Showing papers on "Ohnesorge number published in 2016"

Capillary breakup of a liquid bridge : identifying regimes and transitions

Abstract: Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular viscous-inertial balances, that is different limits of the Ohnesorge number Oh. To accurately establish the transitions between regimes, the minimum bridge radius is resolved through four orders of magnitude using a purpose-built multiscale finite element method. This allows us to construct a quantitative phase diagram for the breakup phenomenon which includes the appearance of a recently discovered low-Oh viscous regime. The method used to quantify the accuracy of the similarity solutions allows us to identify a number of previously unobserved features of the breakup, most notably an oscillatory convergence towards the viscous-inertial similarity solution. Finally, we discuss how the new findings open up a number of challenges for both theoretical and experimental analysis.

Electrokinetics of isolated electrified drops

Abstract: Using a recently developed multiphase electrokinetic model, we simulate the transient electrohydrodynamic response of a liquid drop containing ions, to both small and large values of electric field. The temporal evolution is found to be governed primarily by two dimensionless groups: (i) Ohnesorge number (Oh), a ratio of viscous to inertio-capillary effects, and (ii) inverse dimensionless Debye length (κ), a measure of the diffuse regions of charge that develop in the drop. The effects of dielectric polarization dominate at low Oh, while effects of separated charge gain importance with increase in Oh. For small values of electric field, the deformation behaviour of a drop is shown to be accurately described by a simple analytical expression. At large electric fields, the drops are unstable and eject progeny drops. Depending on Oh and κ this occurs via dripping or jetting; the regime transitions are shown by a Oh-κ phase map. In contrast to previous studies, we find universal scaling relations to predict size and charge of progeny drops. Our simulations suggest charge transport plays a significant role in drop dynamics for 0.1 ≤ Oh ≤ 10, a parameter range of interest in microscale flows.

Electrohydrodynamics of a viscous drop with inertia

Abstract: Most of the existing numerical and theoretical investigations on the electrohydrodynamics of a viscous drop have focused on the creeping Stokes flow regime, where nonlinear inertia effects are neglected. In this work we study the inertia effects on the electrodeformation of a viscous drop under a DC electric field using a novel second-order immersed interface method. The inertia effects are quantified by the Ohnesorge number $\text{Oh}$, and the electric field is characterized by an electric capillary number ${\text{Ca}}_{E}$. Below the critical ${\text{Ca}}_{E}$, small to moderate electric field strength gives rise to steady equilibrium drop shapes. We found that, at a fixed ${\text{Ca}}_{E}$, inertia effects induce larger deformation for an oblate drop than a prolate drop, consistent with previous results in the literature. Moreover, our simulations results indicate that inertia effects on the equilibrium drop deformation are dictated by the direction of normal electric stress on the drop interface: Larger drop deformation is found when the normal electric stress points outward, and smaller drop deformation is found otherwise. To our knowledge, such inertia effects on the equilibrium drop deformation has not been reported in the literature. Above the critical ${\text{Ca}}_{E}$, no steady equilibrium drop deformation can be found, and often the drop breaks up into a number of daughter droplets. In particular, our Navier-Stokes simulations show that, for the parameters we use, (1) daughter droplets are larger in the presence of inertia, (2) the drop deformation evolves more rapidly compared to creeping flow, and (3) complex distribution of electric stresses for drops with inertia effects. Our results suggest that normal electric pressure may be a useful tool in predicting drop pinch-off in oblate deformations.

Capillary Breakup of a Liquid Bridge: Identifying Regimes and Transitions

Abstract: Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular viscous-inertial balances, that is different limits of the Ohnesorge number $Oh$. To accurately establish the transitions between regimes, the minimum bridge radius is resolved through four orders of magnitude using a purpose-built multiscale finite element method. This allows us to construct a quantitative phase diagram for the breakup phenomenon which includes the appearance of a recently discovered low-$Oh$ viscous regime. The method used to quantify the accuracy of the similarity solutions allows us to identify a number of previously unobserved features of the breakup, most notably an oscillatory convergence towards the viscous-inertial similarity solution. Finally, we discuss how the new findings open up a number of challenges for both theoretical and experimental analysis.

A computational study of high-speed microdroplet impact onto a smooth solid surface

Abstract: Numerical solutions of high-speed microdroplet impact onto a smooth solid surface are computed, using the interFoam VoF solver of the OpenFOAM CFD package. Toward the solid surface, the liquid microdroplet is moving with an impinging gas flow, simulating the situation of ink droplets being deposited onto substrate with a collimated mist jet in the Optomec Aerosol Jet printing process. The computed values of maximum spread factor, for the range of parameters of practical interest to Aerosol Jet printing, were found in very good agreement with some of the correlation formulas proposed by previous authors in the literature. Combining formulas selected from different authors with appropriate modifications yields a maximum spread factor formula that can be used for first-order evaluations of deposited in droplet size during the Aerosol Jet technology development. The computational results also illustrate droplet impact dynamics with lamella shape evolution throughout the spreading, receding-relaxation, and wetting equilibrium phases, consistent with that observed and described by many previous authors. This suggests a scale-invariant nature of the basic droplet impact behavior such that experiments with larger droplets at the same nondimensional parameter values may be considered for studying microdroplet impact dynamics. Significant free surface oscillations can be observed when the droplet viscosity is relatively low. The border line between periodic free surface oscillations and aperiodic creeping to capillary equilibrium free surface shape appears at the value of Ohnesorge number around 0.25. Droplet bouncing after receding is prompted with large contact angles at solid surface (as consistent with findings reported in the literature), but can be suppressed by increasing the droplet viscosity.

Response of driven sessile drops with contact-line dissipation

Abstract: A partially-wetting sessile drop is driven by a sinusoidal pressure field that produces capillary waves on the liquid/gas interface. Response diagrams and phase shifts for the droplet, whose contact-line moves with contact-angle that is a smooth function of the contact line speed, are reported. Contact-line dissipation originating from the contact-line speed condition leads to damping for drops with finite contact-line mobility, even for inviscid fluids. The critical mobility and associated driving frequency to generate the largest contact-line dissipation is computed. Viscous dissipation is approximated using the irrotational flow and the critical Ohnesorge number bounding regions beyond which a given mode becomes over-damped is computed. Regions of modal coexistence where two modes can be simultaneously excited by a single forcing frequency are identified. Predictions compare favorably to related experiments on vibrated drops.

Linear dynamics modelling of droplet deformation in a pulsatile electric field

Abstract: A linear dynamic model of water droplet deformation in the presence of an electric field has been developed. Analytical solutions of the differential equation of motion are provided with different waveforms as forcing terms, namely in the case of half-sinusoidal, square and sawtooth waves. The main dimensionless groups are identified as a result of this analysis. The predictions of the model are compared with some data of droplet deformation available in the literature. The calculations based on this model show that the waveform affects the response of the droplet to the electric field stimulus. Resonance is possible only when the droplets are sufficiently large (i.e. for Ohnesorge number less than 1). The oscillation amplitude decreases rapidly with the electric field frequency. A qualitative comparison with some experiments of droplet-interface coalescence available in the literature has also been addressed, suggesting a correlation between the formation of secondary droplets and the amplitude of oscillation of the mother droplet. The outcomes of this analysis can be useful for the selection of the best operating conditions to improve the electrocoalescence process efficiency, as they can provide guidelines to the choice of the most suitable electric field parameters.

Numerical Models for Viscoelastic Liquid Atomization Spray

Abstract: Atomization spray of non-Newtonian liquid plays a pivotal role in various engineering applications, especially for the energy utilization. To operate spray systems efficiently and well understand the effects of liquid rheological properties on the whole spray process, a comprehensive model using Euler-Lagrangian approaches was established to simulate the evolution of the atomization spray for viscoelastic liquid. Based on the Oldroyd model, the viscoelastic linear dispersion relation was introduced into the primary atomization; an extended viscoelastic version of Taylor analogy breakup (TAB) model was proposed; and the coalescence criteria was modified by rheological parameters, such as the relaxation time, the retardation time and the zero shear viscosity. The predicted results are validated with experimental data varying air-liquid mass flow ratio (ALR). Then, numerical calculations are conducted to investigate the characteristics of viscoelastic liquid atomization process. Results showed that the evolutionary trend of droplet mean diameter, Weber number and Ohnesorge number of viscoelastic liquids along with axial direction were qualitatively similar to that of Newtonian liquid. However, the mean size of polymer solution increased more gently than that of water at the downstream of the spray, which was beneficial to stable control of the desirable size in the applications. As concerned the effects of liquid physical properties, the surface tension played an important role in the primary atomization, which indicated the benefit of selecting the solvents with lower surface tension for finer atomization effects, while, for the evolution of atomization spray, larger relaxation time and zero shear viscosity increased droplet Sauter mean diameter (SMD) significantly. The zero shear viscosity was effective throughout the jet region, while the effect of relaxation time became weaken at the downstream of the spray field.

Study of Liquid Breakup Process in Solid Rocket Motors

Abstract: In a solid rocket motor, when the aluminum based propellant combusts, the fuel is oxidized into alumina (Al2O3). It tends to agglomerate into molten droplets, impinge on the chamber walls, and then flow along the nozzle wall. Such agglomerates cause erosive damage. The focus of the current research is to characterize the agglomerate flow within the nozzle section by studying the breakup process of the liquid film that flows along the wall of a straight test channel while a relatively higher-speed gas moves over it. We have used an unsteady-flow Reynolds-averaged Navier–Stokes code to investigate the interaction of the liquid film flow with the gas flow. The rate of the wave breakup was characterized by introducing breakup length, Ohnesorge number, and Weber number for various flow conditions. Based on the volume fraction of the liquid, these three numbers are indicators of the level of liquid breakup. We summarize that a larger breakup length relates to a high breakup state of the liquid because the appea...

The necking time of gas bubbles in liquids of arbitrary viscosity

Abstract: We report an experimental and theoretical study of the collapse time of a gas bubble injected into an otherwise stagnant liquid under quasi-static conditions and for a wide range of liquid viscosities. The experiments were performed by injecting a constant flow rate of air through a needle with inner radius a into several water/glycerine mixtures, providing a viscosity range of 20 cP ≲ μ ≲ 1500 cP. By analyzing the temporal evolution of the neck radius, R0(t), the collapse time has been extracted for three different stages during the collapse process, namely, Ri/a = 0.6, 0.4, and 0.2, being Ri = R0(t = 0) the initial neck radius. The collapse time is shown to monotonically increase with both Ri/a and with the Ohnesorge number, Oh=μ/ρσRi, where ρ and σ represent the liquid density and the surface tension coefficient, respectively. The theoretical approach is based on the cylindrical Rayleigh-Plesset equation for the radial liquid flow around the neck, which is the appropriate leading-order representation o...

Two-Pronged Jet Formation Caused by Droplet Impact on Anisotropic Superhydrophobic Surfaces

Abstract: When a liquid droplet impacts a superhydrophobic surface with anisotropic surface patterning in the form of alternating ribs and cavities, the rebounding droplet may exhibit a unique two-pronged jet emission. Droplet impact experiments with 11 different fluids of viscosity that varied by more than three orders of magnitude were conducted, and this paper quantifies the Capillary number, Ca, and Ohnesorge number, Oh, ranges over which the two-pronged phenomenon occurs. For Oh > 0.0154, the behavior was never observed, while at lower values of Oh, the behavior occurs for an intermediate range of Ca that depends on Oh.

Dynamics of sessile drops. Part 3. Theory of forced oscillations

Abstract: A partially-wetting sessile drop is driven by a sinusoidal pressure field that produces capillary waves on the liquid/gas interface. The analysis presented in Part 1 of this series (Bostwick & Steen 2014) is extended by computing response diagrams and phase shifts for the viscous droplet, whose three phase contact-line moves with contact-angle that is a smooth function of the contact line speed. Viscous dissipation is incorporated through the viscous potential flow approximation and the critical Ohnesorge number bounding regions beyond which a given mode becomes over-damped is computed. Davis dissipation originating from the contact-line speed condition leads to damped oscillations for drops with finite contact-line mobility, even for inviscid fluids. The critical mobility and associated driving frequency to generate the largest Davis dissipation is computed. Lastly, regions of modal coexistence where two modes can be simultaneously excited by a single forcing frequency are identified. Predictions compare favorably to related experiments on vibrated drops.