Oscillation, liquid droplets

Abstract Sonoluminescence from alkali-metal salt solutions reveals excited state alkali - metal atom emission which exhibits asymmetrically-broadened lines. The location of the emission site is of interest as well as how nonvolatile ions are reduced and electronically excited. This chapter reviews sonoluminescence studies on alkali-metal atom emission in various environments. We focus on the emission mechanism does the emission occur in the gas phase within bubbles or in heated fluid at the bubble/liquid interface Many studies support the gas phase origin. The transfer of nonvolatile ions into bubbles is suggested to occur by means of liquid droplets, which are injected into bubbles during nonspherical bubble oscillation, bubble coalescence and/or bubble fragmentation. The line width of the alkali-metal atom emission may provide the relative density of gas at bubble collapse under the assumption of the gas phase origin. 

Recently, the size and shape of a liquid droplet at the molten tip of an arc electrode have been studied,12151 and an iterative method for the shape of static drops has been proposed. 216 Shapes, stabilities and oscillations of pendant droplets in an electric field have also been addressed in some investigations. 217 218 The pendant drop process has found applications in determining surface tensions of molten substances. 152 However, the liquid dripping process is not an effective means for those practical applications that necessitate high liquid flow rates and fine droplets (typically 1-300 pm). For such fine droplets, gravitational forces become negligible in the droplet formation mechanism. 

It will be assumed here for simplicity that one parameter r (the radius in the case of a spherical liquid droplet) is sufficient to specify the size and shape of a particle. For solid particles (or liquid droplets), this assumption will be valid in spray combustion when either the particles are geometrically similar or their shape is of no consequence in the combustion process. Liquid droplets will obey this hypothesis in particular if they are spherical, which will not be true unless (1) they collide with each other so seldom that collision-induced oscillations are viscously damped to a negligible amplitude for most droplets, and (2) their velocity relative to the gas is sufficiently low. An alternative parameter to the radius is the mass of the droplet [10] the choice between this, the droplet volume, or the radius of a sphere of equal volume is a matter of individual preference. 

It has been shown [11] that the degree of deformation and the amplitude of oscillation of a liquid droplet depend on the ratio of the dynamic force to the surface-tension force, which is given by the Weber number, We = 2rp — u /S. Here S is the surface tension of the liquid, p... 

Abstract A bquid droplet may go through shape oscillation if it is forced out of its equilibrium spherical shape, while gas bubbles undergo both shape and volume oscillations because they are compressible. This can happen when droplets and bubbles are exposed to an external flow or an external force. Liquid droplet oscillation is observed during the atomization process when a liquid ligament is first separated from a larger mass or when two droplets are collided. Droplet oscillations may change the rate of heat and mass transport. Bubble oscillations are important in cavitation problems, effervescent atomizers and flash atomization where large number of bubbles oscillate and interact with each other. This chapter provides the basic theory for the oscillation of liquid droplet and gas bubbles. 

A liquid droplet free from any other forces except its surface tension forces tends to remain in equilibrium, spherical shape. Oscillations occur when a liquid droplet is forced out of its equilibrium shape. An initially spherical inviscid droplet wifli radius R that is perturbed by C will oscillate according to [1]... 

Other studies have considered oscillations of a liquid droplet placed on a flat plate [28-30]. For instance, Yoshiyasu et al. [31] observed induced polygonal vibrations of a water drop placed on a vertically oscillating plate, relating to the self-induced vibration of a liquid drop as mentioned above (see Figure 5.6). Their study concludes that the axisymmetric polygonal vibration of a drop caused by an oscillating plate is... 

Similar to energy transfer between different shapes of a liquid droplet, coupling between the volume oscillation and different shape oscillations occur for bubbles in acoustic fields [43]. Interaction between modes can lead to chaotic response of the bubble to the external forcing. For a large enough bubble, the spectrum of distortion modes is dense, and several distortion modes attribute to the shape. Development of chaos depends on the number of excited shape modes. 

E. Becker, W. J. Hiller, and T. A. Kowalewsld, Experimental and theoretical investigation of large amplitude oscillations of liquid droplets, J. Fluid Mech. 231, 180, 1991. 

Based on an analogy between the oscillations of a two-dimensional (2D) droplet and a mass spring system (similar to the Taylor analogy breakup (TAB) model), we assume that the deformation of our 2D liquid droplet is dependent on the viscous (Fv), surface tension (Fj), and inertial (Fa) forces. So, performing a force balance in the X2-direction for the half element (shaded) in Fig. 29.2c, we can write... 

The frequencies of the various Legendre modes of oscillating spherical droplets of liquid were first described by Lord Rayleigh [8] as... 

The secondary liqmd-liquid droplet or droplet-film structure is considered as a macroscopic system with internal structure determined by the way the molecules (ions) are tuned (structured) into the primary components of a cluster configuration. How the tuning or structuring occurs depends on the physical fields involved, both potential (elastic forces) and nonpotential (resistance forces). All these microelements of the primary structure can be considered as electromechanical oscillators assembled into groups, so that an excitation by an external physical field may cause... 

The first mechanism is due to interfacial turbulence, which may occur as a result of mass transfer. In many cases the interface shows unsteady motions streams of one phase are ejected and penetrate into the second phase, shredding small droplets (Figure 14.1). Localised reductions in interfacial tension are caused by the non-uniform adsorption of the surfactant at the oil/water interface [14] or by mass transfer of surfactant molecules across the interface [15, 16]. With two phases that are not in chemical equilibrium, convection currents may form, conveying liquid rich in surfactants towards areas of liquid deficient of surfactant [17, 18]. These convection currents may give rise to local fluctuations in interfacial tension, causing oscillation of the interface. Such disturbances may amplify themselves, leading to violent interfadai perturbations and eventual disintegration of the interface, when liquid droplets of one phase are thrown into the other [19]. 

Ertl, M., Roth, N., Brenn, G., Gomaa, H., Weigand, B. (2013). Simulations and experiments on shape oscillations of Newtonian and non-Newtonian liquid droplets. In ILASS- urope 2013, 25th European Conference on Liquid Atomization and Spray Systems, September 1—4, 2013, Chania, Greece. 

Firm mounting is necessary to eliminate the influence of other oscillating plant parts. And installation position is also important to prohibit buildup of interfering second phases for example, an instrument for detection of a gas flow should be oriented as shown in Figure 14.5 so that liquid droplets will not collect in the curved tubes. In industrial processes, especially cyclic high-pressure processes, a decision has to be made considering optional positions with different parameters (temperature, pressure rating, risk of contamination, or two-phase flow). 

A jet emerging from a nonciicular orifice is mechanically unstable, not only with respect to the eventual breakup into droplets discussed in Section II-3, but, more immediately, also with respect to the initial cross section not being circular. Oscillations develop in the Jet since the momentum of the liquid carries it past the desired circular cross section. This is illustrated in Fig. 11-20. 

Other noncontact AFM methods have also been used to study the structure of water films and droplets [27,28]. Each has its own merits and will not be discussed in detail here. Often, however, many noncontact methods involve an oscillation of the lever in or out of mechanical resonance, which brings the tip too close to the liquid surface to ensure a truly nonperturbative imaging, at least for low-viscosity liquids. A simple technique developed in 1994 in the authors laboratory not only solves most of these problems but in addition provides new information on surface properties. It has been named scanning polarization force microscopy (SPFM) [29-31]. SPFM not only provides the topographic stracture, but allows also the study of local dielectric properties and even molecular orientation of the liquid. The remainder of this paper is devoted to reviewing the use of SPFM for wetting studies. 

Ultrasonic atomization is sometimes also termed capillary-wave atomization. In its most common form, 142 a thin film of a molten metal is atomized by the vibrations of the surface on which it flows. Standing waves are induced in the thin film by an oscillator that vibrates vertically to the film surface at ultrasonic frequencies. The liquid metal film is broken up at the antinodes along the surface into fine droplets once the amplitude of the capillary wave exceeds a certain value. The most-frequent diameter of the droplets generated is approximately one fourth of the wavelength of the capillary wave,1 421 and thus decreases with increasing frequency. 

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