A continuum method for modeling surface tension
01 Jun 1992-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 100, Iss: 2, pp 335-354
TL;DR: In this paper, a force density proportional to the surface curvature of constant color is defined at each point in the transition region; this force-density is normalized in such a way that the conventional description of surface tension on an interface is recovered when the ratio of local transition-reion thickness to local curvature radius approaches zero.
About: This article is published in Journal of Computational Physics.The article was published on 1992-06-01. It has received 7863 citations till now. The article focuses on the topics: Capillary surface & Capillary length.
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TL;DR: An overview of the lattice Boltzmann method, a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities, is presented.
Abstract: We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.
6,565 citations
Cites methods from "A continuum method for modeling sur..."
...Traditional numerical schemes have been successfully used for simple interfacial boundaries (Glimm et al 1981, Brackbill et al 1992, Chang et al 1996)....
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3,822 citations
TL;DR: The level set method is couple to a wide variety of problems involving external physics, such as compressible and incompressible flow, Stefan problems, kinetic crystal growth, epitaxial growth of thin films, vortex-dominated flows, and extensions to multiphase motion.
2,174 citations
Cites methods from "A continuum method for modeling sur..."
...See [87] and [12] for earlier front tracking and VOF methods (respectively) using a similar formulation....
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TL;DR: In this paper, a front-tracking method for multiphase flows is presented, which is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties.
2,011 citations
TL;DR: In this paper, the authors consider the formation of droplet clouds or sprays that subsequently burn in combustion chambers, which is caused by interfacial instabilities, such as the Kelvin-Helmholtz instability.
Abstract: The numerical simulation of flows with interfaces and free-surface flows is a vast topic, with applications to domains as varied as environment, geophysics, engineering, and fundamental physics. In engineering, as well as in other disciplines, the study of liquid-gas interfaces is important in combustion problems with liquid and gas reagents. The formation of droplet clouds or sprays that subsequently burn in combustion chambers originates in interfacial instabilities, such as the Kelvin-Helmholtz instability. What can numerical simulations do to improve our understanding of these phenomena? The limitations of numerical techniques make it impossible to consider more than a few droplets or bubbles. They also force us to stay at low Reynolds or Weber numbers, which prevent us from finding a direct solution to the breakup problem. However, these methods are potentially important. First, the continuous improvement of computational power (or, what amounts to the same, the drop in megaflop price) continuously extends the range of affordable problems. Second, and more importantly, the phenomena we consider often happen on scales of space and time where experimental visualization is difficult or impossible. In such cases, numerical simulation may be a useful prod to the intuition of the physicist, the engineer, or the mathematician. A typical example of interfacial flow is the collision between two liquid droplets. Finding the flow involves the study not only of hydrodynamic fields in the air and water phases but also of the air-water interface. This latter part
1,949 citations
Cites methods from "A continuum method for modeling sur..."
...After Brackbill et al (1992), this method is sometimes called the continuous surface force (CSF) method....
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...As in the method used by Brackbill et al (1992), this approximation converges in theory toward the true normal asH → δS....
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References
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TL;DR: In this article, the behavior of fluids in microgravity conditions is examined, with particular regard to applications in the growth of single crystals, and the effects of gravity on fluid behavior are reviewed, and a Shuttle flight is noted to offer extended time for experimentation and processing in a null-gravity environment, with accelerations resulting solely from maneuvering rockets.
Abstract: The behavior of fluids in micro-gravity conditions is examined, with particular regard to applications in the growth of single crystals. The effects of gravity on fluid behavior are reviewed, and the advent of Shuttle flights are noted to offer extended time for experimentation and processing in a null-gravity environment, with accelerations resulting solely from maneuvering rockets. Buoyancy driven flows are considered for the cases stable-, unstable-, and mixed-mode convection. Further discussion is presented on g-jitter, surface-tension gradient, thermoacoustic, and phase-change convection. All the flows are present in both gravity and null gravity conditions, although the effects of buoyancy and g-jitter convection usually overshadow the other effects while in a gravity field. Further work is recommended on critical-state and sedimentation processes in microgravity conditions.
394 citations
DOI•
01 Jan 1991
276 citations
"A continuum method for modeling sur..." refers methods in this paper
...with a 2D, incompressible hydrocode [27] using the VOF ....
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...25 cm) with a 2D, incompressible hydrocode [27] using the VOF method to describe the free surface [26]....
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...The results are computed with a 2D, incompressible hydrocode [27] using the VOF method to describe the free surface [26]....
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TL;DR: In this article, the authors investigate the flow induced by a localized insoluble surfactant on a thin film and derive equations that describe the evolution of the film thickness and surface tension.
Abstract: We investigate the flow induced by a localized insoluble surfactant on a thin film. This problem is intended to model the behaviour of the lung's thin-film lining after an aerosol droplet lands on its surface. The surfactant-induced surface-tension gradients drive convection (Marangoni convection) within the film, disrupting the film surface and causing the surfactant to spread. The surfactant may also spread on the film's surface by surface diffusion without inducing convection. Gravity provides a restoring force that decreases film disturbances.Lubrication theory is employed to derive equations that describe the evolution of the film thickness and surfactant concentration. A nonlinear surface-tension equation of state describes the relationship between the surfactant concentration and the surface tension. Solutions of the evolution equations are found numerically using the method of lines and analytically under limiting cases of small and large surface diffusivity. The results elucidate the behaviour of the thin-film/surfactant system.We find that surface-tension-induced convection creates film disturbances that increase the film thickness near the surfactant's leading edge, and thins the film in the central region. Surface diffusion causes more rapid spreading of the surfactant, and decreases the film disturbances. Gravity decreases the film disturbances by creating bi-directional flow in the form of a ring vortex. This behaviour may have implications for the delivery of medications or toxins by aerosol inhalation.
238 citations