Steady-State Thickness of Liquid–Gas Foams

This paper presents an approach for predicting the thickness of isothermal foams produced by blowing gas in a liquid solution under steady-state conditions. The governing equation for the transient foam thickness has been non-dimensionalized, and two dimensionless numbers have been identified to describe the formation and stability of this type of foam: \Pi_1 = {Re}/{Fr} and \Pi_2 = Ca H_{\infty}/r_0. Physical interpretation of the dimensionless numbers has been proposed, a power-law type relation has been assumed between \Pi_1 and \Pi_2 (i.e., \Pi_2=K \Pi^n_1). Experimental data available in the literature have been used to determine the empirical parameters of the correlation K and n. The experimental conditions cover a wide range of viscosity, density, surface tension, gas superficial velocity, and average bubble radius. The model is valid for foams formed from high viscosity liquids bubbled with nitrogen, air, helium, hydrogen, and argon injected through single, multi-orifice nozzles or porous medium. Comparison between the correlation developed and the experimental data yields reasonable agreements (within 35% error), given the broadness of the bubble radius distribution around the mean value, the uncertainty of the experimental data and of the thermophysical properties. Predictions have been found to be very sensitive to the average bubble radius. A more refined model is still needed which should be supported by a careful experimental studies. Finally, suggestions are given to extend the present work to foams generated from low viscosity solutions.

[1]  R. E. Pattle.  The control of foaming. II. The breakdown mechanisms and volume of dynamic foams , 1950 .

[2]  Rajinder Kumar,et al.  Flow through a plateau border of cellular foam , 1982 .

[3]  E. Ruckenstein,et al.  Hydrodynamics, enrichment, and collapse in foams , 1986 .

[4]  E. Ruckenstein,et al.  Effect of bubble size distribution on the enrichment and collapse in foams , 1986 .

[5]  Kenneth C. Mills,et al.  PHYSICAL PROPERTIES OF BOS SLAGS , 1987 .

[6]  Richard J. Fruehan,et al.  Study on the foaming of CaO-SiO2-FeO slags: Part II. Dimensional analysis and foaming in iron and steelmaking processes , 1989 .

[7]  Richard J. Fruehan,et al.  Study on the foaming of CaO-SiO2-FeO slags: Part I. Foaming parameters and experimental results , 1989 .

[8]  P. Hrma.  Model for a steady state foam blanket , 1990 .

[9]  Ganesan Narsimhan,et al.  A model for unsteady state drainage of a static foam , 1991 .

[10]  Richard J. Fruehan,et al.  Slag foaming in bath smelting , 1991 .

[11]  J. Bourne,et al.  A study of disproportionation effects in semi-batch foams—II. Comparison between experiment and theory , 1993 .

[12]  Didier Huin,et al.  Physical Model of Slag Foaming. , 1993 .

[13]  John R. Blake,et al.  Gas bubbles bursting at a free surface , 1993, Journal of Fluid Mechanics.

[14]  A. H. Pendray,et al.  Graphitization of plain carbon steels , 1995 .

[15]  R. J. Fruehan,et al.  Effect of carbonaceous particles on slag foaming , 1995 .

[16]  R. J. Fruehan,et al.  Effect of temperature on slag foaming , 1995 .

[17]  Richard J. Fruehan,et al.  Effect of the bubble size and chemical reactions on slag foaming , 1995 .

[18]  Eli Ruckenstein,et al.  Decay of standing foams: drainage, coalescence and collapse , 1997 .

[19]  P. Hayes,et al.  The Prediction of Gas Residence Times in Foaming CaO–SiO2–FeO Slags , 1998 .

[20]  Peter C. Hayes,et al.  Model Development of Slag Foaming , 1998 .

[21]  Peter C. Hayes,et al.  Physical Model Studies on Slag Foaming , 1998 .

[22]  Keng Wu,et al.  Investigation into rheological characteristic and foaming behaviour of molten slags , 1999 .

[23]  Andrei G. Fedorov,et al.  Radiative transfer in a semitransparent glass foam blanket , 2000 .

[24]  R. J. Fruehan,et al.  Foaming Characteristics of BOF Slags , 2000 .

[25]  Miao‐yong Zhu,et al.  Modelling study of slag foaming phenomenon , 2000 .