Internal instability of thin liquid sheets
TL;DR: In this article, a linear stability analysis of an inviscid liquid sheet with different velocity profiles across its thickness is reported, and the velocity profiles for which there is a progressive increase or decrease in velocities between the two interfaces are demonstrated to be inherently unstable even in the absence of the destabilizing aerodynamic shear at the liquid-gas interfaces.
Abstract: Linear stability analysis of an inviscid liquid sheet with different velocity profiles across its thickness is reported. The velocity profiles for which there is a progressive increase or decrease in velocities between the two interfaces are demonstrated to be inherently unstable even in the absence of the destabilizing aerodynamic shear at the liquid-gas interfaces. Compared to a flat velocity profile, a linear or a parabolic profile, symmetric at the center line of the sheet reduced both the maximum growth rate and the wavelength range over which the waves grow. The convective acceleration from the velocity gradient is found to stabilize longer waves while the growth of shorter waves is hampered by the combined effect of the surface tension and a decrease in the interface velocity between gas and liquid media. The wave forms are dominantly sinuous for symmetric velocity profiles; however, with larger velocity gradients the dilatational modes are observed. The inherent instability of liquid sheets with a progressive change in velocities between the interfaces is seen to arise from the differential convective acceleration at the two interfaces in the plane of reference of the liquid sheets.
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TL;DR: The findings will contribute to clarifying the interplay between graphene and Cu crystal faces, and reducing surface roughness of graphene by engineering the crystallographic orientation of Cu substrates.
Abstract: Corrugation is a ubiquitous phenomenon for graphene grown on metal substrates by chemical vapor deposition, which greatly affects the electrical, mechanical, and chemical properties. Recent years have witnessed great progress in controlled growth of large graphene single crystals; however, the issue of surface roughness is far from being addressed. Here, the corrugation at the interface of copper (Cu) and graphene, including Cu step bunches (CuSB) and graphene wrinkles, are investigated and ascribed to the anisotropic strain relaxation. It is found that the corrugation is strongly dependent on Cu crystallographic orientations, specifically, the packed density and anisotropic atomic configuration. Dense Cu step bunches are prone to form on loose packed faces due to the instability of surface dynamics. On an anisotropic Cu crystal surface, Cu step bunches and graphene wrinkles are formed in two perpendicular directions to release the anisotropic interfacial stress, as revealed by morphology imaging and vibrational analysis. Cu(111) is a suitable crystal face for growth of ultraflat graphene with roughness as low as 0.20 nm. It is believed the findings will contribute to clarifying the interplay between graphene and Cu crystal faces, and reducing surface roughness of graphene by engineering the crystallographic orientation of Cu substrates.
41 citations
TL;DR: In this article, the authors present a comprehensive modeling of spray formation in liquid fuel injectors, including internal hydrodynamics of fuel injector, break up of liquid sheet leading to primary and secondary atomization and prediction of size and velocity distributions of droplets in the spray.
Abstract: Comprehensive modeling of spray formation in liquid fuel injectors involves modeling of (i) internal hydrodynamics of fuel injector (ii) break up of liquid sheet leading to primary and secondary atomization and (iii) prediction of size and velocity distributions of droplets in the spray. Comprehensive models addressing all the three aspects are rare though some work has been reported that incorporate two of the three aspects. However, significant volume of literature exists on the individual modules. In the present work, progress and current trends in the individual modules have been extensively reviewed and their implications on development of comprehensive models have been discussed. The unresolved issues and future research directions are also indicated.
17 citations
Cites background from "Internal instability of thin liquid..."
...The effect of lateral wave modes on the spatial growth of longitudinal waves was determined by Tharakan and Ramamurthi [105]....
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...The effect of 3D disturbances on stability of planar liquid sheets 138 Trends in Comprehensive Modeling of Spray Formation was investigated by Tharakan and Ramamurthi [105] for different gas velocities over the liquid sheet interfaces....
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...Linear analysis of a planar liquid sheet exposed to unequal gas velocities was extended by Tharakan and Ramamurthi [105] to include simultaneous presence of longitudinal and lateral waves, a configuration which is likely to occur in practical devices....
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...Tharakan and Ramamurthi [117] investigated the effect of compressibility of liquid and gas on the instability of a planar liquid sheet exposed to unequal gas velocities....
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...Rao and Ramamurthi [94] showed that axisymmetric axial velocity profiles to be more stable compared to a constant velocity liquid sheet travelling at velocity corresponding to the mean of the varying velocities....
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TL;DR: In this article, the presence of a liquid phase on a copper surface during graphene growth by chemical vapour deposition at temperatures of 1000 and 1050 °C has been experimentally obtained, and it was established that the liquid phase formed a groove structure and bubble-like nanoobjects on the copper surface.
Abstract: Evidence for the presence of a liquid phase on a copper surface during graphene growth by chemical vapour deposition at temperatures of 1000 and 1050 °C has been experimentally obtained. It was established that, first, the liquid phase forms a groove structure and bubble-like nanoobjects on the copper surface. Second, the liquid phase promotes the propagation of the wavy relief of a growing graphene film to the adjacent copper, and, third, the surface flows of the liquid phase can influence the waviness and orientation of the graphene islands. From the obtained data, it was concluded that surface melting plays an important role in graphene formation by chemical vapour deposition at temperatures below the melting point of copper.
16 citations
TL;DR: In this article, a two phase spatially oscillating planar jet in a quiescent air was modeled by solving the Navier-Stokes equations and using the volume of fluid method to track the air-water interface.
Abstract: The liquid jet when perturbed sinusoidally will lead to instability under certain conditions. Understanding the causes and consequences of such a behavior is still obscure. Hence, numerical investigations are reported in the present study for a two phase spatially oscillating planar jet in a quiescent air. Simulations are performed by solving the Navier-Stokes equations and using the volume of fluid method to track the air-water interface. It is demonstrated that an increase in amplitude of oscillation is caused due to the formation of a low pressure region created by the vortical structures in air near the leading edge of the jet when deflected. This two way coupling between air and water is analyzed with the help of enstrophy, divergence of the Lamb vector, and vortex forces. It is found through a parametric study that surface tension and viscosity stabilize the perturbations in an oscillating planar jet. On the other hand, an increase in Froude number (Fr) initially leads to an augmentation of perturbation amplitude and later causes its damping when surface tension forces become dominant. The numerical analysis for different inlet velocity profiles establishes that the jet is more stable when subjected to a parabolic inlet velocity profile as compared to a uniform profile due to lower relative velocity at the interface. The present work also reveals the role of capillary instability in addition to Kelvin-Helmholtz and Rayleigh-Taylor instabilities that induce primary breakup in the jet.
16 citations
TL;DR: In the presence of the slot, the variation of the radial breakup distance of the circular sheet with Wejet changed from the monotonically decreasing trend (Rb,CS∼Wejet−0.44) to a nonmonotonic increasing and decreasing one.
Abstract: The radially expanding twin (circular and vertical) liquid sheets produced by impingement of a vertical cylindrical liquid jet onto a horizontally placed cone-disk deflector with a single slot were examined experimentally in the present work. Dynamics of these liquid sheets and the events leading to their breakup were studied by carrying out high-speed shadowgraphy simultaneously from side, front, and top views at a 5.4 kHz framing rate and for the jet Weber number (Wejet) range of 993 < Wejet < 3776. In the presence of the slot, the variation of the radial breakup distance of the circular sheet (Rb,CS) with Wejet changed from the monotonically decreasing trend (Rb,CS∼Wejet−0.44) to a nonmonotonic increasing and decreasing one. Furthermore, Rb,CS was found to be lowered by about 42% compared to the breakup distance Rb,CS,no-slot of the circular sheet for the no-slot deflector. The vertical sheet breakup distance (Rb,Vs) was found to increase monotonically with the slot Weber number Weslot0.44. Three primary sources of droplet production, namely, the lower and front edges of the vertical sheet and the rim of the circular sheet, were identified. The smallest droplets were seen to originate from the front edge (D32,FE) and the largest droplets from the lower edge (D32,LE) of the vertical sheet. The measured droplet diameters followed D32,LE∼Wejet−1/3 and D32,FE∼Wejet−1/4, whereas the droplets originating at the rim of the circular sheet followed D32,rim∼Wejet−2/3. The droplets at all three edges were found to depend more strongly on the ligament thickness than the ligament length. Following conservation of mass, a linear relation between the droplet diameter, D32, and the ligament thickness, tlig, at each edge has been obtained.The radially expanding twin (circular and vertical) liquid sheets produced by impingement of a vertical cylindrical liquid jet onto a horizontally placed cone-disk deflector with a single slot were examined experimentally in the present work. Dynamics of these liquid sheets and the events leading to their breakup were studied by carrying out high-speed shadowgraphy simultaneously from side, front, and top views at a 5.4 kHz framing rate and for the jet Weber number (Wejet) range of 993 < Wejet < 3776. In the presence of the slot, the variation of the radial breakup distance of the circular sheet (Rb,CS) with Wejet changed from the monotonically decreasing trend (Rb,CS∼Wejet−0.44) to a nonmonotonic increasing and decreasing one. Furthermore, Rb,CS was found to be lowered by about 42% compared to the breakup distance Rb,CS,no-slot of the circular sheet for the no-slot deflector. The vertical sheet breakup distance (Rb,Vs) was found to increase monotonically with the slot Weber number Weslot0.44. Three prima...
7 citations
References
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TL;DR: In this paper, the stability of a thin layer of liquid moving in still air is studied theoretically with the object of throwing light on the break-up of films during atomization, and it is found that instability occurs if W = T/ρ 1U2h < 1 and that the wavelength for maximum growth factor, for W « 1, is λ = (4πT/ρ 2U2U2).
Abstract: The stability of a thin layer of liquid moving in still air is studied theoretically with the object of throwing light on the break-up of films during atomization. It is found that instability occurs if W = T/ρ1U2h < 1 and that the wavelength for maximum growth factor, for W « 1, is λ = (4πT/ρ2U2) where ρ1 is the liquid density, ρ2 is the air density, U is the film velocity, 2h is the film thickness and T is the surface tension of the liquid. Comparison with experimental data shows fair agreement with the observed wavelengths.
500 citations
TL;DR: In this paper, a review of the early atomization step of liquid spray can be found, where the main instability mechanisms, which control primary breakup processes, are rather well described, as well as the significant parameters they depend on.
Abstract: The production of a liquid spray can be summarized as the succession of the following three steps; the liquid flow ejection, the primary breakup mechanism and the secondary breakup mechanism. The intermediate step—the primary breakup mechanism—covers the early liquid flow deformation down to the production of the first isolated liquid fragments. This step is very important and requires to be fully understood since it constitutes the link between the flow issuing from the atomizer and the final spray. This paper reviews the experimental investigations dedicated to this early atomization step. Several situations are considered: cylindrical liquid jets, flat liquid sheets, air-assisted cylindrical liquid jets and air-assisted flat liquid sheets. Each fluid stream adopts several atomization regimes according to the operating conditions. These regimes as well as the significant parameters they depend on are listed. The main instability mechanisms, which control primary breakup processes, are rather well described. This review points out the internal geometrical nozzle characteristics and internal flow details that influence the atomization mechanisms. The contributions of these characteristics, which require further investigations to be fully identified and quantified, are believed to be the main reason of experimental discrepancies and explain a lack of universal primary breakup regime categorizations.
350 citations
Book•
01 Jan 2003TL;DR: In this article, the authors discuss the role played by interfacial shear in the role of a viscous jet and its role in liquid sheet breaking and nonlinear capillary instability of liquid jets and sheets.
Abstract: Notation list Preface 1. Introduction 2. Uniform inviscid liquid sheets 3. Nonuniform inviscid liquid sheets 4. Viscous liquid sheets 5. Waves on liquid sheets 6. Phenomena of jet breakup 7. Inviscid jets 8. A viscous jet 9. Roles played by interfacial shear 10. Annular liquid jets 11. Nonlinear capillary instability of liquid jets and sheets 12. Epilogue Appendices Author index Subject Index.
236 citations
212 citations
TL;DR: In this paper, a theoretical and computational investigation of the inviscid Kelvin-Helmholtz instability of a two-dimensional fluid sheet is presented, including the effect of surface tension and the density difference between the fluid in the sheet and the surrounding fluid.
Abstract: A theoretical and computational investigation of the inviscid Kelvin–Helmholtz instability of a two‐dimensional fluid sheet is presented. Both linear and nonlinear analyses are performed. The study considers the temporal dilational (symmetric) and sinuous (antisymmetric) instability of a sheet of finite thickness, including the effect of surface tension and the density difference between the fluid in the sheet and the surrounding fluid. Previous linear‐theory results are extended to include the complete range of density ratios and thickness‐to‐wavelength ratios. It is shown that all sinuous waves are stable when the dimensionless sheet thickness is less than a critical value that depends on the density ratio. At low density ratios, the growth rate of the sinuous waves is larger than that of the dilational waves, in agreement with previous results. At higher density ratios, it is shown that the dilational waves have a higher growth rate. The nonlinear calculations indicate the existence of sinuous oscillating modes when the density ratio is of the order of 1. Sinuous modes may result in ligaments interspaced by half of a wavelength. Dilational modes grow monotonically and may result in ligaments interspaced by one wavelength.
130 citations