growth rates even in the Newtonian flow limit for m=1 mode, compared to m=0 mode where the singularity of growth rate was observed for the Maxwell fluid above Decr.

Direct numerical simulations of turbulent viscoelastic jets

Direct numerical simulations (DNS) of spatially evolving turbulent planar jets of viscoelastic fluids described by the FENE-P model, such as those consisting of a Newtonian fluid solvent carrying long chain polymer molecules, are carried out in order to develop a theory for the far field of turbulent jets of viscoelastic fluids. New evolution relations for the jet shear-layer thickness , centreline velocity and maximum polymer stresses are derived and validated by the new DNS data, yielding , , and , respectively, where is the coordinate in the streamwise direction. It is shown that, compared with a classical (Newtonian) turbulent jet, the effect of the polymers is to reduce the spreading rate, centreline velocity decay, Reynolds stresses and viscous dissipation rate. The self-preserving character of the flow is analysed and it is shown that profiles of mean velocity, Reynolds stresses and polymer stresses are self-similar provided the proper scales are used in the normalisation of these quantities. A fundamental difference from the Newtonian jet in this regard is the necessity for two, instead of only one, different velocity and length scales to properly characterise the evolution of the turbulent flow. These extra velocity and length scales are directly related to a time scale associated with the characteristic fading memory property of viscoelastic fluids.

Temporal instability analysis of a confined non-Newtonian liquid jet with heat and mass transfer

In this study, the instability behavior of a confined non-Newtonian liquid jet in an annular gas layer is investigated theoretically. The viscosity of the non-Newtonian liquid is described using the power law model, and the corresponding dispersion relation is obtained by conducting a linear stability analysis. Additionally, the effects of heat and mass transfer, gas-to-liquid axial velocity ratio, power law index, and gas layer thickness on the instability of the power law liquid jet are investigated. The results demonstrate that the heat and mass transfer at the liquid–gas interface destabilizes the power law liquid jet flow. The results also indicate that an increase in the thickness of the gas layer makes the confined power law liquid jet unstable. Furthermore, the confined shear-thickening liquid jet is the most difficult to breakup in comparison with the shear-thinning and Newtonian liquid jets.

Numerical simulation of jet mode in electrospraying of Newtonian and viscoelastic fluids

This study aims to model the role of the viscoelastic properties of polymeric solutions in the jet mode of the electrospray process numerically. For this purpose, first, the computational challenges in front of a numerical investigation of such complex physics are explained, and the recent advances in rectifying these problems, especially the high Weissenberg instability, is described. Then, a numerical procedure based on the Log-conformation method (LCM) is introduced, and several numerical simulations are performed to model the behavior of electrified Newtonian and viscoelastic jets. In the first step, the discrete model for the LCM equations is validated by simulating the benchmark problem of the sedimenting sphere. The obtained results show that the proposed algorithm can improve the previous Weissenberg threshold reported for a stable solution. Then, an electrified deionized (DI) water jet is simulated, and the obtained jet profile is compared with the experimental data. Finally, the proposed algorithm is used to simulate viscoelastic electrified jets, where the effect of the Weissenberg number (Wi) on the jet profile is examined. In agreement with the previously obtained experimental results, the numerical results show that by increasing the solution concentration, the asymptotic jet profile is reached at a smaller length from the nozzle, while the final thickness of the jet is slightly reduced.

Liquid sheet formed by a Newtonian jet obliquely impinging on pro/hydrophobic surfaces

The collision process between a Newtonian liquid jet and pro/hydrophobic surfaces was investigated in this paper. Based on the theory of impinging-jets, a theoretical model of liquid sheet was established which comprehensively considered the effects of pro/hydrophobicity on surface tension force and the energy loss during the entire impinging process. The sheet parameters such as the size, velocity and thickness distribution were obtained. In order to validate the theoretical model, a corresponding experimental set-up has been developed, using deionized water as experimental working medium and 3 different pro/hydrophobic surfaces as experimental parts. The comparisons showed the theoretical results are in good agreement with the experimental data. In addition, the influence of surface pro/hydrophobicity on the sheet characteristics was theoretically discussed, and the results showed the surface pro/hydrophobicity could significantly affect the size of liquid sheet on solid surface.

Oscillatory motion and merging responses of primary and satellite droplets from Newtonian liquid jets

Numerical simulations of laminar Newtonian liquid jets are presented that divulge several breakup and merging responses for both primary and satellite droplets. Using an axisymmetric VOF model, we predict the presence of surface oscillations of droplets disintegrated from jets, which at times lead to merging of droplets when travelling downstream. Our simulations indicate that when primary droplets undergo merging, they exhibit characteristics such as (i) permanent and (ii) partial coalescence. We find that the partial coalescence of droplets can lead to a reflexive-like separation and then show re-merge responses. The formation of an air-bubble during the merging of binary droplets is predicted. Characteristics such as forward, rear, and simultaneous merging patterns of satellites with primary droplets are captured in our numerical simulations. Furthermore, a new merging pattern is reported wherein, satellites formed from the swellings of the jet can be absorbed back into the moving core of the liquid jet.