Journal articles: 'Faraday instability'

1

Mahr, T., and I. Rehberg. "Magnetic Faraday instability." Europhysics Letters (EPL) 43, no. 1 (July 1, 1998): 23–28. http://dx.doi.org/10.1209/epl/i1998-00313-4.

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Samanta, Arghya. "Effect of porous layer on the Faraday instability in viscous liquid." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (July 2020): 20200208. http://dx.doi.org/10.1098/rspa.2020.0208.

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A linear stability analysis of a viscous liquid on a vertically oscillating porous plane is performed for infinitesimal disturbances of arbitrary wavenumbers. A time-dependent boundary value problem is derived and solved based on the Floquet theory along with the complex Fourier series expansion. Numerical results show that the Faraday instability is dominated by the subharmonic solution at high forcing frequency, but it responds harmonically at low forcing frequency. The unstable regions corresponding to both subharmonic and harmonic solutions enhance with the increasing value of permeability and yields a destabilizing effect on the Faraday instability. Further, the presence of porous layer makes faster the transition process from subharmonic instability to harmonic instability in the wavenumber regime. In addition, the first harmonic solution shrinks gradually and becomes an unstable island, and ultimately disappears from the neutral curve if the porous layer thickness is increased. In contrast, the first and second subharmonic solutions coalesce, and the onset of Faraday instability is dominated by the subharmonic solution. In a special case, the study of Faraday instability of a viscous liquid on a porous substrate can be replaced by a study of Faraday instability of a viscous liquid on a slippery substrate when the permeability of the porous substrate is very low. Further, the Faraday instability can be destabilized by introducing a slip effect at the bottom plane.

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3

Liu, Junxiu, Wenqiang Song, Gan Ma, and Kai Li. "Faraday Instability in Viscous Fluids Covered with Elastic Polymer Films." Polymers 14, no. 12 (June 9, 2022): 2334. http://dx.doi.org/10.3390/polym14122334.

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Faraday instability has great application value in the fields of controlling polymer processing, micromolding colloidal lattices on structured suspensions, organizing particle layers, and conducting cell culture. To regulate Faraday instability, in this article, we attempt to introduce an elastic polymer film covering the surface of a viscous fluid layer and theoretically study the behaviors of the Faraday instability phenomenon and the effect of the elastic polymer film. Based on hydrodynamic theory, the Floquet theory is utilized to formulate its stability criterion, and the critical acceleration amplitude and critical wave number are calculated numerically. The results show that the critical acceleration amplitude for Faraday instability increases with three increasing bending stiffness of the elastic polymer film, and the critical wave number decreases with increasing bending stiffness. In addition, surface tension and viscosity also have important effects on the critical acceleration amplitude and critical wave number. The strategy of controlling Faraday instability by covering an elastic polymer film proposed in this paper has great application potential in new photonic devices, metamaterials, alternative energy, biology, and other fields.

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4

Douady, S., and S. Fauve. "Pattern Selection in Faraday Instability." Europhysics Letters (EPL) 6, no. 3 (June 1, 1988): 221–26. http://dx.doi.org/10.1209/0295-5075/6/3/006.

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5

Cabeza, C., C. Negreira, A. C. Sicardi-Schifino, and V. Gibiat. "Temporal behavior in Faraday instability." Physica A: Statistical Mechanics and its Applications 283, no. 1-2 (August 2000): 250–54. http://dx.doi.org/10.1016/s0378-4371(00)00162-x.

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6

Alessio, Guarino. "Anomalous modes in Faraday instability." Scientific Research and Essays 12, no. 1 (January 15, 2017): 1–8. http://dx.doi.org/10.5897/sre2016.6392.

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7

Pucci, G., M. Ben Amar, and Y. Couder. "Faraday instability in floating drops." Physics of Fluids 27, no. 9 (September 2015): 091107. http://dx.doi.org/10.1063/1.4930911.

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8

Delon, G., D. Terwagne, N. Adami, A. Bronfort, N. Vandewalle, S. Dorbolo, and H. Caps. "Faraday instability on a network." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 4 (December 2010): 041103. http://dx.doi.org/10.1063/1.3518693.

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9

Bacot, Vincent, Guillaume Durey, Antonin Eddi, Mathias Fink, and Emmanuel Fort. "Phase-conjugate mirror for water waves driven by the Faraday instability." Proceedings of the National Academy of Sciences 116, no. 18 (April 17, 2019): 8809–14. http://dx.doi.org/10.1073/pnas.1818742116.

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The Faraday instability appears on liquid baths submitted to vertical oscillations above a critical value. The pattern of standing ripples at half the vibrating frequency that results from this parametric forcing is usually shaped by the boundary conditions imposed by the enclosing receptacle. Here, we show that the time modulation of the medium involved in the Faraday instability can act as a phase-conjugate mirror––a fact which is hidden in the extensively studied case of the boundary-driven regime. We first demonstrate the complete analogy with the equations governing its optical counterpart. We then use water baths combining shallow and deep areas of arbitrary shapes to spatially localize the Faraday instability. We give experimental evidence of the ability of the Faraday instability to generate counterpropagating phase-conjugated waves for any propagating signal wave. The canonical geometries of a point and plane source are implemented. We also verify that Faraday-based phase-conjugate mirrors hold the genuine property of being shape independent. These results show that a periodic modulation of the effective gravity can perform time-reversal operations on monochromatic propagating water waves, with a remarkable efficiency compared with wave manipulation in other fields of physics.

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10

Tang, Rong-An, Hao-Cai Li, and Ju-Kui Xue. "Faraday instability and Faraday patterns in a superfluid Fermi gas." Journal of Physics B: Atomic, Molecular and Optical Physics 44, no. 11 (May 17, 2011): 115303. http://dx.doi.org/10.1088/0953-4075/44/11/115303.

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11

Residori, S., A. Guarino, and U. Bortolozzo. "Two-mode competition in Faraday instability." Europhysics Letters (EPL) 77, no. 4 (February 2007): 44003. http://dx.doi.org/10.1209/0295-5075/77/44003.

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12

MARTÍN, ELENA, CARLOS MARTEL, and JOSÉ M. VEGA. "Drift instability of standing Faraday waves." Journal of Fluid Mechanics 467 (September 24, 2002): 57–79. http://dx.doi.org/10.1017/s0022112002001349.

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We consider the weakly nonlinear evolution of the Faraday waves produced in a vertically vibrated two-dimensional liquid layer, at small viscosity. It is seen that the surface wave evolves to a drifting standing wave, namely a wave that is standing in a moving reference frame. This wave is determined up to a spatial phase, whose calculation requires consideration of the associated mean flow. This is just the streaming flow generated in the boundary layer attached to the lower plate supporting the liquid. A system of equations is derived for the coupled slow evolution of the spatial phase and the streaming flow. These equations are numerically integrated to show that the simplest reflection symmetric steady state (the usual array of counter-rotating eddies below the surface wave) becomes unstable for realistic values of the parameters. The new states include limit cycles (the array of eddies oscillating laterally), drifted standing waves (patterns that are standing in a uniformly propagating reference frame) and some more complex attractors.

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13

Douady, S. "Experimental study of the Faraday instability." Journal of Fluid Mechanics 221 (December 1990): 383–409. http://dx.doi.org/10.1017/s0022112090003603.

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An experimental study of surface waves parametrically excited by vertical vibrations is presented. The shape of the eigenmodes in a closed vessel, and the importance of the free-surface boundary conditions, are discussed. Stability boundaries, wave amplitude, and perturbation characteristic time of decay are measured and found to be in agreement with an amplitude equation derived by symmetry. The measurement of the amplitude equation coefficients explains why the observed transition is always supercritical, and shows the effect of the edge constraint on the dissipation and eigen frequency of the various modes. The fluid surface tension is obtained from the dispersion relation measurement. Several visualization methods in large-aspect-ratio cells are presented.

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14

Szwaj, Christophe, Serge Bielawski, Dominique Derozier, and Thomas Erneux. "Faraday Instability in a Multimode Laser." Physical Review Letters 80, no. 18 (May 4, 1998): 3968–71. http://dx.doi.org/10.1103/physrevlett.80.3968.

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15

Raynal, F., S. Kumar, and S. Fauve. "Faraday instability with a polymer solution." European Physical Journal B 9, no. 2 (May 1999): 175–78. http://dx.doi.org/10.1007/s100510050753.

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16

Tadrist, Loïc, Jeong-Bo Shim, Tristan Gilet, and Peter Schlagheck. "Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers." Journal of Fluid Mechanics 848 (June 13, 2018): 906–45. http://dx.doi.org/10.1017/jfm.2018.358.

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A walker is a fluid entity comprising a bouncing droplet coupled to the waves that it generates at the surface of a vibrated bath. Thanks to this coupling, walkers exhibit a series of wave–particle features formerly thought to be exclusive to the quantum realm. In this paper, we derive a model of the Faraday surface waves generated by an impact upon a vertically vibrated liquid surface. We then particularise this theoretical framework to the case of forcing slightly below the Faraday instability threshold. Among others, this theory yields a rationale for the cosine dependence of the wave amplitude to the phase shift between impact and forcing, as well as the characteristic time scale and length scale of viscous damping. The theory is validated with experiments of bead impact on a vibrated bath. We finally discuss implications of these results for the analogy between walkers and quantum particles.

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17

Chang, Pengyuan, Hangbo Shi, Jianxiang Miao, Tiantian Shi, Duo Pan, Bin Luo, Hong Guo, and Jingbiao Chen. "Frequency-stabilized Faraday laser with 10⁻¹⁴ short-term instability for atomic clocks." Applied Physics Letters 120, no. 14 (April 4, 2022): 141102. http://dx.doi.org/10.1063/5.0083390.

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In this Letter, stabilizing a Faraday laser frequency to the atomic transition is proposed and experimentally demonstrated, where the Faraday laser can work at single- or dual-frequency modes. High-resolution spectroscopy of a cesium atom induced by a Faraday laser is obtained. By stabilizing a Faraday laser with atomic spectroscopy, the frequency fluctuations of the Faraday laser are suppressed without the need of a high-cost Pound–Drever–Hall system. The fractional frequency Allan deviation of the residual error signal is 3 × 10[Formula: see text] at the single-frequency mode. While at the dual-frequency mode, the linewidth of the beat-note spectra between the two modes of the Faraday laser after locking is narrowed to be 85 Hz, which is an order of magnitude better than the free-running linewidth. It can be used for microwave atomic clocks and may have the potential to be used in the application of optical microwave generation when the performance is further improved.

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18

Decent, S. P., and A. D. D. Craik. "Sideband instability and modulations of Faraday waves." Wave Motion 30, no. 1 (July 1999): 43–55. http://dx.doi.org/10.1016/s0165-2125(98)00048-1.

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19

Ebo-Adou, A., L. S. Tuckerman, S. Shin, J. Chergui, and D. Juric. "Faraday instability on a sphere: numerical simulation." Journal of Fluid Mechanics 870 (May 10, 2019): 433–59. http://dx.doi.org/10.1017/jfm.2019.252.

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We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the interface motion of the parametrically forced oscillating viscous drop, as well as the velocity field inside and outside the drop. Forcing frequencies are chosen so as to excite spherical harmonic wavenumbers ranging from 1 to 6. We excite gravity waves for wavenumbers 1 and 2 and observe translational and oblate–prolate oscillation, respectively. For wavenumbers 3 to 6, we excite capillary waves and observe patterns analogous to the Platonic solids. For low viscosity, both subharmonic and harmonic responses are accessible. The patterns arising in each case are interpreted in the context of the theory of pattern formation with spherical symmetry.

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20

Ballesta, P., and S. Manneville. "The Faraday instability in wormlike micelle solutions." Journal of Non-Newtonian Fluid Mechanics 147, no. 1-2 (November 2007): 23–34. http://dx.doi.org/10.1016/j.jnnfm.2007.06.006.

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21

Ebo Adou, Ali-higo, and Laurette S. Tuckerman. "Faraday instability on a sphere: Floquet analysis." Journal of Fluid Mechanics 805 (September 23, 2016): 591–610. http://dx.doi.org/10.1017/jfm.2016.542.

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Standing waves appear at the surface of a spherical viscous liquid drop subjected to radial parametric oscillation. This is the spherical analogue of the Faraday instability. Modifying the Kumar & Tuckerman (J. Fluid Mech., vol. 279, 1994, pp. 49–68) planar solution to a spherical interface, we linearize the governing equations about the state of rest and solve the resulting equations by using a spherical harmonic decomposition for the angular dependence, spherical Bessel functions for the radial dependence and a Floquet form for the temporal dependence. Although the inviscid problem can, like the planar case, be mapped exactly onto the Mathieu equation, the spherical geometry introduces additional terms into the analysis. The dependence of the threshold on viscosity is studied and scaling laws are found. It is shown that the spherical thresholds are similar to the planar infinite-depth thresholds, even for small wavenumbers for which the curvature is high. A representative time-dependent Floquet mode is displayed.

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22

Martín, Elena, Carlos Martel, and José M. Vega. "Mean Flow Effects in the Faraday Instability." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 4278–83. http://dx.doi.org/10.1142/s0217979203022313.

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We study the weakly nonlinear evolution of Faraday waves in a 2D container that is vertically vibrated. In the small viscosity limit, the evolution of the surface waves is coupled to a non-oscillatory mean flow that develops in the bulk of the container. The corresponding long time (Navier-Stokes+amplitude) equations are derived and analyzed numerically. The results indicate that the (usually ignored) mean flow plays an essential role in the stability of the surface waves and in the bifurcated wave patterns.

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23

Diwakar, S. V., Farzam Zoueshtiagh, Sakir Amiroudine, and Ranga Narayanan. "The Faraday instability in miscible fluid systems." Physics of Fluids 27, no. 8 (August 2015): 084111. http://dx.doi.org/10.1063/1.4929401.

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24

Beyer, J., and R. Friedrich. "Faraday instability: Linear analysis for viscous fluids." Physical Review E 51, no. 2 (February 1, 1995): 1162–68. http://dx.doi.org/10.1103/physreve.51.1162.

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25

Abe, H., T. Ueda, M. Morikawa, Y. Saitoh, R. Nomura, and Y. Okuda. "Faraday instability of crystallization waves in 4He." Journal of Physics: Conference Series 92 (December 1, 2007): 012157. http://dx.doi.org/10.1088/1742-6596/92/1/012157.

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26

Müller, H. W., and W. Zimmermann. "Faraday instability in a linear viscoelastic fluid." Europhysics Letters (EPL) 45, no. 2 (January 15, 1999): 169–74. http://dx.doi.org/10.1209/epl/i1999-00142-5.

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27

ZOUESHTIAGH, F., S. AMIROUDINE, and R. NARAYANAN. "Experimental and numerical study of miscible Faraday instability." Journal of Fluid Mechanics 628 (June 1, 2009): 43–55. http://dx.doi.org/10.1017/s0022112009006156.

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A study of the Faraday instability of diffuse interfaces between pairs of miscible liquids of different densities, by means of experiments and by a nonlinear numerical model, is presented. The experimental set-up consisted of a rectangular cell in which the lighter liquid was placed above the denser one. The cell in this initially stable configuration was then subjected to vertical vibrations. The subsequent behaviour of the ‘interface’ between the two liquids was observed with a high-speed camera. This study shows that above a certain acceleration threshold an instability developed at the interface. The amplitude of the instability grew during the experiments which then led to the mixing of the liquids. The instability finally disappeared once the two liquids were fully mixed over a volume, considerably larger than the initial diffuse region. The results of a companion two-dimensional nonlinear numerical model that employs a finite volume method show very good agreement with the experiments. A physical explanation of the instability and the observations are advanced.

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28

Woods, David R., and S. P. Lin. "Instability of a liquid film flow over a vibrating inclined plane." Journal of Fluid Mechanics 294 (July 10, 1995): 391–407. http://dx.doi.org/10.1017/s0022112095002941.

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The problem of the onset of instability in a liquid layer flowing down a vibrating inclined plane is formulated. For the solution of the problem, the Fourier components of the disturbance are expanded in Chebychev polynomials with time-dependent coefficients. The reduced system of ordinary differential equations is analysed with the aid of Floquet theory. The interaction of the long gravity waves, the relatively short shear waves and the parametrically resonated Faraday waves occurring in the film flow is studied. Numerical results show that the long gravity waves can be significantly suppressed, but cannot be completely eliminated by use of the externally imposed oscillation on the incline. At small angles of inclination, the short shear waves may be exploited to enhance the Faraday waves. For a given set of relevant flow parameters, there exists a critical amplitude of the plane vibration below which the Faraday wave cannot be generated. At a given amplitude above this critical one, there also exists a cutoff wavenumber above which the Faraday wave cannot be excited. In general the critical amplitude increases, but the cutoff wavenumber decreases, with increasing viscosity. The cutoff wavenumber also decreases with increasing surface tension. The application of the theory to a novel method of film atomization is discussed.

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29

Pucci, G., M. Ben Amar, and Y. Couder. "Faraday instability in floating liquid lenses: the spontaneous mutual adaptation due to radiation pressure." Journal of Fluid Mechanics 725 (May 14, 2013): 402–27. http://dx.doi.org/10.1017/jfm.2013.166.

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AbstractFluid dynamics instabilities are usually investigated in two types of situations, either confined in cells with fixed boundaries, or free to grow in open space. In this article we study the Faraday instability triggered in a floating liquid lens. This is an intermediate situation in which a hydrodynamical instability develops in a domain with flexible boundaries. The instability is observed to be initially disordered with fluctuations of both the wave field and the lens boundaries. However, a slow dynamics takes place, leading to a mutual adaptation so that a steady regime is reached with a stable wave field in a stable lens contour. The most recurrent equilibrium lens shape is elongated with the Faraday wave vector along the main axis. In this self-organized situation an equilibrium is reached between the radiation pressure exerted by Faraday waves on the borders and their capillary response. The elongated shape is obtained theoretically as the exact solution of a Riccati equation with a unique control parameter and compared with the experiment.

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30

Bevilacqua, Giulia, Xingchen Shao, John R. Saylor, Joshua B. Bostwick, and Pasquale Ciarletta. "Faraday waves in soft elastic solids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (September 2020): 20200129. http://dx.doi.org/10.1098/rspa.2020.0129.

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Recent experiments have observed the emergence of standing waves at the free surface of elastic bodies attached to a rigid oscillating substrate and subjected to critical values of forcing frequency and amplitude. This phenomenon, known as Faraday instability, is now well understood for viscous fluids but surprisingly eluded any theoretical explanation for soft solids. Here, we characterize Faraday waves in soft incompressible slabs using the Floquet theory to study the onset of harmonic and subharmonic resonance eigenmodes. We consider a ground state corresponding to a finite homogeneous deformation of the elastic slab. We transform the incremental boundary value problem into an algebraic eigenvalue problem characterized by the three dimensionless parameters, that characterize the interplay of gravity, capillary and elastic waves. Remarkably, we found that Faraday instability in soft solids is characterized by a harmonic resonance in the physical range of the material parameters. This seminal result is in contrast to the subharmonic resonance that is known to characterize viscous fluids, and opens the path for using Faraday waves for a precise and robust experimental method that is able to distinguish solid-like from fluid-like responses of soft matter at different scales.

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31

Ward, Kevin, Satoshi Matsumoto, and Ranga Narayanan. "The electrostatically forced Faraday instability: theory and experiments." Journal of Fluid Mechanics 862 (January 14, 2019): 696–731. http://dx.doi.org/10.1017/jfm.2018.940.

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The onset of interfacial instability in two-fluid systems using a viscous, leaky dielectric model is studied. The instability arises as a result of resonance between the parametric frequency of an imposed electric field and the system’s natural frequency. In addition to a rigorous model that uses Floquet instability analysis, where both viscous and charge effects are considered, this study also provides convincing validating experiments. In other results, it is shown that (a) the imposition of a periodic electrostatic potential acts to counter gravity and this countering effect becomes more effective if a DC voltage is also added, (b) a critical DC voltage exists at which the interface becomes unstable such that no parametric frequency is required to completely destabilize the interface and (c) the leaky dielectric model approaches a model for a perfect dielectric/perfect conductor pair as the conductivity ratio becomes large. It is also shown via experiments that parametric resonant instability using electrostatic forcing may be reliably used to estimate interfacial tension to sufficient accuracy.

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32

Kumar, Satish. "Mechanism for the Faraday instability in viscous liquids." Physical Review E 62, no. 1 (July 1, 2000): 1416–19. http://dx.doi.org/10.1103/physreve.62.1416.

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33

Garih, H., J. L. Estivalezes, and G. Casalis. "On the transient phase of the Faraday instability." Physics of Fluids 25, no. 12 (December 2013): 124104. http://dx.doi.org/10.1063/1.4842895.

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34

MANCEBO, FRANCISCO J., and JOSÉ M. VEGA. "Faraday instability threshold in large-aspect-ratio containers." Journal of Fluid Mechanics 467 (September 24, 2002): 307–30. http://dx.doi.org/10.1017/s0022112002001398.

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We consider the Floquet linear problem giving the threshold acceleration for the appearance of Faraday waves in large-aspect-ratio containers, without further restrictions on the values of the parameters. We classify all distinguished limits for varying values of the various parameters and simplify the exact problem in each limit. The resulting simplified problems either admit closed-form solutions or are solved numerically by the well-known method introduced by Kumar & Tuckerman (1994). Some comparisons are made with (a) the numerical solution of the original exact problem, (b) some ad hoc approximations in the literature, and (c) some experimental results.

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35

Bacri, J. C., A. Cebers, J. C. Dabadie, S. Neveu, and R. Perzynski. "Threshold and Marginal Curve of Magnetic Faraday Instability." Europhysics Letters (EPL) 27, no. 6 (August 20, 1994): 437–43. http://dx.doi.org/10.1209/0295-5075/27/6/005.

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36

Li, Yikai, and Akira Umemura. "Threshold condition for spray formation by Faraday instability." Journal of Fluid Mechanics 759 (October 20, 2014): 73–103. http://dx.doi.org/10.1017/jfm.2014.569.

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AbstractA vertically vibrating liquid layer produces liquid ligaments that disintegrate to form a spray with drops of a controllable size. Previous experimental investigations of ultrasonic atomisation have shown that when such a spray forms, there exists a predominant surface-wave mode from which drops are generated with a mean diameter that follows Lang’s equation. In this paper, we determined this predominant surface-wave mode physically and, by utilising the coupled level-set and volume-of-fluid method, we numerically studied the threshold condition for spray formation based on a cell model of the predominant surface wavelength that excludes the effects of the container walls. We defined a condition whereby the broken drop holds a zero area-averaged vertical velocity in the laboratory reference frame as the criterion for the formation of a spray. The results of our calculations indicated that the onset of a spray occurs in the subharmonic unstable region for a threshold dimensionless forcing strength ${\it\beta}_{c}=({\it\rho}_{l}{\it\Delta}_{0}^{3}{\it\Omega}^{2})/{\it\sigma}\sim O(1)$, where ${\it\rho}_{l}$ and ${\it\sigma}$ denote the liquid density and surface tension coefficient, respectively, ${\it\Delta}_{0}$ is the forcing displacement amplitude and ${\it\Omega}$ is the forcing angular frequency. Spray formation due to the Faraday instability can be considered as a process whereby the liquid layer absorbs energy from the inertial force, and releases it by producing drops that leave the surface of the liquid layer. We demonstrated that for a deep liquid layer, the threshold condition for the formation of a spray is determined only by the forcing strength, and is independent of the initial conditions of the liquid surface.

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Labrador, E., P. Salgado Sánchez, J. Porter, and V. Shevtsova. "Secondary Faraday waves in microgravity." Journal of Physics: Conference Series 2090, no. 1 (November 1, 2021): 012088. http://dx.doi.org/10.1088/1742-6596/2090/1/012088.

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Abstract Recent microgravity experiments have demonstrated that Faraday waves can arise in a secondary instability over the primary columnar patterns that develop after the frozen wave instability. While some numerical studies have investigated this phenomenon, theoretical analyses are only found in the works of Shevtsova et al. (2016) [1] and Lyubimova et al. (2019) [2]. Here, we extend these efforts by analysing the stability of a three-layer system, and derive the critical onset of Faraday waves, which appear via Hopf bifurcation. Numerical simulations — based on a model that reproduces the frozen wave mode with lowest wavenumber — are carried out to test this result and to analyse the character of the bifurcation. The predicted Hopf bifurcation is confirmed, which constitutes the first observation of modulated secondary Faraday waves. The abrupt growth of these modulated waves above onset indicates that the primary bifurcation is subcritical and is accompanied by a saddle-node bifurcation of periodic orbits that stabilises the (branch of) unstable solutions created in the subcritical Hopf bifurcation. Further above onset, these modulated waves are destroyed via a saddle-node heteroclinic bifurcation. Results for an N-layer configuration, which represents a more general frozen wave pattern, are also presented and compared with the three-layer case.

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CABEZA, C., and M. ROSEN. "COMPLEXITY IN FARADAY EXPERIMENT WITH VISCOELASTIC FLUID." International Journal of Bifurcation and Chaos 17, no. 05 (May 2007): 1599–607. http://dx.doi.org/10.1142/s0218127407017938.

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A systematic experimental study of the Faraday instability in viscoelastic fluid is presented. We have used a shear thinning polymer solution in which the elastic effects are predominant within our work range. We have analyzed the dependence of the threshold instability as a function of the depth in layer. Depending on the fluid layer depth and the driving frequency, harmonic or subharmonic regimes are developed. We have focused our work on the subharmonic region and temporal and spatial behaviors were analyzed. In addition, we have used the onset acceleration to estimate the rheological properties of the fluid. These predictions are supported by experimental measurements.

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39

Bechhoefer, John, Valerie Ego, Sebastien Manneville, and Brad Johnson. "An experimental study of the onset of parametrically pumped surface waves in viscous fluids." Journal of Fluid Mechanics 288 (April 10, 1995): 325–50. http://dx.doi.org/10.1017/s0022112095001169.

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We measure the threshold accelerations necessary to excite surface waves in a vertically vibrated fluid container (the Faraday instability). Under the proper conditions, the thresholds and onset wavelengths agree with recent theoretical predictions for a laterally infinite, finite-depth container filled with a viscous fluid. Experimentally, we show that by using a viscous, non-polar fluid, the finite-size effects of sidewalls and the effects of surface contamination can be made negligible. We also show that finite-size corrections are of order h/L, where h is the fluid depth and L the container size. Based on these measurements, one can more easily interpret certain unexpected observations from previous experimental studies of the Faraday instability.

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40

Li, Xin, Shouxin Wang, Yuqi Chu, Hui Lian, Yinxian Jie, Rongjie Zhu, Yi Yuan, et al. "Local current shrinkage induced by the MARFE in L mode discharges on EAST tokamak." AIP Advances 13, no. 3 (March 1, 2023): 035037. http://dx.doi.org/10.1063/5.0141494.

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In this study, the multifaceted asymmetric radiation from the edge (MARFE) was observed in high-density discharges or during impurity gas injection on the EAST tokamak. The MARFE onset indicated by spectral and radiation signals can also be detected by the POlarimeter-INTerferometer (POINT) diagnostic, which measures the horizontal line-integrated density and the Faraday rotation. The fluctuation amplitude of the density signal resulting from the MARFE oscillation increases with the edge safety factor, which is consistent with the thermal instability theory. By combining density and the Faraday rotation, the local current shrinkage in the MARFE region is observed during the MARFE movement. The density and the current profile calculated by the POINT become more peak during the MARFE, which may lead to a strong magnetohydrodynamic instability that can result in disruption.

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41

Bhattacherjee, Aranya B. "Faraday instability in a two-component Bose–Einstein condensate." Physica Scripta 78, no. 4 (October 2008): 045009. http://dx.doi.org/10.1088/0031-8949/78/04/045009.

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42

Ueda, T., H. Abe, Y. Saitoh, R. Nomura, and Y. Okuda. "Faraday Instability on a Free Surface of Superfluid 4He." Journal of Low Temperature Physics 148, no. 5-6 (June 23, 2007): 553–57. http://dx.doi.org/10.1007/s10909-007-9432-8.

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43

Kumar, Satish, and Omar K. Matar. "On the Faraday instability in a surfactant-covered liquid." Physics of Fluids 16, no. 1 (January 2004): 39–46. http://dx.doi.org/10.1063/1.1629128.

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44

van Saarloos, Wim, and John D. Weeks. "Faraday Instability of Crystallization Waves at theHe4Solid-Liquid Interface." Physical Review Letters 74, no. 2 (January 9, 1995): 290–93. http://dx.doi.org/10.1103/physrevlett.74.290.

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45

Bacri, J. C., A. Cebers, J. C. Dabadie, and R. Perzynski. "Roll-rectangle transition in the magnetic fluid Faraday instability." Physical Review E 50, no. 4 (October 1, 1994): 2712–15. http://dx.doi.org/10.1103/physreve.50.2712.

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46

Chen, Weizhong, and Rongjue Wei. "Instability analysis for Faraday waves under arbitrarily periodic vibration." Science in China Series A: Mathematics 41, no. 12 (December 1998): 1302–8. http://dx.doi.org/10.1007/bf02882271.

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47

Huo, Qiang, and Xiaopeng Wang. "Faraday instability of non-Newtonian fluids under low-frequency vertical harmonic vibration." Physics of Fluids 34, no. 9 (September 2022): 094107. http://dx.doi.org/10.1063/5.0108295.

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Abstract:

Resonance Acoustic Mixing® (RAM) technology applies an external low-frequency vertical harmonic vibration to convey and mix the non-Newtonian fluid across space. However, although this method is used for various applications, its mechanism is yet not well understood. In this paper, we investigate the Faraday instability of power-law non-Newtonian fluids in RAM utilizing theory and simulations. According to the Floquet analysis and the dimensionless Mathieu equation, the critical stable region besides the stable region and the unstable region is discovered. Based on the numerical solutions of the two-dimensional incompressible Euler equations for a prototype Faraday instability flow, the temporal evolution of the surface displacement and the mechanism of Faraday waves for two cases are explored physically. For the low forcing displacement, there are only stable and critical stable regions. The surface deformation increases linearly and then enters the steady-state in which the fluctuation frequency is twice the vertical harmonic vibration. For the large forcing displacement, there are only stable and unstable regions. Under the effect of the inertial force, both cases have a sudden variation after the brief stabilization period. Furthermore, a ligament structure is observed, which signals that the surface is destabilized. In addition, a band-like pressure minimum distribution below the interface is formed. The fluid flows from the bottom to the crest portion to balance the pressure difference, which raises the crest.

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Shevtsova, V., Y. A. Gaponenko, V. Yasnou, A. Mialdun, and A. Nepomnyashchy. "Two-scale wave patterns on a periodically excited miscible liquid–liquid interface." Journal of Fluid Mechanics 795 (April 15, 2016): 409–22. http://dx.doi.org/10.1017/jfm.2016.222.

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We have discovered a peculiar behaviour of the interface between two miscible liquids placed in a finite-size container under horizontal vibration. We provide evidence that periodic wave patterns created by the Kelvin–Helmholtz instability and Faraday waves simultaneously exist in the same system of miscible liquids. We show experimentally in reduced and normal gravity that large-scale frozen waves yield Faraday waves with a smaller wavelength on a diffusive interface. The emergence of the different scale patterns observed in the experiments is confirmed numerically and explained theoretically.

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Edwards, W. S., and S. Fauve. "Patterns and quasi-patterns in the Faraday experiment." Journal of Fluid Mechanics 278 (November 10, 1994): 123–48. http://dx.doi.org/10.1017/s0022112094003642.

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Parametric excitation of surface waves via forced vertical oscillation of a container filled with fluid (the Faraday instability) is investigated experimentally in a small-depth large-aspect-ratio system, with a viscous fluid and with two simultaneous forcing frequencies. The asymptotic pattern observed just above the threshold for the first instability of the flat surface is found to depend strongly on the frequency ratio and the amplitudes and phases of the two sinusoidal components of the driving acceleration. Parallel lines, squares, and hexagons are observed. With viscosity 100 cS, these stable standing-wave patterns do not exhibit strong sidewall effects, and are found in containers of various shapes including an irregular shape. A ‘quasi-pattern’ of twelvefold symmetry, analogous to a two-dimensional quasi-crystal, is observed for some even/odd frequency ratios. Many of the experimental phenomena can be modelled via cubic-order amplitude equations derived from symmetry arguments.

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Belonozhko, D. F. "On the Influence of the Surface Electric Charge on the Regularities of the Formation of Faraday Ripples on the Surface of a Low-Viscosity Liquid." Proceedings of the Southwest State University. Series: Engineering and Technology 13, no. 3 (September 29, 2023): 117–27. http://dx.doi.org/10.21869/2223-1528-2023-13-3-117-127.

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The purpose of the study is to analyze the effect of a surface electric charge on the formation conditions of the Faraday ripples on a horizontal surface of a low-viscosity liquid in a vibration field.Methods. The problem is solved analytically in the limit of small amplitude deformation of the free surface of the liquid. The final relation is derived under the condition that the dissipation is small. The liquid was considered ideally conductive with a surface-distributed electric charge. Results. A simple analytical expression is derived that quantitatively describes the effect of suppression of the Faraday ripple if the surface density of the electric charge increases. It is shown that the increase in the surface density of the electric charge significantly enlarge the threshold value of the vibration field amplitude, the excess of which leads to the formation of ripples. The threshold value of the vibration amplitude is proportional to the viscosity of the liquid and depends on its density, surface tension coefficient and the specific horizontal scale of the ripple.Conclusion. The Faraday’s ripple formed on the surface of a liquid in a vertically oscillating container is very sensitive to the value of the surface density of the electric charge. An increase of the surface charge density leads to suppression of the ripple formation. The effect can be used to prevent the appearance of parasitic convective flows that arise in liquid layers placed in vibration fields. The physical mechanism of Faraday ripple suppression is the rivalry between two qualitatively different types of flows near the liquid surface. Increasing the surface charge density changes the balance of surface forces in such a way as to promote the appearance of aperiodic motions and suppress oscillatory ones. In particular, oscillatory motions responsible for the development of Faraday instability caused by vertical vibrations of the liquid container are suppressed.

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Journal articles on the topic 'Faraday instability'

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