Droplet oscillation

In a supersonic gas flow, the convective heat transfer coefficient is not only a function of the Reynolds and Prandtl numbers, but also depends on the droplet surface temperature and the Mach number (compressibility of gas). 154 156 However, the effects of the surface temperature and the Mach number may be substantially eliminated if all properties are evaluated at a film temperature defined in Ref. 623. Thus, the convective heat transfer coefficient may still be estimated using the experimental correlation proposed by Ranz and Marshall 505 with appropriate modifications to account for various effects such as turbulence,[587] droplet oscillation and distortion,[5851 and droplet vaporization and mass transfer. 555 It has been demonstrated 1561 that using the modified Newton s law of cooling and evaluating the heat transfer coefficient at the film temperature allow numerical calculations of droplet cooling and solidification histories in both subsonic and supersonic gas flows in the spray. 

Figure 1.39 Liquid mixing time as a function of the droplet oscillation frequency, given for two-, three- and four-electrode structures [97]...

Dispersion phase transfer is greatly improved due to sustained droplet oscillation. 

Surface charge is important for the electrostatic stabi liza-tion of emulsions (1) and in certain cases protecting the oil from oxidization catalysts (30). A dynamic accumulation of oppositely charged ions surrounds a charged droplet surface. When the droplet oscillates in an ultrasonic wave, the charge distribution is perturbed. If the droplet is moving slowly (low frequency, large particle inertia) the distribution is never out of phase with the droplet, and when the... 

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. 

Keywords Bjerknes force Bubble breakup Bubble interaction Bubble oscillation Chaotic oscillation Damping rate Droplet oscillation Nonlinear oscillation Oscillation frequency RPNNP equation Shape modes Spherical harmonics Volume oscillation... 

When a spherical drop first enters a disruptive flow field, an unequal static pressure distribution over the drop surface causes initial deformation into a shape which resembles an oblate spheroid (Fig. 6.1). Surface tension acts to restore the drop to its initial spherical shape. At low We, this results in droplet oscillation similar to that described in the previous chapter. 

The Enhanced-TAB Model (E-TAB) has been developed by Taimer in 1997 [7] and reflects a cascade of droplet breakups, in which the breakup condition is determined by the Taylor droplet oscillator dynamics (this method is further described in the next section). The droplet size is reduced in a continuous manner, until the product droplets reach a stable condition. The model maintains the droplet deformation dynamics of the TAB model [5]. According to this approach, the droplet distortion is described by a forced damped harmonic oscillator, in which the forcing term corresponds to the aerodynamic droplet-gas interaction, the restoring force is due to surface tension, while damping is attributed to the liquid s viscosity. 

Mugele F, Baret JC, Steinhauser D (2006) Microfluidic mixing through electrowetting-induced droplet oscillations. Appl Phys Lett 88(1-3) 204106... 

Fig. 6 Snapshots of a 7 pi KCl droplet oscillating with a 60 V AC forcing at 180 Hz. Snapshots are 1 ms apart. Snapshots show n = 6 mode at several phases during oscillation. Scale bar corresponds to 0.5 mm...

As an illustration, let us consider the case of a small droplet oscillating with a given frequency m. By substituting the solution of the respective diffusion problem into Eq. (87), we derive... 

At low-to-moderate field strengths, droplets oscillate in the electric field. We have examined both the mass transfer and the fluid mechanics of oscillating drops. Our experimental and theoretical results indicated that we can expect a maximum mass transfer enhancement of approximately 50% through this type of operation over the conventional equipment which is currently in commercial use. To proceed beyond this level we must consider droplet rapture. 

Fig. 1.26 Collision with encapsulation. Upper row visualization of simulation results of interface geometry and velocity Bottom row schematics of the encapsulation. Phase 1 shortly delayed coalescence Phase 2 penetration Phase 3 receding of convex curvature Phase 4 damped droplet oscillation [10]. The figure is reproduced with permission...

The coordinates of the center of the ellipsoid were transferred to the control unit of the positioning tables. If the center deviates by a defined value of pixels from the middle of the picture, the camera position is adjusted automatically to center the shadow of the droplet. This adjustment could be established for both dimensions of the 2D picture, but not for the focal plane as the droplet oscillated faster in this dimension than the positioning table could be controlled. 

We then simulate shape oscillations of shear-thinning droplets. At first the implementation of the Carreau-Yasuda model is validated against experimental data. We then analyze the droplet oscillations and compare them to Newtonian droplets with the same Ohnesorge number. We investigate the viscosity distribution... 

The domain is discretized with a Cartesian grid of 128 cells with a length of 6.25 X10 m in each spatial direction, resulting in a total of about two million cells. The gravity is set to zero and continuous (Neumann) boundary conditions are selected for all sides. The droplet is initialized quiescent at the center of the domain as an oblate ellipsoid with an aspect ratio of the semiaxis to the two short semiaxis of 5tl and a volume corresponding to the volume of a sphere with the diameter >0 = 2 mm. For the surrounding medium we take air with density 1.1894 kg/m and dynamic viscosity 1.82 x 10 Pa s. The computational domain is shown in Fig. 17.14. For the droplet oscillation simulations only, we use the balanced CSF model by BrackbUl [37] instead of the CSS model for the calculation of the surface... 

A difference in the behavior of the two non-Newtonian droplets is also seen in Fig. 17.17. While both droplets oscillate, the P2500 solution droplet is dampened... 

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