Showing papers on "Ohnesorge number published in 2018"

Coalescence-induced jumping of droplets on superomniphobic surfaces with macrotexture

Abstract: When two liquid droplets coalesce on a superrepellent surface, the excess surface energy is partly converted to upward kinetic energy, and the coalesced droplet jumps away from the surface. However, the efficiency of this energy conversion is very low. In this work, we used a simple and passive technique consisting of superomniphobic surfaces with a macrotexture (comparable to the droplet size) to experimentally demonstrate coalescence-induced jumping with an energy conversion efficiency of 18.8% (i.e., about 570% increase compared to superomniphobic surfaces without a macrotexture). The higher energy conversion efficiency arises primarily from the effective redirection of in-plane velocity vectors to out-of-plane velocity vectors by the macrotexture. Using this higher energy conversion efficiency, we demonstrated coalescence-induced jumping of droplets with low surface tension (26.6 mN m−1) and very high viscosity (220 mPa·s). These results constitute the first-ever demonstration of coalescence-induced jumping of droplets at Ohnesorge number >1.

Coalescence-Induced Jumping of Two Unequal-Sized Nanodroplets.

Abstract: Coalescence-induced self-propelled jumping of droplets on superhydrophobic surfaces has potential applications for condensation heat transfer enhancement, anti-icing, self-cleaning, antidew, and so forth. However, most of the previous studies focused on two identical droplets which are not commonly encountered in the nature. In this work, coalescence-induced jumping phenomena of two unequal-sized droplets on superhydrophobic surfaces were investigated theoretically and numerically. First, by introducing modified inertial-capillary velocity (uic*) and Ohnesorge number (Oh*) with consideration of radius ratio (r*) of two coalescing droplets, we proposed a generalized inertial-capillary scaling law for the jumping velocity of coalesced droplets, which is expected to be applicable for both two identical droplets and two unequal-sized droplets coalescing on superhydrophobic surfaces. Subsequently, we employed molecular dynamics simulations to investigate the coalescence-induced jumping process of two unequal-s...

Analysis of droplet stability after ejection from an inkjet nozzle

Abstract: Inkjet technology is a commendable tool in many applications including graphics printing, bioengineering and micro-electromechanical systems (MEMS). Droplet stability is a key factor influencing inkjet performance. The stability can be analysed using dimensionless numbers that usually combine thermophysical properties and system dimensions. In this paper, a drop-on-demand (DOD) inkjet experimental system is established. A numerical model is developed to investigate the influence of the operating conditions on droplet stability, including nozzle dimensions, driving parameters (the pulse amplitude and width used to drive droplet formation) and fluid properties. The results indicate that the stability can be improved by decreasing the pulse amplitude and width, decreasing the fluid density and viscosity or increasing the nozzle diameter and fluid surface tension. Based on case analysis and modelling, a dimensionless number ( ), the reciprocal of the Ohnesorge number, is numerically determined for a stable droplet to lie in a range between 4 and 8. To explicitly combine the driving parameters, a new stability criterion, , is further proposed. A general rule taking into account both and is proposed for choosing appropriate driving parameters to eject stable droplets for a known nozzle and fluid, which is further validated by experiments.

Pinch-off of a viscous suspension thread

Abstract: The pinch-off of a capillary thread is studied at large Ohnesorge number for non-Brownian, neutrally buoyant, mono-disperse, rigid, spherical particles suspended in a Newtonian liquid with viscosity .

Axisymmetric lattice Boltzmann simulation of droplet impact on solid surfaces

Abstract: Droplet-solid interaction is a ubiquitous fluid phenomenon that underpins a wide range of applications. To further the understanding of this important problem, we use an axisymmetric lattice Boltzmann method (LBM) to model the droplet impact on a solid surface with different wettability. The method applies a popular free-energy LBM developed by Lee and Liu [T. Lee and L. Liu, J. Comput. Phys. 229, 8045 (2010)10.1016/j.jcp.2010.07.007] to simulate incompressible binary fluids with physical density and viscosity contrasts. The formulation is recast in cylindrical coordinates for modeling the normal impact of a three-dimensional (3D) droplet in the no-splashing regime, in which an axisymmetric flow is considered. The droplet deposits on or rebounds from the surface, governed by three key parameters: Weber number, Ohnesorge number, and equilibrium contact angle, which quantifies the surface wettability. We elucidate the distinct impact dynamics by probing droplet morphology and contact line behavior in great detail, which are quantitatively characterized by spreading factor, droplet aspect ratio, and dynamic contact angle. The simulations also resolve fluid velocity field inside and outside the droplet, which provides additional insight into the morphological evolution and mass-momentum transfer during impact. Explicit comparison between axisymmetric and conventional 2D LBM highlights the importance of axisymmetric terms in governing equations for reproducing physical impact behavior. The axisymmetric LBM significantly reduces computational cost as compared with 3D LBMs and offers an effective means to study droplet impact in applicable conditions.

Numerical simulation for a rising bubble interacting with a solid wall: Impact, bounce, and thin film dynamics

Abstract: Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using the Ohnesorge number and Bond number as the two dimensionless control parameters. Finally, we turn to the late stage of the bubble rise characterized by a small flux of liquid escaping from the thin film between the wall and the bubble. Since the thin film dynamics can be accurately described by the lubrication approximation, we carry out numerical simulations to compare the simulation results with the predictions of the lubrication approximation. Remarkable agreement is obtained to further demonstrate the accuracy of the simulations.

Inertio-capillary cross-streamline drift of droplets in Poiseuille flow using dissipative particle dynamics simulations

Abstract: We find using dissipative particle dynamics (DPD) simulations that a deformable droplet sheared in a narrow microchannel migrates to steady-state position that depends upon the dimensionless particle capillary number , which controls the droplet deformability (with Vmax the centerline velocity, μf the fluid viscosity, Γ the surface tension, R the droplet radius, and H the gap), the droplet (particle) Reynolds number , which controls inertia, where ρ is the fluid density, as well as on the viscosity ratio of the droplet to the suspending fluid κ = μd/μf. We find that when the Ohnesorge number is around 0.06, so that inertia is stronger than capillarity, at small capillary number Cap < 0.1, the droplet migrates to a position close to that observed for hard spheres by Segre and Silberberg, around 60% of the distance from the centerline to the wall, while for increasing Cap the droplet steady-state position moves smoothly towards the centerline, reaching around 20% of the distance from centerline to the wall when Cap reaches 0.5 or so. For higher Oh, the droplet position is much less sensitive to Cap, and remains at around 30% of the distance from centerline to the wall over the whole accessible range of Cap. The results are insensitive to viscosity ratios from unity to the highest value studied here, around 13, and the drift towards the centerline for increasing Cap is observed for ratios of droplet diameter to gap size ranging from 0.1 to 0.3. We also find consistency between our predictions and existing perturbation theory for small droplet or particle size, as well as with experimental data. Additionally, we assess the accuracy of the DPD method and conclude that with current computer resources and methods DPD is not readily able to predict cross-stream-line drift for small particle Reynolds number (much less than unity), or for droplets that are less than one tenth the gap size, owing to excessive noise and inadequate numbers of DPD particles per droplet.

Weakly nonlinear instability of a Newtonian liquid jet

Abstract: A weakly nonlinear stability analysis of an axisymmetric Newtonian liquid jet is presented. The calculation is based on a small-amplitude perturbation method and performed to second order in the perturbation parameter. The obtained solution includes terms derived from a polynomial approximation of a viscous contribution containing products of Bessel functions with different arguments. The use of such an approximation is not needed in the inviscid case and the planar case, since the equations of those problems can be solved in an exact form. The developed model depends on three dimensionless parameters: the initial perturbation amplitude, the perturbation wavenumber and the liquid Ohnesorge number, the latter being the dimensionless liquid viscosity. The influence of the approximate terms was shown to be relatively small for a large range of Ohnesorge numbers so that they can be ignored. This simplification provides a jet model as simple to use as the previous ones, but taking into account the liquid viscosity and the cylindrical geometry. The jet model is used to reveal the effect of both the wavenumber and the Ohnesorge number on the formation of satellite drops, which is known as a nonlinear effect. Results are found in good agreement with direct numerical simulations and forced liquid jet experiments for wavenumbers lower than a threshold value. Satellite drop formation is retarded with increasing Ohnesorge number and wavenumber, as expected by the damping and size effects of viscosity. The threshold number corresponds to the maximum wavenumber for which satellite drop formation is predicted before jet breakup, and for which volume conservation is satisfied within a certain amount. The volume conservation criterion is imposed to ensure that the conclusions inferred by our model are safe.

Numerical Investigation of Coalescence-Induced Droplet Jumping from a Hydrophobic Fiber

Abstract: Coalescence-induced droplet jumping from a round hydrophobic fiber was studied by phase-field-based hybrid lattice-Boltzmann finite-difference simulations in which the interface dynamics is handled by the finite-difference solution of the Cahn–Hilliard equation and the hydrodynamics is handled by the lattice-Boltzmann method. It was found that at a small Ohnesorge number of O(0.01), several different outcomes, including normal jumping at a positive velocity, jumping with a negative velocity, jumping after wrapping the fiber, and oscillating on the fiber, may occur after droplet coalescence, depending on the wettability of the fiber and the droplet-to-fiber radius ratio. In accordance with previous reports, normal droplet jumping from the fiber happens only when the radius ratio exceeds some critical value for a given contact angle. The critical radius ratio decreases as the fiber becomes more hydrophobic. For a given contact angle and radius ratio, it was observed that there exists an Ohnesorge number at ...

The role of wettability of nonideal nozzle plate: From drop-on-demand droplet jetting to impact on solid substrate

Abstract: The dynamics of drop-on-demand (DoD) droplet formation and subsequently impact on the solid substrate are investigated using a three-dimensional (3-D) multirelaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model. The wettability of nonideal nozzle plate and solid substrate is modeled by a geometric scheme within the LB framework. The dynamics of droplet formation are explored in a range of the inverse of Ohnesorge number Z=4.95, 11.57, and 28.17, and the Reynolds number Re=39.6, 58.9, and 136.4. For Z=4.95, no satellite droplet is observed and the wettability of nozzle plate greatly influences the velocity and length of jetting fluids. For Z=11.57, the filament breakup and recombination are observed. The moment of filament breakup is delayed with advancing contact angle θA increasing. For Z=28.17 with Re=136.4, the primary and satellite droplets could not be recombined with θA=30° and θA=60° which agree with the literature. Whereas with θA=90°, the recombination occurs. The dynamics of subsequent oscillating droplet impact on the substrate are similar to that of equilibrium droplet which could obtain high-resolution printed features. Consequently, considering θA=90° with large Z and Re numbers, the printable range could be extended which could help increase the printing frequency and boost the production outputs of inkjet printing. © 2018 American Institute of Chemical Engineers AIChE J, 2018

One Dimensional Model for Droplet Ejection Process in Inkjet Devices

Abstract: In recent years, physics-based computer models have been increasingly applied to design the drop-on-demand (DOD) inkjet devices. The initial design stage for these devices often requires a fast turnaround time of computer models, because it usually involves a massive screening of a large number of design parameters. Thus, in the present study, a 1D model is developed to achieve the fast prediction of droplet ejection process from DOD devices, including the droplet breakup and coalescence. A popular 1D slender-jet method (Egger, 1994) is adopted in this study. The fluid dynamics in the nozzle region is described by a 2D axisymmetric unsteady Poiseuille flow model. Droplet formation and nozzle fluid dynamics are coupled, and hence solved together, to simulate the inkjet droplet ejection. The arbitrary Lagrangian–Eulerian method is employed to solve the governing equations. Numerical methods have been proposed to handle the breakup and coalescence of droplets. The proposed methods are implemented in an in-house developed MATLAB code. A series of validation examples have been carried out to evaluate the accuracy and the robustness of the proposed 1D model. Finally, a case study of the inkjet droplet ejection with different Ohnesorge number (Oh) is presented to demonstrate the capability of the proposed 1D model for DOD inkjet process. Our study has shown that 1D model can significantly reduce the computational time (usually less than one minute) yet with acceptable accuracy, which makes it very useful to explore the large parameter space of inkjet devices in a short amount of time.

Investigation of the primary breakup length and instability of non-Newtonian viscoelastic liquid jets

Abstract: The temporal instability and primary breakup length of a non-Newtonian viscoelastic liquid jet moving in an inviscid gaseous environment were carried out by solving a set of linearized Navier-Stokes equations and employing the linear viscoelastic model, respectively. The dimensionless dispersion equation that governs the instability was derived and solved by a numerical method. The effects of fluid properties on the instability and primary breakup length of viscoelastic liquid jets were carried out. It could be seen that by increasing the growth rate, the instability range and the primary breakup length of the viscoelastic liquid jets could result in an increase in the liquid Weber number and the ratio of gas to liquid density. Moreover, the significant findings are that an increase in the time constant ratio, and also the Ohnesorge number reduced both of the growth rates of disturbances and primary breakup length. Though, increasing the elasticity number resulted in a higher growth rate of disturbances and enhanced the breakup mechanism.

An experimental study on oil droplet size distribution in subsurface oil releases

Abstract: Oil droplet size distribution (ODSD) plays a critical role in the rising velocity and transport of oil droplets in subsurface oil releases. In this paper, subsurface oil release experiments were conducted to study ODSD under different experimental conditions in a laboratory water tank observed by two high-speed cameras in March and April 2017. The correlation formulas Oh=10.2Re–1 and Oh=39.2Re–1 (Re represents Reynolds number and Oh represents Ohnesorge number) were established to distinguish the boundaries of the three instability regimes in dimensionless space based on the experimental results. The oil droplet sizes from the experimental data showed an excellent match to the Rosin–Rammler distribution function with determination coefficients ranging from 0.86 to 1.00 for Lvda 10-1 oil. This paper also explored the influence factors on and change rules of oil droplet size. The volume median diameter d50 decreased steadily with increasing jet velocity, and a sharp decrease occurred in the laminar-breakup regime. At Weber numbers (We) <100, the orifice diameter and oil viscosity appeared to have a large influence on the mean droplet diameter. At 100

Ejection of Droplets from a Bursting Bubble on a Free Liquid Surface-A Dimensionless Criterion for "Jet" Droplets.

Abstract: This work examines the ejection of droplets from a bursting gas bubble on a free liquid surface, both experimentally and numerically. We explore the physical processes which govern the bursting of bubbles and the subsequent formation of "jet" droplets. We present new relationships regarding the dependence of jet drop formation on bubble diameter. Furthermore, we propose a new dimensionless parameter to describe the region of properties where "jet" drops will occur. This parameter, termed the droplet number ( Dn), complements existing parameters defining jet drop formation, namely, a maximum Ohnesorge number and a maximum Bond number.

On retraction of a ruptured film and the viscous effects

Abstract: A numerical study is conducted on film retraction (or hole expanding) after the film is ruptured. A finite element method coupled with phase field model (governed by the Cahn-Hilliard equation) is applied. It is found that our method can successfully reproduce the film retraction process. Two modes of the retraction are found depending on viscous effect. When the viscous effect is small (mode II), a “ring-like” ridge appears at the end of the film. Between the ridge and the undisturbed part of the film, there is a necking region. When the viscous effect is strong, there are no necking regions (mode I), and the film thickness decreases gradually from the ridge. The two modes can be characterized by Ohnesorge number, with the critical value around 0.1. Our results show that the neck region thinners linearly in mode II in the early age. A very rough estimation of the breaking time can be obtained by extrapolating the measured data at around t B = 16 ρ l e 3 / γ . In the expression, ρ l , e , γ denote the liquid density, half of the film thickness, and the interfacial tension, respectively. In a later stage, the concave interface leads to a capillary pressure pointing outward, and further decelerates the thinning process. During this stage, the capillary number, denoting the ratio between the viscous stress and capillary force, is greatly smaller than unity. On the other hand, we also note that the previous theoretical model, which predicts the expanding speed of the hole, mainly concerns the later retraction stage. In the stage, the entrained liquid volume from the film into the ridge can be neglected. We modified the theory with considering of the ridge growth in early stage. The prediction is consistent with the numerical results very well. The analyses show that the viscous effects play subtle roles during the film retraction process, even when Ohnesorge number is very small: half of the released surface energy is dissipated.

Visualization study on coalescence of droplets with different sizes in external liquid

Abstract: We experimentally investigate the coalescence between two droplets with different sizes in the surrounding water via high-speed visualization. We identify three coalescence patterns by clarifying the dynamic interface evolutions, including liquid bridge evolution, capillary wave propagation, and pinch-off behaviours. The results indicate that the coalescence patterns are directly related to the propagation of capillary waves on the coalescent droplet, which is governed by the competition among the capillary force, viscous force, and inertia involved in the draining from the original droplets into the liquid bridge. The external water can efficiently damp the oscillation in capillary wave propagation after the coalescence. In the inertial regime after the droplet coalescence, the evolution of liquid bridge is observed to follow a linear scaling law, when the capillary force induced by the azimuthal interface of the liquid bridge drives the liquid bridge expansion. Accordingly, a phase diagram is organized to characterize these coalescence patterns depending on Ohnesorge number, relative viscosity between external water and droplet, and size ratio between two coalesced droplets. This article is protected by copyright. All rights reserved

Self-propelled upspring jump regime in nanoscale droplet collisions: a molecular dynamics study

Abstract: Self-propelled jump of droplets is among the most striking phenomena in droplet collisions on substrates. Self-propelled jump phenomena of droplets have been observed in experiments, which have also been reproduced in macro- or mesoscale numerical simulations. However, there have been few previous studies on the phenomena at nanoscales. To unravel the dynamics and mechanisms of nanoscale binary droplet collisions on substrates, head-on collision processes of two identical water droplets with diameters of 10nm on graphite substrates are investigated by molecular dynamics (MD) simulations. By varying the impact Reynolds number of binary droplet collisions on hydrophilic or hydrophobic substrates, we successfully reproduce self-propelled jump of droplets on a super-hydrophobic surface with a contact angle of 143◦ and a relatively high impact Reynolds number of 17.5. Parametric studies indicate that both high impact Reynolds numbers and high hydrophobicity promote self-propelled jump. Moreover, the criterion based on the Ohnesorge number derived from the mesoscopic self-propelled jump regime is insufficient to precisely predict a nanoscale self-propelled jump phenomenon. For this reason, our study includes the impact Reynolds number and the substrate properties like contact angle as additional criteria to refine and extend the current theory for the self-propelled jump behaviours to nanoscales. The study provides insight into the mechanism of self-propelled jump phenomenon at nanoscales.

Thermocapillary instability of a liquid sheet with centrifugal force

Abstract: The thermocapillary instability of liquid sheets subjected to a temperature gradient that is perpendicular to the gas–liquid interface and moving in a gas medium is investigated in this paper. A linear instability analysis accounting for the weak form of the centrifugal force along the flow direction is proposed. The instability of liquid sheets with a temperature gradient is compared to that of isothermal liquid sheets, and the effect of the temperature difference is analyzed. The effect of the centrifugal force is also investigated. Furthermore, the effect of the density ratio, viscosity of liquid sheet and Weber number are also discussed by solving the dispersion equation. The results show that, when the thermocapillary effects are taken into account, the temporal growth rate of the varicose mode can become greater than that of the sinuous mode, in contrast to the condition of an isothermal liquid sheet. When the Marangoni number is relatively small, the swirl decreases the maximum growth rate for the sinuous mode. In other conditions, the swirl has only minor effects on the stability of the liquid sheets. The increase of the density ratio and Weber number enhances the instability of the sheets, while the increased Prandtl number has the opposite effect. The effect of the Ohnesorge number is relatively complicated.

Breakup of finite-size liquid filaments: Transition from no-breakup to breakup including substrate effects

Abstract: This work studies the breakup of finite-size liquid filaments, when also including substrate effects, using direct numerical simulations. The study focuses on the effects of three parameters: Ohnesorge number, the ratio of the viscous forces to inertial and surface tension forces, the liquid filament aspect ratio, and where there is a substrate, a measure of the fluid slip on the substrate, i.e. slip length. Through these parameters, it is determined whether a liquid filament breaks up during the evolution toward its final equilibrium state. Three scenarios are identified: a collapse into a single droplet, the breakup into one or multiple droplets, and recoalescence into a single droplet after the breakup (or even possibly another breakup after recoalescence). The results are compared with the ones available in the literature for free-standing liquid filaments. The findings show that the presence of the substrate promotes breakup of the filament. The effect of the degree of slip on the breakup is also discussed. The parameter domain regions are comprehensively explored when including the slip effects. An experimental case is also carried out to illustrate the collapse and breakup of a finite-size silicon oil filament supported on a substrate, showcasing a critical length of the breakup in a physical configuration. Finally, direct numerical simulations reveal striking new details into the breakup pattern for low Ohnesorge numbers, where the dynamics are fast and the experimental imaging is not available; our results therefore significantly extend the range of Ohnesorge number over which filament breakup has been considered.