Film-flow

Extensive treatments of general two-phase flow problems have been given in the monograph by Kutateladze and Styrikovich (K25) and in recent surveys by Dukler and Wicks (Dl7), and Scott (S4), all of which indicate clearly the important place of film flow in the over-all scheme of two-phase flow phenomena. Film flow is more amenable to detailed study than most other types of two-phase flow, and a detailed knowledge of the phenomena occurring in film flow (with or without an adjacent gas stream) would assist greatly in understanding many of the more complex types of two-phase flow and the mechanisms of heat and mass transfer in such flows. Numerous experimental studies have been made of various two-phase transfer processes, but these have led mainly to empirical correlations of more or less limited applicability. 

An attempt is made in the present survey to collect and review the more important results of the studies of liquid film flow scattered throughout the literature. It is hoped that this will avoid future duplication of work and enable investigators to concentrate on the many aspects of film flow which have been insufficiently studied in the past. 

Studies of heat and mass transfer to films and film condensation are considered only insofar as the results throw light on the flow behavior a brief review of such studies has been published elsewhere (F6). In addition, annular gas/liquid flow in horizontal ducts will not be considered here, since this is usually complicated by droplet entrainment. 

As in other flows, various types of film flow can be distinguished. The most important of these are steady flow and uniform flow, in which the properties of the flow are constant with respect to time and with respect to distance in the direction of flow. 

the flow of a smooth film outside the acceleration zone is both steady and uniform. The flow in the smooth entry zone of a wetted-wall column where acceleration occurs is steady but nonuniform, while certain wavy film flows are both unsteady and nonuniform. 

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The second mechanism can be explained by the wall liquid film flow from one meniscus to another. Thin adsorptive liquid layer exists on the surface of capillary channel. The larger is a curvature of a film, the smaller is a pressure in a liquid under the corresponding part of its film. A curvature is increasing in top s direction. Therefore a pressure drop and flow s velocity are directed to the top. 

Thus it is necessary to find alternative approach to describe the physical mechanism of two-side filling of conical capillaries with hquids. Theoretical model of film flow in conical dead-end capillary is based on the concept of disjoining pressure II in thin liquid film [13]... 

The problem of film flow is formulated on the assumption that the film thickness h is much smaller than the length 1 (in our case h/1 10 ). In Cartesian coordinates with transversal axis y and longitudinal one z we can write the equation for a film flow as follows ... 

Use now this equation to describe liquid film flow in conical capillary. Let us pass to spherical coordinate system with the origin coinciding with conical channel s top (fig. 3). It means that instead of longitudinal coordinate z we shall use radial one r. Using (6) we can derive the total flow rate Q, multiplying specific flow rate by the length of cross section ... 

One more experimental result, which is important for PT is as follows. Only polar liquids fill conical capillaries from both sides. We used various penetrants to fill conical defects Pion , LZh-6A , LZhT , LUM-9 etc. It was established that only the penetrants containing polar liquid as the basic liquid component (various alcohols, water and others) manifest two-side filling phenomenon. This result gives one more confirmation of the physical mechanism of the phenomenon, based on liquid film flow, because the disjoining pressure strongly depends just on the polarity of a liquid. 

Physical mechanism of two-side filling of dead-end capillaries with liquids, based on liquid film flow along the wall, is proposed for the first time. Theoretical model correlates with experimental data. 

Another unique phenomenon exhibited by Hquid helium II is the Rollin film (62). AH surfaces below the lambda point temperature that are coimected to a helium II bath are covered with a very thin (several hundredths llm) mobile film of helium II. For example, if a container is dipped into a helium II bath, fiUed, and then raised above the bath, a film of Hquid helium flows up the inner waH of the container, over the Hp, down the outer waH, and drips from the bottom of the suspended container back into the helium II bath. SinHlady, if the empty container is partiaHy submerged in the helium II bath with its Hp above the surface, the helium film flows up the outer waH of the container, over its Hp, and into the container. This process continues until the level of Hquid in the partiaHy submerged container reaches that of the helium II bath. 

R Liquid film flowing over solid particles with air present, trickle bed reactors, fixed bed... 

Ripple flow has an upward-moving wavy layer of liquid on the pipe wall it may be thought of as a transition region to annular, annular mist, or film flow, in which gas flows in the core of the pipe while an anniilus of hquid flows up the pipe wall. Some of the liquid is entrained as droplets in the gas core. Mist flow occurs when all the liquid is carried as fine drops in the gas phase this pattern occurs at high gas velocities, typically 20 to 30 m/s (66 to 98 ft/s). 

For laminar non-Newtonian film flow, see Bird, Armstrong, and Hassager Dynamics of Polymciic Liquids, vol. 1 Fluid Mechanics, Wiley, New York, 1977, p. 215, 217), Astarita, Marrucci, and Palumbo (Jnd. Eng. Chem. Fundam., 3, 333-339 [1964]) and Cheng (Jnd. Eng. Chem. Fundam., 13,394—395 [1974]). 

Absorbers These have a two-phase flow system. The absorbing medium is put in film flow during its fall downward on the tubes as it is cooled by a coohng medium outside the tubes. The film absorbs the gas which is introduced into the tubes. This operation can be cocurrent or countercurrent. 

Effective area should not be confused with wetted area. While film flow of liquid across the packing surface is a contributor, effective area includes also contribiidons from rivulets, drippings, and gas bubbles. Because of this complex physical picture, effecdve interfacial area is difficnlt to measure directly. 

The first part of Eq. (89), proportional to the inverse viscosity r] of the liquid film, describes a creeping motion of a thin film flow on the surface. In the (almost) dry area the contributions of both terms to the total flow and evaporation of material can basically be neglected. Inside the wet area we can, to lowest order, linearize h = hoo[ + u x,y)], where u is now a small deviation from the asymptotic equilibrium value for h p) in the liquid. Since Vh (p) = 0 the only surviving terms are linear in u and its spatial derivatives Vw and Au. Therefore, inside the wet area, the evolution equation for the variable part u of the height variable h becomes... 

Fig. 5. Device for measuring the wall-film flow rate with annular flow in a tube [from Hewitt et al. (H5)].

The above experimenters have used the technique described to obtain flow rate measurements of the liquid wall-film at various mass velocities, tube dimensions, etc., and some typical results from Staniforth and Stevens (S7) are shown in Fig. 7. Also shown are the values of burn-out heat flux obtained at the four different mass velocities indicated. It can be seen that the liquid-film flow rate decreases steadily with increasing heat flux until at burn-out the flow rate becomes zero or very close to zero. We thus have confirmation of a burn-out mechanism in the annular flow regime which postulates a liquid film on the heated wall diminishing under the combined effects of evaporation, entrainment, and deposition until at burn-out, the film has become so thin that it breaks up into rivulets which cause dry spots and consequent overheating. 

The annular flow regime is very extensive, and the above mechanism of burn-out is stated (S7) to be consistent with the film-flow measurement data over a range of exit qualities from 10 to 100% for uniformly heated round tubes. A summary of experimental observations on flow patterns produced... 

Fig. 7. Variation of wall-film flow rate with heat flux and mass velocity [from Staniforth and Stevens (S7)]. Based on tests with Freon 12 in a uniformly heated tube, L = 102 in., d = 0.38 in., P = 155 psia, Ah 12 Btu/lb.

In order to develop the above burn-out mechanism further, it will be necessary to know more about the entrainment and deposition processes occurring. Experimentally, it is likely that these processes will be very difficult to measure separately and under conditions comparable to those prevailing in a boiling channel. From analysis of their film flow-rate data, Staniforth et al. (S8) have deduced that under burn-out conditions, the deposition of liquid droplets from the vapor core plays an important part in reinforcing the liquid film, particularly at high mass velocities. At low mass velocities, they conclude that deposition and entrainment rates must be nearly equal, and, therefore, since a thin liquid film can be expected to be tenacious and give rise to very little entrainment, they argue that both deposition and entrainment tend to zero near the burn-out location with low mass velocities. 

Confirmation that a thicker tube wall may slightly increase the burn-out flux has been given by Hewitt et al. (H6). These authors have even gone to the extent of showing that not only the burn-out flux, but the wall-film flow rate prior to burn-out as well, is affected by the wall thickness, as shown in Fig. 16. The technique of measuring the film flow-rate has been described in Section II,D. The reason a thicker-walled tube should maintain a higher wall-film flow rate is not clearly understood. 

Fig. 16. Effect of tube-wall thickness on the film flow rate [from Hewitt el al. (H6)]. Based on tests with water in uniformly heated stainless steel tubes, d — 0.366 in., P = 55 psia, G = 0.219 x 106 lb/hr-ft2.

Staniforth, R., Stevens, G. F., and Wood, R. W., An experimental investigation into the relationship between burnout and film flow-rate in a uniformly heated round tube, AEEW-R430, H. M. Stationery Office, London (1965). 

In considering the heat that is transferred, the method first put forward by NussELT(%i and later modified by subsequent workers is followed. If the vapour condenses on a vertical surface, the condensate film flows downwards under the influence of gravity, although it is retarded by the viscosity of the liquid. The flow will normally be streamline and the heal flows through the film by conduction. In Nusselt s work it is assumed that the temperature of the film at the cool surface is equal to that of the surface, and at the other side was at the temperature of the vapour. In practice, there must be some small difference in temperature between the vapour and the film, although this may generally be neglected except where non-condensable gas is present in the vapour. 

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). 

Now consider the case of two-dimensional flow subjected to the lubrication geometry assumptions that result from analyzing the order of magnitude for the velocities in thin film flow ... 

The schematic diagram of the experimental setup is shown in Fig. 2 and the experimental conditions are shown in Table 2. Each gas was controlled its flow rate by a mass flow controller and supplied to the module at a pressure sli tly higher than the atmospheric pressure. Absorbent solution was suppUed to the module by a circulation pump. A small amount of absorbent solution, which did not permeate the membrane, overflowed and then it was introduced to the upper part of the permeate side. Permeation and returning liquid fell down to the reservoir and it was recycled to the feed side. The dry gas through condenser was discharged from the vacuum pump, and its flow rate was measured by a digital soap-film flow meter. The gas composition was determined by a gas chromatograph (Yanaco, GC-2800, column Porapak Q for CO2 and (N2+O2) analysis, and molecular sieve 5A for N2 and O2 analysis). The performance of the module was calculated by the same procedure reported in our previous paper [1]. 

Liquid Metal Sources. The source feed is a metal of low melting point - Ga and In are commonly employed. It is introduced as a liquid film flowing over a needle towards the tip whose radius is relatively blunt (10 pm). The electrostatic and surface tension forces form the liquid into a sharp point known as the Taylor cone. Here the high electric field is sufficient to allow an electron to tunnel from the atom to the surface, leaving the atom ionized. 

Figure 3.5 Flow regimes in vertical downflow (A) bubbly flow (B) slug flow (C) falling film flow (D) bubbly falling film flow (E) chum flow (F) dispersed annular flow. (From Oshimowo and Charles, 1974. Copyright 1974 by Canadian Society of Chemical Engineers, Ottawa, Ont. Reprinted with permission.)...

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. 

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