Prediction of Wavy Liquid Film Profile for Thin Film on a Falling Film Absorber

Hamza M. Habib, Essam R. El-Zahar, Ahmed M. Ebady

Department of Mathematics, College of Sciences and Humanities, Salman Bin Abdulaziz University, Alkharj, KSA.
[e-mail].

DOI: 10.4236/am.2013.45107                

Abstract

A hydrodynamic model of thin, laminar, gravity-driven, wavy-film flow over a vertical plate was considered. To make advantage of the cyclic boundary conditions and due to the nature of the wavy flow, a solution based on a Fourier series was implemented. Two representative cases of practical importance were studied; Re = 25, Re = 100. This range of Reynolds numbers is of the most practical importance in the process industry. Multiple solutions were obtained. Most of these solutions are mathematically correct but physically are not. It is observed that realistic wave profiles are always obtained once we approach the Froude number corresponding to thin film.

Keywords

Wavy Film Flow; Gravity-Driven Flow; Analytical Numerical Methods

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. I. Hirshburg and L. W. Florschuetz, “Laminar Wavy Film Flow: Part I, Hydrodynamic Analysis,” Journal of Heat Transfer, Vol. 104, No. 3, 1982, pp. 452-458. doi:10.1115/1.3245114
[2]	R. E. Emmert and R. L. Pigford, “A Study of Gas Ab sorption in Falling Liquid Films,” Chemical Engineering Progress, Vol. 50, 1954, pp. 87-93.
[3]	D. R. Oliver and T. E. Atherinos, “Mass Transfer to Liquid Films on an Inclined Plane,” Chemical Engineering Science, Vol. 23, No. 6, 1968, pp. 525-536. doi:10.1016/0009-2509(68)89001-3
[4]	S. M. Yih and R. C. Seagrave, “Mass Transfer in Laminar Falling Liquid Films with Accompanying Heat Transfer and Interfacial Shear,” International Journal of Heat and Mass Transfer, Vol. 23, No. 6, 1980, pp. 749-758. doi:10.1016/0017-9310(80)90028-9
[5]	V. Patnaik and H. Perez-Blanco, “Roll Waves in Falling Films: An Approximate Treatment of the Velocity Field,” International Journal of Heat and Fluid Flow, Vol. 17, No. 1, 1996, pp. 63-70. doi:10.1016/0142-727X(95)00075-2
[6]	P. Adomeit and U. Renz, “Hydrodynamics of Three-Di mensional Waves in Laminar Falling Films,” Interna tional Journal of Multiphase Flow, Vol. 26, No. 7, 2000, pp. 1183-1208. doi:10.1016/S0301-9322(99)00079-8
[7]	W. Ambrosinr, N. Forgione and F. Oriolo, “Statistical Characteristics of a Water Film Falling down a Flat Plate at Different Inclinations and Temperatures,” International Journal of Multiphase Flow, Vol. 28, No. 3, 2002, pp. 1521-1540. doi:10.1016/S0301-9322(02)00039-3
[8]	E. I. P. Drosos, S. V. Paras and A. J. Karabe las, ”Characteristics of Developing Free Falling Films at Intermediate Reynolds and High Kapitza Numbers,” In ternational Journal of Multiphase Flow, Vol. 30, No. 7, 2004, pp. 853-876. doi:10.1016/j.ijmultiphaseflow.2004.03.003
[9]	C. P. Berbente and E. Ruckenstein, “Hydrodynamics of Wave Flow,” AIChE Journal, Vol. 14, No. 5, 1968, pp. 772-782. doi:10.1002/aic.690140517
[10]	K. Javdani, “Mass Transfer in Wavy Liquid Films,” Chemical Engineering Science, Vol. 29, No. 1, 1974, pp. 61-69. doi:10.1016/0009-2509(74)85030-X
[11]	V. Beschkov and C. Boyadjiev, “ Numerical Investigation of Gas Absorption in a Wavy Film Flow,” Chemical Engineering Communications, Vol. 20, No. 3-4, 1983, pp. 173-182. doi:10.1080/00986448308940588
[12]	A. E. Dukler, “Characteristic Effects and Modeling of the Wavy Gas-Liquid Interface,” Heat and Mass Transfer, Vol. 6, 1972, pp. 207-234.
[13]	L. T. Nguyen and V. Balakotaiah, “Modeling and Ex perimental Studies of Wave Evolution on Free Falling Films,” Physics of Fluids, Vol. 12, No. 2236, 2000, pp. 2236-2256. doi:10.1063/1.1287612
[14]	P. L. Kapitza, “Wave Flow of Thin Layers of a Viscous Fluid,” Pergamon Press, Oxford, 1965, pp. 261-272.
[15]	V. Ya. Shkadov, “Wave Flow theory for a Thin Viscous Liquid Layer,” Fluid Dynamics, Vol. 3, No. 2, 1968, pp. 20-25.
[16]	R. Yang, “Heat and Mass Transfer in Laminar Wavy Film Absorption with the Presence of Non-Absorbable Gases,” Ph.D. Dissertation, Arizona State University, Tempe, 1987,
[17]	T. Ueda and H. Tanaka, “Measurements of Velocity, Temperature and Velocity Fluctuation Distribution in Falling Liquid Films,” International Journal of Multiphase Flow, Vol. 2, No. 3, 1975, pp. 261-272. doi:10.1016/0301-9322(75)90014-2
[18]	F. W. Pierson and S. Whitaker, “Some Theoretical and Experimental Observations of the Wave Structure of Falling Liquid Films,” Industrial & Engineering Chemistry Fundamentals, Vol. 16, No. 4, 1977, pp. 401-408. doi:10.1021/i160064a002