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.
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...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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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.
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...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 paper, a boundary integral method was used to compute the wave growth on a cylindrical jet and the initial wave growth is in agreement with Rayleigh's linear theory, when followed to completion these waves pinch off large drops separated by smaller satellite drops that decrease in size with decreasing wavelength.
Abstract: Computations of finite‐amplitude, spatially periodic wave growth on a cylindrical jet have been carried out using a boundary integral method. The initial wave growth is in agreement with Rayleigh’s linear theory. When followed to completion these waves pinch off large drops separated by smaller satellite drops (spherules) that decrease in size with decreasing wavelength. The computed sizes of both drops and satellites agree with experiment. It is found that satellites will form for all unstable wave numbers. The small satellites that are computed at wave numbers near the critical wave number were not predicted by near‐linear analysis but are observed in experimental photographs of jet breakup. Computation of the collapse of elongated satellites shows short waves propagating on their surfaces.
145 citations
TL;DR: In this paper, a new technique for including the effect of surface tension in time-dependent, incompressible flow calculations is used to examine the linear and nonlinear phases of Rayleigh-Taylor instability.
Abstract: A new technique for including the effect of surface tension in time‐dependent, incompressible flow calculations is used to examine the linear and nonlinear phases of Rayleigh‐Taylor instability. The variation of the linear growth rate with the surface tension coefficient and (for a fixed coefficient) with the wavenumber of the perturbation is shown to be in good agreement with Chandrasekhar's analytic prediction. In the nonlinear regime, it is shown how surface tension affects the growth of the Rayleigh‐Taylor spike and provides the mechanism for drop separation from the spike.
115 citations
TL;DR: In this paper, the motion of immiscible fluids with arbitrary viscosities flowing through a capillary with an almost flat fluid-fluid interface is investigated in the limit of small capillary and Reynolds numbers.
Abstract: The motion of two immiscible fluids with arbitrary viscosities flowing through a capillary with an almost flat fluid-fluid interface is investigated in the limit of small capillary and Reynolds numbers. A complete description of the dynamics of the fluids is presented. It is shown that the motion of the fluid away from the moving contact line can be completely determined in terms of one material parameter, and how the capillary can be viewed as a device for measuring it. The dynamic behaviour of various contact angles, measured by others, is calculated. It is shown that they all depend on the radius of the capillary; hence, they do not represent properties of only the materials of the system.
82 citations
Book•
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30 Oct 1992
TL;DR: In this paper, the authors present a program for Harmonic Oscillation, Damping, Forced Oscillations and Resonance, which is based on the Continuum Limit and Fourier Series.
Abstract: 1. Harmonic Oscillation. 2. Damping, Forced Oscillations and Resonance. 3. Normal Modes. 4. Symmetries. 5. Waves. 6. The Continuum Limit and Fourier Series. 7. Longitudinal Oscillations and Sound. 8. Traveling Waves. 9. The Boundary at a. 10. Signals and Fourier Analysis. 11. Two and Three Dimensions. 12. Polarization. 13. Diffraction. Appendix A: The Programs. Appendix B: The Solutions. Index.
80 citations
TL;DR: In this article, the stability of laminar flows involving surface-tension variation is briefly discussed, and a correction of a previous result [C.S. Yih, J.F. Fluid Mech. 28, 493] is made.
Abstract: Fluid motion in a long straight channel induced by longitudinally varying surface tension has been discussed by Levich. This problem is re‐examined and a different solution is given. In addition, the stability of laminar flows involving surface‐tension variation is briefly discussed, and a correction of a previous result [C.‐S. Yih, J. Fluid Mech. 28, 493 (1967)] is made.
77 citations