Stable Drop Shapes under Disjoining Pressure

Zhang, Xianzhong; Neogi, Partho

doi:10.1006/jcis.2002.8234

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…In the present case it is being assumed that the drop is thin and flat and hence η = h , a perturbation to the local thickness h. We also choose those perturbations where the volume remains unchanged, such as in the form of simple periodic waves. When the disjoining pressure is used as a body force, the pressure term can be expressed in terms of the disjoining pressure [11]. Thus, if φ i is a potential, then the hydrostatics is given by 0 = −∇ p i − ∇φ i which can be used to rewrite the last term on the left in equation ( 6) to get −ηn∇(φ 1 − φ 2 ) to be evaluated at the interface.…”

Section: Stabilitymentioning

confidence: 99%

“…Now, a system where surface tension is important is characterized by a critical wavelength where disturbances of wavelengths smaller than the critical one are stable due to the surface tension. Thus, if the critical wavelength in any particular piece is larger than the piece itself, then the unstable disturbances of larger wavelengths cannot be accommodated as well, and this leads to a conclusion that the piece is stable, particularly when the piece is isolated [11]. However, when the overall system is large, then it is possible to envisage that disturbances of sufficiently large wavelengths, larger than the critical wavelength in either piece, can be accommodated in the overall system.…”

Section: Stabilitymentioning

confidence: 99%

“…Originally, the use of the word 'wavy' was made to denote the almost sinusoidal nature of undulation in the film thickness. A strict wavy system is very likely unstable [11] and a close approximation in figure 2 which is more stable is being used here. Here, the sine wave has been flattened from below and the sharp change in the profile at the contact line is only an approximation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Labyrinthine instability in thin liquid films

Neogi

2010

J. Phys.: Condens. Matter

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When a thin liquid film on a solid surface has a thickness corresponding to a particular part the spinodal region of the disjoining pressure versus thickness isotherm, the film breaks down. One of the patterns that emerges on the breakdown has been referred to as wavy instability. It is compared here to the labyrinthine instability seen in magnetic films. The system is modeled following the procedure used in magnetic systems, and the pattern of wavy instability is broken down into a curved thick-thin film in equilibrium with a flat thin-thin film of constant thickness. Minimization of free energy leads to expressions for various length scales that characterize the system. Comparisons with published experimental results on nematic liquid crystals for a number of very different features are satisfactory. They include film thicknesses in the bulk at equilibrium where the capillary pressure is not zero, and is determined as a part of the solution, as well as film thicknesses in the ledge where the capillary pressure is zero. Stability analysis shows that the system is unstable in both directions with some qualifiers. A model is proposed in the form of a tiled structure to explain the labyrinthine form.

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Section: Stabilitymentioning

confidence: 99%

Section: Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Labyrinthine instability in thin liquid films

Neogi

2010

J. Phys.: Condens. Matter

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“…Since the diameter of the microlens in our experiment is sufficiently larger than the height of the microlens, the disjoining pressure can be neglected [21] and then equation ( 17…”

Section: Analysis Of Microlens Shapementioning

confidence: 99%

Physical modeling and analysis of microlens formation fabricated by a modified LIGA process

Kim¹,

Yang²,

Lee³

et al. 2003

J. Micromech. Microeng.

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In this paper, we present the physical modeling and analysis method of microlens formation using deep x-ray lithography followed by the thermal treatment of a polymethylmethacrylate (PMMA) sheet. According to the modeling, x-ray irradiation causes a decrease of the molecular weight of PMMA, which in turn decreases the glass transition temperature and consequently causes a net volume increase during the thermal cycle, resulting in a swollen microlens. In this modeling, the free volume theory including volume relaxation phenomena was considered during the thermodynamically non-equilibrium cooling process. Based on this modeling, an analysis method has been proposed to predict the shape of the microlens with the surface tension effect taken into account. The analysis results are favorably compared with experimental data. The present analysis method enables us to predict the fabricated microlens shapes and the variation pattern of the maximum heights of the microlens, which depend on the conditions of the thermal treatment. The prediction model could eventually be used in determining the detailed thermal treatment conditions for a desired microlens shape fabricated by a modified LIGA process.

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A Variational Model of Disjoining Pressure: Liquid Film on a Nonplanar Surface

Silin

Virnovsky

2009

Transp Porous Med

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ABSTRACT. Variational methods have been successfully used in modelling thin liquid films in numerous theoretical studies of wettability. In this paper, the variational model of the disjoining pressure is extended to the general case of a two-dimensional solid surface. The Helmgoltz free energy functional depends both on the disjoining pressure isotherm and the shape of the solid surface. The augmented Young-Laplace equation (AYLE) is a nonlinear second-order partial differential equation. A number of solutions describing wetting films on spherical grains have been obtained. In the case of cylindrical films, the phase portrait technique describes the entire variety of mathematically feasible solutions. It turns out that a periodic solution, which would describe wave-like wetting films, does not satisfy the Jacobi's condition of the classical calculus of variations. Therefore, such a solution is nonphysical. The roughness of the solid surface significantly affects liquid film stability. AYLE solutions suggest that film rupture is more likely at a location where the pore-wall surface is most exposed into the pore space and the curvature is positive.

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Stable Drop Shapes under Disjoining Pressure

Cited by 7 publications

References 12 publications

Labyrinthine instability in thin liquid films

Labyrinthine instability in thin liquid films

Physical modeling and analysis of microlens formation fabricated by a modified LIGA process

A Variational Model of Disjoining Pressure: Liquid Film on a Nonplanar Surface

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