Drop oscillation

Ozawa M, Akagawa K, Sakaguchi T, Tsukahara T, Fuji T (1979) Oscillatory flow instabilities in air-water two-phase flow systems. Report. Pressure drop oscillation. Bull JSME 22 1763-1770 Qu W, Yoon S-M, Mudawar 1 (2004) Two-phase flow and heat transfer in rectangular microchannels. J Electron Packag 126 288-300... 

In the study by Hetsroni et al. (2006b) the test module was made from a squareshaped silicon substrate 15 x 15 mm, 530 pm thick, and utilized a Pyrex cover, 500 pm thick, which served as both an insulator and a transparent cover through which flow in the micro-channels could be observed. The Pyrex cover was anod-ically bonded to the silicon chip, in order to seal the channels. In the silicon substrate parallel micro-channels were etched, the cross-section of each channel was an isosceles triangle. The main parameters that affect the explosive boiling oscillations (EBO) in an individual channel of the heat sink such as hydraulic diameter, mass flux, and heat flux were studied. During EBO the pressure drop oscillations were always accompanied by wall temperature oscillations. The period of these oscillations was very short and the oscillation amplitude increased with an increase in heat input. This type of oscillation was found to occur at low vapor quality. 

Density-wave oscillations Pressure drop oscillations Flow regime-induced instability... 

Pressure drop oscillations (Maulbetsch and Griffith, 1965) is the name given the instability mode in which Ledinegg-type stability and a compressible volume in the boiling system interact to produce a fairly low-frequency (0.1 Hz) oscillation. Although this instability is normally not a problem in modern BWRs, care frequently must be exercised to avoid its occurrence in natural-circulation loops or in downflow channels. 

Compound dynamic instabilities as secondary phenomena. Pressure-drop oscillations are triggered by a static instability phenomenon. They occur in systems that have a compressible volume upsteam of, or within, the heated section. Maul-betsch and Griffith (1965, 1967), in their study of instabilities in subcooled boiling water, found that the instability was associated with operation on the negative-sloping portion of the pressure drop-versus-flow curve. Pressure drop oscillations were predicted by an analysis (discussed in the next section), but because of the... 

Figure 6.4 Density wave and pressure drop oscillation. (From Stenning and Verizoglu, 1965. Reprinted with permission of Stanford University Press, Stanford, CA.)...

Computer codes Because of the computer s ability to handle the complicated mathematics, most of the compounded and feedback effects are built into computer codes for analyzing dynamic instabilities. Most of these codes can analyze one or more of the following instabilities density wave instability, compound dynamic instabilities such as BWR instability and parallel-channel instability, and pressure drop oscillations. 

Little quantitative work has been published on drop oscillations in liquid-liquid systems. Lamb (L2) reviews two methods for the analysis of a spherical mass of liquid. Elzinga and Banchero (El) use the primary mode of oscillation... 

In practice, this model is oversimplified since the exciting wake shedding is by no means harmonic and is itself coupled with the shape oscillations and since Eq. (7-30) is strictly valid only for small oscillations and stationary fluid particles. However, this simple model provides a conceptual basis to explain certain features of the oscillatory motion. For example, the period of oscillation, after an initial transient (El), becomes quite regular while the amplitude is highly irregular (E3, S4, S5). Beats have also been observed in drop oscillations (D4). If /w and are of equal magnitude, one would expect resonance to occur, and this is one proposed mechanism for breakage of drops and bubbles (Chapter 12). 

The internal resistance is always decreased substantially when a bubble or drop oscillates, but the external resistance may be unaffected if the Reynolds number is high enough. A rough criterion can be obtained from Eq. (11-63) for vibration of a particle in an axial stream. Oscillation has negligible effect on the external resistance if... 

The sO Called spheroidal state, in which a drop of water or other volatile liquid rolls about on a hot metal plate (or on the surface of a boiling liquid) with only very slow evaporation, is mainly a consequence of the very slow transmission of heat from the solid through the thin layer of vapour separating it from the liquid drop. A beam of light may be passed between the drop and the plate. Poggendorff said that an electric current will not pass from the drop to the hot plate, but Buff showed that a weak current passes and that the drop oscillates, sometimes touching the support. Stark showed that the drop is supported by a layer of vapour but executes oscillations which may sometimes reach the support. 

Figure 6. Polarogram (d.c.) (left) and differential-pulse polarogram (right) of reduction of (h -CjHj)jCo in 1,2-dimethoxyethane with phenol added. The waves owing to reduction of (h -CjH jCo and h -CjHjCoCjHj-h are labeled. Drop oscillations are not shown in the d.c. polarogram. [Reproduced with permission from W. Geiger, W. Bowden, N. El Murr, Inorg. Chem., 18. 2358 (1979).]...

Theoretical solution of the Navier-Stokes equation for prediction of the collision efficiency, E(Dp,dp), for the general raindrop-aerosol interaction case is a difficult undertaking. Complications arise because the aerosol size varies over orders of magnitude, and also because the large raindrop size results in complicated flow patterns (drop oscillations, wake creation, eddy shedding, etc.) Pruppacher and Klett (1997) present a critical overview of the theoretical attempts for the solution of the problem. A detailed discussion of these efforts is outside our scope. However, it is important to understand at least qualitatively the various processes involved. 

To complete the mathematical problem a relationship r(c), a so-called adsorption isotherm, is needed. For the simple case of bubble or drop oscillations (with the surfactant only outside the drop) a solution was derived in Ref. 189 in analogy to the capillary wave theory (183, 184). 

A systematic analysis of the stability of bubble and drop oscillations in open and closed cells has been performed recently and hydrodynamic limits have been given as a function of the geometry of the bubble and capillary as well as of the bulk properties of the two adjacent liquids (212,213). 

Other aspects of the drop oscillation problem, such as oscillation of liquid drops immersed in another fluid [17-21], oscillations of pendant drops [22, 23], and oscillations of charged drops [24, 25], have also been considered. In particular, there are numerous works on the oscillation of acoustically levitated drops in acoustic field. In such studies, high-frequency acoustic pressnre is required to levitate the droplet and balance the buoyancy force for the experimental studies performed on the Earth. As a result of balance between buoyancy and acoustic forces, the equilibrium shape of the droplet changes from sphere to a slightly flattened oblate shape [26]. Then a modulating force with frequency close to resonant frequencies of different modes is applied to induce small to large amplitude oscillations. Figure 5.4 shows a silicon oil droplet levitated in water and driven to its first three resonant modes by an acoustic force and time evolution for each mode. 

Increasing the amplitude of drop oscillation decreases the resonant frequency mainly due to the larger time required between successive oscillations [13, 25]. When the magnitude of the time varying driving force is high enough, in addition... 

E. Trinh, A. Zwem, and T. G. Wang, An experimental study of small amplitude drop oscillations in immiscible liquid systems, J. Huid Mech. 115,453, 1982. 

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