The Stability of Radially Bounded Thin Films

Gumerman, Raymond J.; Homsy, G. M.

doi:10.1080/00986447508960444

Cited by 66 publications

(50 citation statements)

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“…Here, we introduce a method of stability analysis for the free film problem based on the dissipation method of viscous potential flow (8). Stability studies based on the Navier-Stokes equations for long waves were considered by Ruckenstein and Jain (6), Gumerman and Homsy (9), and in the nonlinear case by Williams and Davis (10) and Erneux and Davis (11). Maldarelli et al (12) considered short-and long-wavelength perturbations of symmetrical and unsymmetrical membranes, assimilated with viscous liquids.…”

Section: Thin Film | Irrotational Flow | Dissipation Methodsmentioning

confidence: 99%

Instability of stationary liquid sheets

Ardekani

Joseph

2009

Proc. Natl. Acad. Sci. U.S.A.

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The rupture of a 3D stationary free liquid film under the competing effects of surface tension and van der Waals forces is studied as a linearized stability problem in a purely irrotational analysis utilizing the dissipation method. The results of the foregoing analysis are compared with a 2D long-wave approximation that has given rise to an extensive literature on the rupture problem. The irrotational and long-wave approximations are here compared with the exact 2D solution. The exact solution and the two approximate theories give the same results for infinitely long waves. The problem considered depends on two dimensionless parameters, the Hamaker number and the Ohnesorge number. The Hamaker number is a dimensionless number defined as a measure of the ratio of van der Waals forces to surface tension. The exact solution and the two approximate solutions differ by <1% when the Hamaker number is small for all values of the Ohnesorge number. When the Ohhnesorge number is close to one, as in the case of water films separated by distance 100 Å, the long-wave approximation overestimates and the potential flow approximation underestimates the exact solution by similar small amounts. The high accuracy of the dissipation method shows that the effects of vorticity are small for small to moderate Hamaker numbers. thin film | irrotational flow | dissipation methodA stable free liquid layer in balance between stabilizing surface tension and destabilizing van der Waals molecular forces can become unstable and be driven to rupture. Molecular forces are important in thin films in the range 100-1,000 Å. Ultrathin "black films" may arise from the stabilizing effects of electric double-layer potentials discussed by Overbeek (1).The rupture of a film often occurs in many contexts, the coalescence of droplets and bubbles, in the creation of dry patches, in the problem of aerodynamic dissemination (2), and in the formation of holes in moving sheets from atomizers studied by Dombrowski and Fraser (3). Stability analysis based on the free energy of stationary films for the critical thickness at which spontaneous local thinning first occurs was given by Vrij (4) and Scheludko (5). Ruckenstein and Jain (6) introduced the fundamental analytic simplification by introducing the disjoining pressure as an "extra pressure" analogous to other prescribed body forces in potential form and constructed a dynamic analysis based on the linear theory of stability. The term "disjoining pressure" was introduced by Deryagin to designate the excess pressure in a thin layer compared with a thick one. If film thickness h is small enough, the stabilizing effects of surface tension are insufficient and the film will thin under the influence of the large disjoining pressure. For a planar film, molecular interactions are accounted for in a strict thermodynamic theory through the concept of a disjoining pressure by Ivanov and Tosev (7). The stability analysis gives the critical h, the wave length, and the maximum growth rate of the most unstable disturbance. He...

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Section: Thin Film | Irrotational Flow | Dissipation Methodsmentioning

confidence: 99%

Instability of stationary liquid sheets

Ardekani

Joseph

2009

Proc. Natl. Acad. Sci. U.S.A.

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“…This work is preceded by numerous experimental [2][3][4][5][6] and theoretical [2,5,[7][8][9][10] studies that address film stability and the critical or rupture condition. Despite this wealth of information, significant confusion and uncertainty remains in the ability to predict the critical film thickness from basic physicochemical properties.…”

Section: Introductionmentioning

confidence: 99%

“…The conditions of the onset of instability have been described previously [8,11]. Unstable capillary waves located along the interfaces of a thin film grow towards the middle of the film, in the direction of the opposing interface.…”

Section: Introductionmentioning

confidence: 99%

Scaling laws for the critical rupture thickness of common thin films

Coons

Halley

McGlashan

et al. 2005

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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Abstract. Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness.According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves at the interfaces begin to grow. In a horizontal film with symmetry at the midplane, unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture. Uncertainty stems from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, the linear stability of small amplitude waves was investigated in the context of

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“…Substitution of the first order approximate leads to a velocity dependent wave growth rate expression consistent with linear stability theory (Gumerman and Homsy, 1975;Sharma and Ruckenstein, 1987;Coons et al, 2003). In a previous review, it was shown that the corrugation growth rate expression obtained by neglecting the effect of thinning velocity is the same expression derived by introducing a zeroth order (h 3 ) function (Coons et al, 2003).…”

Section: Introductionmentioning

confidence: 61%

Bounding the Stability and Rupture Condition of Emulsion and Foam Films

Coons

Halley

McGlashan

et al. 2005

Chemical Engineering Research and Design

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A scaling law is presented that provides a complete solution to the equations bounding the stability and rupture of thin films. The scaling law depends on the fundamental physicochemical properties of the film and interface to calculate bounds for the critical thickness and other key film thicknesses, the relevant waveforms associated with instability and rupture, and film lifetimes. Critical thicknesses calculated from the scaling law are shown to bound the values reported in the literature for numerous emulsion and foam films. The majority of critical thickness values are between 15 to 40% lower than the upper bound critical thickness provided by the scaling law.Keywords: thin films; stability; critical thickness; spontaneous rupture; scaling law. INTRODUCTIONDespite decades of experimental (Ivanov et al., 1970;Traykov et al., 1977;Rao et al., 1982;Radoev et al., 1983;Manev et al., 1984;Kumar et al., 2002) and theoretical (Vrij, 1966a;Sheludko, 1967;Ivanov et al., 1970;Radoev et al., 1983;Sharma and Ruckenstein, 1987) investigation into the stability and rupture of thin films, very little has been published on their scaling behaviour. Thin liquid films form between the dispersed phase in emulsions and foams and become unstable when long range van der Waals forces induce the growth of capillary waves on the film interfaces (Vrij, 1966a). Upon reaching a critical thickness, films either rupture or shift to a uniform thickness and form a black film (Manev et al., 1974). Vrij (1966a, b) derived limiting equations for the critical thickness under conditions where either the Plateau border pressure drop or disjoining pressure control film drainage. Many films drain under conditions that fit into the intermediate region where both pressure terms are significant and the limiting equations are not applicable. Vrij's unique theoretical approach forced the critical thickness predictions to lower values by applying a wave-averaged corrugation growth rate expression and by specifying the rupture thickness from the film drainage curve at the minimum lifetime. The lower critical thickness predictions were still much larger than the experimental values on aniline and aqueous foam films. In this case, the overprediction was exacerbated by application of Reynolds equation and unusually large Hamacker constants. Vrij used 7 Â 10 219 J for aniline and 10 219 J for aqueous films, when the non-retarded Hamacker constant predicted from Lifshitz theory is 6.5 Â 10 220 J and 3.6 Â 10 220 J, respectively (Coons et al., 2005b). Vrij also included an undefined parameter ( f), which was inexplicably set to 6.5 and 7 for the validation films. While application of Vrij's limiting equations has the advantage of being relatively simple, frequent discrepancy with experimental results reduce their overall appeal. Ivanov et al. (1970) applied the same corrugation growth rate expressions as Vrij, but based the critical condition upon the first waveform to reach the centre of the film. This rupture criterion increases the critical film thickness...

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The Stability of Radially Bounded Thin Films

Cited by 66 publications

References 1 publication

Instability of stationary liquid sheets

Instability of stationary liquid sheets

Scaling laws for the critical rupture thickness of common thin films

Bounding the Stability and Rupture Condition of Emulsion and Foam Films

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