Liquid film, wavy

Annular flow (wavy and smooth). A liquid film flowed on the tube wall with a continuous central vapor core without churning zones (Fig. 2.30f,g). 

L Stratified wavy annular Minimum inclination angle to show bubble flow Trajectory of drops tom from liquid film Lift versus buoyant forces... 

Needle contact probes These are probably the simplest and least expensive devices. A needle is mounted on a micrometer and insulated from ground, except for the tip, by a nonconducting varnish. The needle is moved into the wavy liquid film flows along a conducting plate, which is grounded. As the needle is moved, the fraction of time during which contact with the liquid top takes place is noted, and is related to the probability that the film thickness is greater than some value. This technique can provide information on the minimum, maximum, and mean thickness with reasonable reliability. 

Profile of wavy liquid film against heater surface (1). Finely... 

Feind (F2) has indicated that, in determining the effect of a liquid film flow on an adjoining gas stream, the velocity of the gas relative to the film surface is an important parameter. At present there are few measurements of film surface velocities for the various cases of gas/film flow, and the problem remains as to whether the gas velocity should be considered relative to the true surface velocity of the film in the wavy regime, or to the wave velocity, or to some effective surface velocity. 

Kapitsa (K9), 1951 Deals theoretically with heat and mass transfer to periodic flows, e.g., to wavy liquid films. 

Shibuya (S10), 1951 Mathematical treatment of onset of wavy flow in liquid films on vertical tubes. Waves appear for No, > 7. Wavelength of first waves = 3 film thicknesses. 

Heartinger (H5), 1960 Study of gas absorption in wavy liquid film a simplified model is given and solved by computer to give rates of transfer under various conditions. 

K.P. Chen, The onset of elastically driven wavy motion in the flow of two viscoelastic liquids films down an inclined plane, J. Non-Newtonian Fluid Mech., 45 (1992) 21-45. 

The Reynolds number for condensation on the outer surfaces of vertical tube or plates increases in the flow direction due to the increase of the liquid filn thickness S. The flow of liquid film exhibits different regimes, depending 01 the value of the Reynolds number. It is observed that the outer surface of th liquid film remains smooth and wave-free for about Re < 30, as shown ii Fig. 10 -23, and thus the flow is clearly laminar. Ripples or waves appear 01 the free surface of the condensate flow as the Reynolds number increases, anr the conden.sale flow becomes fully turbulent at about Re 1800. The con densate flow is called wavy-laminar in the range of 450 < Re < 1800 an turbulent for Re > 1800. However, some disagreement exists about the valu of Re at which the flow becomes wavy-laminar or turbulent. 

At Reynolds numbers greater than about 30, it is observed that waves form at the liquid-vapor interface although the flow in liquid film remains laminar. I he flow in this case is said to be wavy laminar. The waves at the liquid-vapor interface tend to increase heat transfer. But the waves also complicate the analysis and make it very difficult to obtain analytical solutions. Therefore, we have to rely on experimental studies. The increase in heat transfer due to the wave effect is, on average, about 20 percent, but it can exceed 50 percent. The exact amount of enhancement depends on the Reynolds number. Rased on his experimental studies, Kutateladze (1963) recommended the following relation for the average heat transfer coefficient in wavy laminar condensate flow for p p, and 30 < Re < 1800,... 

Chum flow or slug flow-annular (dispersed) flow transition. The flow becomes annular when the gas flow rates are enhanced to a certain point. The high gas flow rate causes a wavy interface of the liquid film. As a consequence, parts of the waves will enter the gas core as entrained drops. This results in an upward flow direction of the liquid, due both to interfacial shear and to drag on the waves and drag on the droplets. Annular flow can therefore exist only when the gas velocity is sufficient to lift the droplets in the gas core. The minimum gas velocity required to suspend a drop is determined from the balance between the gravity and drag forces on the drop. 

Mudawar, I., and Houpt, R. A. (1993) Measurement of Mass and Momentum Transport in Wavy-Laminar Falling Liquid Films, International Journal of Heat and Mass Transfer, Vol. 36(17), pp. 4151-4162. 

Annular Flow is characterized by the continuity of the gas phase along the core of the tube. The liquid phase moves upward partly as wavy liquid film and partially in the form of drops entrained in the gas flow. 

FIGURE 5.5 Wavy deformation of a thin liquid film. 

As has been discussed with reference to Figures 16-17, in practical systems where the gas phase is turbulent and H < 0.5, the role of in controlling the transition from stratified-smooth to stratified-wavy is dominant. At the extreme of 1, — l,the inertia terms of the two phases along the ZNS diminish, and the dynamic interaction that takes place at the phases free interface is the controlling destabilizing mechanism. This extreme of 1 is approached for sufficiently thin liquid layers in large diameter conduits and/or low viscosity of the liquid phase (Table 2). In the extreme of open air flow over a thin liquid film, 8 -> 0, 4S./(Jte) - H" , Re = 4U jH/v, the condition of 1 can be rearranged in terms of the system s physical parameters ... 

Hagiwara, Y., Esmaeilzadeh, E., Tsutsui, H., and Suzuki, K., Simultaneous Measurement of Liquid Film Thickness, Wall Shear Stress and Gas Flow Turbulence of Horizontal Wavy Two-Phase Row, Int. J. Multiphase Flow, Vol. 15, pp. 421-431 (1989). 

However, even at relatively low film Reynolds numbers, the assumption that the condensate layer is in laminar flow is open to some question. Experiments have shown that the surface of the film exhibits considerable waviness (turbulence). This waviness causes increased heat transfer rates. Better heat transfer correlations for vertical condensation were presented by Dukler in 1960. He obtained velocity distributions in the liquid film as a function of the interfacial shear (due to the vapor velocity) and film thickness. From the integration of the velocity and temperature profiles, liquid film thickness and point heat-transfer coefficients were computed. According to the Dukler development, there is no... 

The dynamics of thin liquid films are often dominated by viscous friction. As such, the lubrication approximation is entirely appropriate. In this section, we discuss four examples in order of increasing difficulty. They are the thinning of a vertical liquid film, the levelling of a wavy film, and two examples of interfacial instability (suspended film and liquid cylinder). We restrict our attention here to films of thickness e > 100 nm, for which the long-range interactions described in chapter 4 can be neglected [P e) -> 0]. 

The 3D subharmonic weakly nonlinear instability is due to the resonant excitation of a triad of waves consisting of the fundamental two-dimensional wave and two oblique waves. The evolution of wavy films after the onset of either of these 3D instabilities is complex - however, sufficiently far downstream, large-amplitude solitary waves absorb the smaller waves and become dominant. In Liu, Schneider and Gollub (1995) a detailed study of these instabilities is then presented, along with a qualitative treatment of the further evolution toward an asymptotic turbulent regime. In recent review paper by Oron, Davis and Bankoff (1997), the long-scale evolution of thin (macroscopic) liquid films is considered. 

Shkadov, V. Y., and Sisoev, G. M. (2000b). Wavy falling liquid films theory and computation instead of physical experiment. In Chang, H.-C., ed., lUTAM Symposium on Nonlinear Waves in Multi-Phase Flow, volume 57 of Fluid Mechanics and Its Applications, 1-10. Notre Dame, USA Notre Dame University. 

The different flow patterns largely resemble those known from flow in other continuous flow conduits as pipes, tubes, capillaries, and monoliths [29-40]. Bubbly flow, slug flow (Taylor flow), annular, and churn flow are found and a few more intermediate regimes between the ones mentioned. These comprise different gas-liquid configurations such as segmented flow (bubble-train), gas core with encompassing stable thin liquid film, which wets the channel wall, and dynamic wavy liquid films. In case of high gas contents, spray is created with small droplets in... 

Yih SM, Chen KY (1982) Gas absorption into wavy and turbulent falling liquid films in a wetted-wall. Chem Eng Commiin 17(1-6) 123-136... 

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