The dynamics of liquid film breakup in constricted cylindrical capillaries

Abstract To understand foam generation in porous media, this work considers the dynamics of a wetting viscous film forming an unstable collar (or collars) in a constricted cylindrical capillary. A nonlinear evolution equation is derived and solved numerically to determine the evolution in time of a liquid film deposited by a bubble after it has moved through a constricted capillary. Results show that time to break up depends on the initial film profile, the film thickness, the pore geometry, and also on the fluid viscosity, interfacial tension, and unconstricted capillary radius which combine to form a characteristic scaling time. Excellent agreement is found between breakup times predicted from the hydrodynamic analysis and experimental breakup time data over a wide range of initial film thicknesses and fluid properties. New data for the dynamic collar shape also agree well with the theoretical results.

[1]  P. Hammond.  Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe , 1983, Journal of Fluid Mechanics.

[2]  Clayton J. Radke,et al.  Mechanisms of Foam Generation in Glass-Bead Packs , 1988 .

[3]  L. W. Holm.  Status of CO2 and Hydrocarbon Miscible Oil Recovery Methods , 1976 .

[4]  C. Radke,et al.  An extended evolution equation for liquid film breakup in cylindrical capillaries , 1988 .

[5]  R. W. Hornbeck.  Numerical Methods , 1975 .

[6]  S. Goren.  The instability of an annular thread of fluid , 1962, Journal of Fluid Mechanics.

[7]  Fred Fairbrother,et al.  119. Studies in electro-endosmosis. Part VI. The “bubble-tube” method of measurement , 1935 .

[8]  R. Atherton,et al.  ON THE DERIVATION OF EVOLUTION EQUATIONS FOR INTERFACIAL WAVES , 1976 .

[9]  Eli Ruckenstein,et al.  Spontaneous rupture of thin liquid films , 1974 .

[10]  J. Duerksen,et al.  Two Successful Steam/Foam Field Tests, Sections 15A and 26C, Midway-Sunset Field , 1985 .

[11]  Stephen H. Davis,et al.  Nonlinear theory of film rupture , 1982 .

[12]  S. G. Mason,et al.  The flow of suspensions through tubes. II. Single large bubbles , 1963 .

[13]  J. G. Roof.  Snap-Off of Oil Droplets in Water-Wet Pores , 1970 .

[14]  G. Homsy,et al.  Two-phase displacement in Hele Shaw cells: theory , 1984, Journal of Fluid Mechanics.

[15]  Norman R. Morrow,et al.  Physics and Thermodynamics of Capillary Action in Porous Media , 1970 .

[16]  J. B. Lawson,et al.  Mechanisms of foam flow in porous media: apparent viscosity in smooth capillaries , 1985 .

[17]  G. Taylor.  Deposition of a viscous fluid on the wall of a tube , 1961, Journal of Fluid Mechanics.

[18]  R. Mast.  Microscopic Behavior of Foam in Porous Media , 1972 .

[19]  Leon Lapidus,et al.  Digital computation for chemical engineers , 1962 .

[20]  F. Bretherton.  The motion of long bubbles in tubes , 1961, Journal of Fluid Mechanics.

[21]  H. A. Luther,et al.  Applied numerical methods , 1969 .

[22]  D. H. Everett,et al.  Model studies of capillary condensation. I. Cylindrical pore model with zero contact angle , 1972 .

[23]  Tadeusz W Patzek,et al.  Development of a mechanistic foam simulator: The population balance and generation by snap-off , 1988 .

[24]  B. Finlayson.  Nonlinear analysis in chemical engineering , 1980 .

[25]  K. Udell,et al.  A Finite Element Study of Low Reynolds Number Two-Phase Flow in Cylindrical Tubes , 1985 .

[26]  J. C. Slattery,et al.  Thinning of a liquid film as a small drop or bubble approaches a solid plane , 1982 .