A falling film is the gravity flow of a continuous liquid film down a solid tube having one free surface. Other geometries and conditions are possible variables,1 but normal practice is with a vertical tube and countercurrent gas flow. Falling films are used in industry for distillation, absorption, reactions, condensation, etc.1 Its advantages are that liquid residence time is small, transfer rates are high for comparatively small pressure losses and it possesses a large interface of simple geometry. Design and operation of the equipment need careful attention to eliminate flooding or poor wetting phenomena.2-3 (See also Flooding and Flow Reversal; Capillary Action.)
Immediately under the liquid distributor is a non-uniform entrance region followed by the main film. Both depend on liquid distributor design, Re, KF, We and Fr.4
where is the mass flow rate, η the fluid viscosity, d the tube diameter, Γ the mass flow rate per unit of circumference, ρ is the fluid density, and σ the surface tension.
The entrance region can be under stable accelerating or unstable retarding conditions depending on the film thickness, δ being under or over the distributor entrance setting. The entrance region persists until the growing underlying boundary layer reaches the free surface so frictional and gravitational forces are in equilibrium. Predictions for the entrance region using boundary layer equations show reasonable agreement with data.5-6
Flow regimes in the main film have been detailed,4,7,8 c.f. Table 1.
A falling film consists of a base film with waves on the top of it. The wave structure is complex.10 Small amplitude waves can be overtaken and overridden by larger waves, but the sublayer base film virtually becomes constant when a > 1600. The hydrodynamics are dissimilar for the various flow regimes giving some basis for the wide variation in reported data. Film thickness measurements have been reviewed.4 Prediction models are given in Table 2.
Table 2. 9 Average film thickness correlation (no gas flow) in the form of δ(meter) = a(ν2/g)1/3(4Γ/η)b
A plot of Nusselt number against film Reynolds number can be used to correlate data. Film and wave data are available for falling film flow in the presence of a gas stream.2,4,22 Hydrodynamic stability theory23 and the universal velocity profile24 for turbulent flow have been used to give reasonable agreement with data.25 A general model has been suggested26 which predicted data27 within ±5%. The effect of gas flow,13,28 dampening by surfactants29,30 and wall roughness7 have all been investigated. The onset of waves is predicted successfully by theory13 for vertical flow but is not as reliable at other angles.31 Pressure drops for falling film flow in a vertical tube have been reported for various fluid flow conditions.2,4,32-34
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2. Feind, K. (1960) Stromungsuntersuchungen bei gegenstrom von Riesel-Filmen und Gas in lotrechten Rohren, VDl-Forsclurngsh, 481, 32.
3. Malewski, W. (1968) Wave structure and mass transfer in falling films with ripples, Chem. Ing. Tech., 4, 201-218.
4. Fulford, G. D. (1964) The flow of liquids in thin films. Advances in Chemical Engineering, T. B. Drew, J. W. Hopes and J. V. Vermeulen, eds., Vol. 5, 115-237.
5. Lynn, S. (1960) The acceleration of the surface of a falling film, AlChE J., 6, 703-705.
6. Cerro, R. L. and Whitaker, S. (1971) Entrance region flows with a free surface, Chem. Eng. Sci., 26, 785-798. DOI: 10.1016/0009-2509(71)83040-3
7. Brauer, H. (1956) Flow and heat transfer at falling liquid films, VDI Forschungsh, 457, 40.
8. Uehara, H., Naksoka, T., Egashira, S., Tagucki, Y. (1989) Body forced convection condensation on a vertical smooth surface, Nippon Kikai Gakkai Ranbunshu B-hen, 55, 442-9.
9. Yih, S. M. (1986) Modelling heat and mass transport in falling liquid films in Handbook of Heat and Mass Transfer, N. P. Cheremisinoff, ed.. Vol. 2, C5, 111-210.
10. Chu, K. J. and Dukler, A. E. (1974, 1975) Statistical characteristics of thin, wavy films, AlChE J., 20, 695-706, 21, 583-593. ,
11. Nusselt, W. (1910) Die oberflachen Kondensation das Wasserdampfes, VDI-Zeitschrift. 54, 1154-1178.
12. Jackson, M. L. (1955) Liquid films in viscous flow, AlChE J., 1, 231-240.
13. Kapitza, P. L. (1964) Collected papers by P. L. Kapitza, Macmillan, N.Y., 662.
14. Penev, V., Krylov, V. S., Boyadjiev, C., and Vorotilin, V. P. (1972) Wavy flow of thin liquid films, Int. J. Heat Mass Trans., 15,1395-1406. DOI: 10.1016/0017-9310(72)90019-1
15. Lukach, Y. Y, Radchenko, L. B., and Tananayiko, Y. M. (1972) Determination of the average thickness of a film of water during gravitation of flow along the exterior surface of vertical polymeric pipes, Int. Chem. Eng., 12, 517-519.
16. Brotz, W. (1954) Uber die Vorausberedinung der Absorptions geschwineig von Gayen instromenden flussig kectsschichten, Chem. Ing. Tech., 26, 470-478.
17. Zhivaikin, L. Y. (1962) Liquid film thickness in film-type units, Int. Chem. Eng., 2, 337-345.
18. Gauchev, B. G., Kozlov, X., and Lozovetskig, V. (1972) Heat Transfer Soviet Research, 4, 102.
19. Kosky, P. G. (1971) Thin-liquid films under simultaneous shear and gravity forces, Int. J. Heat Mass Trans., 14, 1220-1224. DOI: 10.1016/0017-9310(71)90216-X
20. Takahama, H. and Katos. (1980) Longitudinal flow characteristics of vertically falling liquid films, Int. J. Multiphase Flow, 6, 203-211. DOI: 10.1016/0301-9322(80)90011-7
21. Mostofizadeh, C. (1980) PhD Thesis, Univ. Stiuttgart.
22. Anshus, B. E. and Goren, S. L. (1966) A method of getting appropriate solutions to the Orr-Sommerfeld equation for flow on a vertical wall, AlChE J., 12, 1004-1008.
23. Roy, R. P. and Jam, S. (1989) A study of thin water film flow down an inclined plate without and with countercurrent air flow, Exp. Fluids, 7, 318-328.
24. Dukler, A. E. and Bergelin, O. P. (1952) Characteristics of flow in falling liquid film, Chem. Eng. Prog., 48, 557-563.
25. Portalski, S. (1963) Studies of falling liquid film flow film thickness on a smooth vertical plate, Chem. Eng. Sci., 18, 787-804. DOI: 10.1016/0009-2509(63)85046-0
26. Yin. S. M. and Liv, J. L. (1983) Prediction of heat transfer in turbulent falling liquid films with or without interfacial shear, AlChE J., 29, 903-909.
27. Ueda, T. and Tanaka, T. (1974) Studies of liquid film flow in two-phase annular and annular-mist flow regions, Bull. JSME, 17, 603-613.
28. Hewitt, G. F. (1961) Analysis of annular two-phase flow application of the Dukler analysis to vertical upward flow in a tube, AERE-R3680.
29. Emmert, R. E. and Pigford, R. L. (1954) Interfacial resistance-gas absorption in falling liquid film, Chem. Eng. Prog., 50, 87-93.
30. Tailby, S. R. and Portalski, S. (1961) The optimum concentration of surface active agents for the suppression of ripples, Trans. Inst. Chem. Eng., 39, 328-336.
31. Binnie, A. M. (1957) Experiments on the onset of wave formation on a film of water flowing down a vertical plane, J. Fluid Mech., 2, 551-553.
32. Chien, S. F. (1961) An experimental investigation of the liquid structure and pressure drop of vertical downward annular two-phase flow. PhD Thesis, Univ. Minnesota.
33. Hewitt, G. P., King, I., and Lovegrave, P. C. (1961) Holdup and pressure drop measurements in the two-phase annular flow of air-water mixtures, AERE-R 3764.
34. Thomas, W. J. and Portalski, S. (1958) Hydrodynamics of countercurrent flow in wetted-wall columns, IEC, 50, 1081-1088.