Showing papers on "Ohnesorge number published in 2011"

Wolfgang von Ohnesorge

Abstract: This manuscript got started when one of us (G.H.M.) presented a lecture at the Institute of Mathematics and its Applications at the University of Minnesota. The presentation included a photograph of Rayleigh and made frequent mention of the Ohnesorge number. When the other of us (M.R.) enquired about a picture of Ohnesorge, we found out that none were readily available on the web. Indeed, little about Ohnesorge is available from easily accessible public sources. A good part of the reason is certainly that, unlike other “numbermen” of fluid mechanics, Ohnesorge did not pursue an academic career. The purpose of this article is to fill the gap and shed some light on the life of Wolfgang von Ohnesorge. We shall discuss the highlights of his biography, his scientific contributions, their physical significance, and their impact today.

A numerical analysis of drop impact on liquid film by using a level set method

Abstract: Splashing and spreading of a liquid by drop impact on liquid film depends on the impact velocity, drop size, drop properties and liquid film thickness. These parameters can be summarized by three main dimensionless parameters: Weber number, Ohnesorge number and non-dimensional film thickness. Upon impact of a drop on liquid film, these parameters influence the shape of the splash and the forma- tion and propagation of the crown. In the present study, the splashing and spreading resulting from drop impact on liquid film has been numerically investigated by using a Level Set method for the interface tracking of the two-phase flow simulation. For various dimen- sionless parameters, characteristics of the crown formation and spreading were predicted, and the results were found to show good agreement with available experimental data in the earlier stage of crown formation and show some discrepancies in the later stage of crown spreading due to the present 2D axi-symmetric computation, which cannot predict the secondary drops.

Secondary breakup of coal water slurry drops

Abstract: To investigate secondary atomization of coal water slurry (CWS), deformation and breakup of eight kinds of CWS drops are presented using high speed digital camera. Based on morphology, deformation and breakup regimes of CWS drops can be termed some different modes: deformation, multimode breakup (including two sub-modes: hole breakup and tensile breakup), and shear breakup. Correlations on the ranges of breakup modes are also obtained. The conventional Weber number and Ohnesorge number are found to be insufficient to classify all breakup modes of CWS drops, so two other non-dimensional numbers based on rheology of CWS are suggested to use in the deformation and breakup regime map. Finally, total breakup time is studied and correlated, which increases with Ohnesorge number.

Experimental Study of Drop Size Distribution in the Bag Breakup Regime

Abstract: The situation of a liquid drop exposed to a continuous air jet flow was investigated experimentally. The drop bag breakup of test liquids which included water, ethanol, and various glycerol mixtures was observed using a high-speed camera. The morphological change, such as drop deformation, was observed and analyzed. Mean fragment sizes were obtained, which were in good agreement with those reported in the literature. Big fragments formed from the ring contained the great mass of the initial drop and were studied in detail, and correlations on fragment mean size and number were obtained. Mean size decreased with the Weber number and increased with the Ohnesorge number; fragment number was in contrast to mean size. Fragment size distribution was another useful parameter. Our results showed that fragment size distribution based on the number formed from the ring was a gamma distribution. Fragment size distribution based on the number formed from the whole drop was an exponential distribution. We also investi...

Asymptotic behavior of a retracting two-dimensional fluid sheet

Abstract: Two-dimensional (2D) capillary retraction of a viscous liquid film is studied using numerical and analytical approaches for both diphasic and free surface flows. Full 2D Navier-Stokes equations are integrated numerically for the diphasic case, while one-dimensional (1D) free surface model equations are used for free surface flows. No pinch-off is observed in the film in any of these cases. By means of an asymptotic matching method on the 1D model, we derive an analytical expansion of the film profile for large times. Our analysis shows that three regions with different timescales can be identified during retraction: the rim, the film, and an intermediate domain connecting these two regions. The numerical simulations performed on both models show good agreement with the analytical results. Finally, we report the appearance of an instability in the diphasic retracting film for small Ohnesorge number. We understand this as a Kelvin-Helmholtz instability arising due to the formation of a shear layer in the ne...

Investigation of droplets impinging on a deep pool: transition from coalescence to jetting

Abstract: An experimental investigation of droplets impinging vertically on a deep liquid pool of the same fluid was conducted. Coalescence and jetting as two of the main regimes were identified and studied. Five fluids, distilled water, technical ethanol, n-pentane, methanol and 1-propanol were used for providing different liquid-phase physical properties with density from 600 to 1,000 kg/m3, viscosity from 0.20 to 2.00 mPa s, and surface tension from 13.7 to 72.0 mN/m. Except for the experimental run of n-pentane, which was carried out in n-pentane saturated vapor, the ambient gas for the other experiments was air. The impact processes of micro-level (diameter below 1 mm) droplets were captured using a high-speed camera with a backlight. The observations, velocity and diameter ranges of the experimental runs were described, and based on them, the effects of the liquid-phase properties were studied. It was found that both low viscosity and low surface tension can increase the instability during impact processes. By curve-fitting, the transition from coalescence to jetting was characterized by using two models, one employing the Weber number (We) and the Ohnesorge number (Oh), and one employing the Froude number (Fr) and the Capillary number (Ca). Both models characterize the coalescence-jetting threshold well. The We-Oh model was based on a commonly used model from Cossali et al. (in Exp Fluids 22:463–472, 1997) for characterizing coalescence-splashing. For the small droplet diameters (below 1 mm) considered in this study, it was required to modify the We-Oh model with a diameter-dependent term to fit the sharp change in thresholds for fluids with relatively high viscosity. The Fr-Ca model has not previously been presented in the literature. A comparison of the two models with literature data (Rodriguez and Mesler, J Colloid Interface Sci 106(2):347–352, 1985) indicates that they are also valid for impacts of droplets with diameters above 1mm. Calculation methods to generalize the two models were proposed.

Rheological Properties of Aqueous Si3N4 and MoSi2 Suspensions Tailor-Made for Direct Inkjet Printing

Abstract: The aim of this study was to reveal the feasibility of adjusting aqueous nonoxide ceramic inks for producing complex-shaped functional ceramic parts by direct inkjet printing using the example of silicon nitride (Si3N4) and molybdenum disilicide (MoSi2). In a first step, aqueous Si3N4 and MoSi2 suspensions with high solid contents were prepared by the addition of organic and inorganic additives to meet the requirements regarding rheological properties of the printing system. For this purpose, viscosity, zeta potential, and surface tension were adjusted. Because of the physical conditions of the printing head, the particle size distribution of the suspensions was optimized. The experiments were verified by calculating the Ohnesorge number of suspensions. The results show that the values fit well into the required range. Printing of 3D-components and Si3N4/MoSi2 multilayers was carried out. Optimal performance and control of the printing process resulted in fabrication of homogeneous green bodies without delaminations or other process-dependent defects.

Lattice Boltzmann study of bubble entrapment during droplet impact

Abstract: The entrapment of bubble during droplet impact on solid surfaces was studied by using a phase-field lattice Boltzmann model (LBM). Numerous three-dimensional simulations were performed and several types of entrapment were found under specific impact conditions. Some cases are similar to previous studies, whereas others are reported for the first time. Dissections of the entrapment processes were carried out, and detailed analyses of the flow fields and interface motions were provided at selected moments for certain cases. The effects of the Reynolds number, the Weber number and the surface wettability were analyzed based on the observation. Besides, some computational issues of phase-field simulations were discussed for the present problem. Finally, the impact condition to prevent entrapment was preliminarily estimated in terms of the Ohnesorge number upon examination of numerous simulations. Copyright q 2009 John Wiley & Sons, Ltd.

Theoretical Investigation of the Influence of Liquid Physical Properties on Effervescent Atomization Performance

Abstract: Background. A comprehensive model in the Eulerian-Lagrangian scheme is used to investigate the performance of the gas-droplet two-phase flow for a typical effervescent atomization spray with different atomized liquids. Method of Approach. Based on the particle tracking method, the droplet primary and secondary breakup, droplets collision and coalescence are taken into consideration. Results. The predicted droplet mean size is compared well with the published experimental data. The influences of liquid physical properties are discussed not only on droplet mean size, but also on droplet velocity, distribution, events of breakup and collision, Weber number, Ohnesorge number and their evolutions. Conclusions. Results show liquid viscosity has a slight effect on the droplet size and its distribution. While a decrease in liquid surface tension serves to get finer droplets and wider droplet spatial distribution. Small liquid density, surface tension and viscosity are benefit for getting higher atomized droplet velocity.

Viscous effects on the oscillations of two equal and deformable bubbles under a step change in pressure

Abstract: According to linear theory and assuming the liquids to be inviscid and the bubbles to remain spherical, bubbles set in oscillation attract or repel each other with a force that is proportional to the product of their amplitude of volume pulsations and inversely proportional to the square of their distance apart. This force is attractive, if the forcing frequency lies outside the range of eigenfrequencies for volume oscillation of the two bubbles. Here we study the nonlinear interaction of two deformable bubbles set in oscillation in water by a step change in the ambient pressure, by solving the Navier–Stokes equations numerically. As in typical experiments, the bubble radii are in the range 1–1000 μm. We find that the smaller bubbles (~5 μm) deform only slightly, especially when they are close to each other initially. Increasing the bubble size decreases the capillary force and increases bubble acceleration towards each other, leading to oblate or spherical cap or even globally deformed shapes. These deformations may develop primarily in the rear side of the bubbles because of a combination of their translation and harmonic or subharmonic resonance between the breathing mode and the surface harmonics. Bubble deformation is also promoted when they are further apart or when the disturbance amplitude decreases. The attractive force depends on the Ohnesorge number and the ambient pressure to capillary forces ratio, linearly on the radius of each bubble and inversely on the square of their separation. Additional damping either because of liquid compressibility or heat transfer in the bubble is also examined.

Viscous contribution to the pressure for electroviscous potential flow analysis of capillary instability

Abstract: Viscous contribution for the Viscous Potential Flow (VPF) analysis of capillary instability with axial electric field at the interface of two viscous fluids has been analysed. In VPF, viscosity enters through normal stress balance and the effects of shearing stresses are completely ignored. To include the effect of shearing stresses, viscous pressure is included in normal stress balance along with irrotational pressure and it is assumed that the viscous contribution to the irrotational pressure will resolve the discrepancy between the tangential stresses at the interface. Stability criterion is given in terms of critical value of electric field. Various graphs have been drawn to show the effect of the parameters, such as electric field, inner fluid fraction, Ohnesorge number, conductivity ratio and permittivity ratio.

Viscous Potential Flow Analysis of Rayleigh-Taylor Instability of Cylindrical Interface

Abstract: The present paper deals with the study of Rayleigh-Taylor instability at the cylindrical interface using viscous potential flow theory. In the inviscid potential flow theory, the viscous term in Navier-Stokes equation vanishes as viscosity is zero. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in viscous potential flow theory and tangential stresses are not considered. A dispersion relation is derived and stability is discussed in terms of various parameters such as Ohnesorge number, density ratio etc. A condition for neutral stability is obtained and it is given in terms of critical value of the wave number. It is observed that the Ohnesorge number has destabilizing effect while inner fluid fraction has stabilizing effect on the stability of the system.

Liquid and gas jet disintegration

Abstract: The mathematical description of jet breakup has attracted the attention of outstanding scientists in the past Lord Rayleigh analyzed for the first time in 1878 the instability of jets Nils Bohr extended Rayleigh’s analysis to include viscous effects, in a prize-winning paper on the evaluation of surface tension in 1909 Constantin Weber went on to obtain the breakup length for a viscous jet in 1936 In 1936 after his experimental observation with a high-speed camera (200 to 12000 frames per second) Wolfgang von Ohnesorge classified four different regimes of jet breakup, introduced a dimensionless number quantifying the properties of the jet, and described successfully two jet transition boundaries Weber in 1936 and later Taylor in Batchelor (1958) introduced in addition to the previous analyses the influence of the environment on jet breakup These are the fundamental works in jet fragmentation theory used in almost all later works on this topic In recent times nozzle geometry has been found to strongly influence jet dynamics Geometries not allowing the establishment of a turbulent boundary layer produce more stable jets than those that promote turbulent boundary layers at the jet interface – see Iciek (1982)