Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids

Journal Article · Tue Sep 06 00:00:00 EDT 2016 · Physics of Fluids

DOI:https://doi.org/10.1063/1.4961549· OSTI ID:1467878

Thete, Sumeet Suresh ^[1]; Anthony, Christopher ^[1]; Doshi, Pankaj ^[2]; Harris, Michael T. ^[1]; Basaran, Osman A. ^[1]

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1. Purdue Univ., West Lafayette, IN (United States). School of Chemical Engineering
2. Pfizer Worldwide R&D, Groton, CT (United States)

Rupture of thin liquid films is crucial in many industrial applications and nature such as foam stability in oil-gas separation units, coating flows, polymer processing, and tear films in the eye. In some of these situations, a liquid film may have two free surfaces (referred to here as a free film or a sheet) as opposed to a film deposited on a solid substrate that has one free surface. The rupture of such a free film or a sheet of a Newtonian fluid is analyzed under the competing influences of inertia, viscous stress, van der Waals pressure, and capillary pressure by solving a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. The dynamics close to the space-time singularity where the film ruptures is asymptotically self-similar and, therefore, the problem is also analyzed by reducing the transient partial differential evolution equations to a corresponding set of ordinary differential equations in similarity space. Here, for sheets with negligible inertia, it is shown that the dominant balance of forces involves solely viscous and van der Waals forces, with capillary force remaining negligible throughout the thinning process in a viscous regime. On the other hand, for a sheet of an inviscid fluid for which the effect of viscosity is negligible, it is shown that the dominant balance of forces is between inertial, capillary, and van der Waals forces as the film evolves towards rupture in an inertial regime. Real fluids, however, have finite viscosity. Hence, for real fluids, it is further shown that the viscous and the inertial regimes are only transitory and can only describe the initial thinning dynamics of highly viscous and slightly viscous sheets, respectively. Moreover, regardless of the fluid’s viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a late stage or final inertial-viscous regime in which inertial, viscous, and van der Waals forces balance each other while capillary force remains negligible, in accordance with the results of Vaynblat, Lister, and Witelski.

• Research Organization: Purdue Univ., West Lafayette, IN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: FG02-96ER14641
• OSTI ID: 1467878
• Alternate ID(s): OSTI ID: 1319950
• Journal Information: Physics of Fluids, Vol. 28, Issue 9; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
36 MATERIALS SCIENCE
42 ENGINEERING