Measurements of surface-wave damping in a container

Howell, David; Buhrow, B.; Heath, Ted; McKenna, Conor; Hwang, Wook; Schatz, Michael F.

doi:10.1063/1.870310

Cited by 40 publications

(47 citation statements)

References 12 publications

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“…From eqs. (13)(14)(15)(16) and the figures 1-3 it is evidently that there are two different scaling regimes for the maximal growth rate as well as for the corresponding wave number. In all three examples, the assumption for the expansion,ν ≫ω 2,m , is well accomplished, see horizontal arrows and solid lines in figs.…”

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confidence: 99%

“…Sinceω 2,m ∼ σ 1/4 ω 2,m , inaccuracies in the surface tension σ may result in incorrect values of c 1 and c 2 . From experiments with surface wave damping on ordinary fluids it is known that deviations in the value of the surface tension due to contamination may account for differences in the order of 20% [14,15]. Excluding the large deviations, the following dependencies of c i onν are suggested (see solid lines in fig.…”

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Scaling behaviour of the maximal growth rate in the Rosensweig instability

Lange¹

2001

Europhys. Lett.

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PACS. 47.20.Ma -Hydrodynamic stability and instability. PACS. 75.50.Mm -Magnetic liquids.Abstract. -The dependence of the maximal growth rate of the modes of the Rosensweig instability on the properties of the magnetic fluid and the external magnetic induction is studied. An expansion and a fit procedure are applied in the appropriate ranges of the supercritical inductionB. With increasingB the scaling of the maximal growth rate changes from linear to a combination of linear and square-root-like scaling. The scaling of the corresponding wave number alternates from quadratic to primarily linear. For very smallB the dependence of the maximal growth rate on the viscosity is given. Suggestions are made for experiments to test the predicted scaling behaviours.Introduction. -The investigation of instabilities in magnetic fluids has a long history where the most prominent instability being the normal field or Rosensweig instability [1,2]. Above a threshold of the induction, the initially flat surface exhibits a stationary array of peaks. Despite its long history, some aspects of the Rosensweig instability have been addressed only recently: the hexagon-square transition [3] or the wave number selection problem [3,4]. The wave number is the absolute value of the wave vector, q = |q|, which characterizes small disturbances. The ground state of a pattern forming system is subjected to such small disturbances in order to study its stability. The corresponding growth rate ω may depend on system parameters {P}, e.g. the viscosity of the fluid, and control parameters {R}, e.g. an external magnetic field, ω = ω(q; {P}, {R}). Generally it is assumed that in the linear stage of the pattern forming process the wave number with the largest growth rate will prevail. Therefore this mode is called linearly most unstable mode. Due to its role in the pattern formation it is of particular interest to examine the maximal growth rate ω m , and its dependence on the different parameters.This dependence has received only limited attention in classical hydrodynamic systems. For the Küppers-Lortz (KL) instability in Rayleigh-Bénard convection rotated about a vertical axis, the growth rate of different KL angles were calculated for one fixed rotation rate and different temperature differences [5]. In surface-tension-driven Bénard convection the growth rates are calculated for two fixed values of heat loss and different temperature differences [6]. But in both systems it was not analysed how ω m depends on the control parameters. In the problem of convection for autocatalytic reaction fronts, the maximal growth rate was analysed

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Scaling behaviour of the maximal growth rate in the Rosensweig instability

Lange¹

2001

Europhys. Lett.

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“…The most interesting spatio-temporal behaviours are associated with nonlinearity Fauve 1995), especially in large-aspect-ratio containers , but unfortunately a complete, consistent weakly nonlinear theory for these waves is still lacking today, and some gaps still remain at the linear level. Among the still unresolved questions, linear damping is not completely understood for low viscosity at modérate aspect ratio, even if the effects of contact line dynamics and surface contamination are eliminated (Henderson & Miles 1994;Martel, Nicolás & Vega 1998;Howell et al 2000). The theoretical and experimental determination of the instability threshold has received considerable attention, both in the modérate Jiang et al 1996) and large (Douady 1990;Edwards & Fauve 1994;Kumar & Tuckerman 1994;Bechhoefer et al 1995;Christiansen, Alstrom & Levinsen 1995;Kumar 1996;Lioubashevski, Fineberg & Tuckerman 1997) aspect-ratio limits.…”

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Faraday instability threshold in large-aspect-ratio containers

Mancebo

Vega

2002

J. Fluid Mech.

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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 valúes of the parameters. We classify all distinguished limits for varying valúes 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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“…Natural frequency computed in this framework differs from the experimental values from less than 1% [5,6] up to around 10% [7][8][9]. In contrast, measurements of damping are associated with larger discrepancies: a theory based on dissipation localized in bottom and wall boundary layers underestimates experimental dissipation from a few percent [7] to as much as a few hundred percent [5,8,9]. These disparities have been ascribed to both surface contamination and capillary effects close to the contact line.…”

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Observation of nonlinear sloshing induced by wetting dynamics

2017

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Back-and-forth oscillations of a container filled with fluid often result in spilling as the gravest mode gets excited, a well-known phenomenon experienced in everyday life and of particular importance in industry. Our understanding of sloshing is largely restricted to linear response, and existing extensions mostly focus on nonlinear coupling between modes. Linear theory is expected to correctly model the dynamics of the system as long as the amplitude of the mode remains small compared to another length scale, so far unknown. Using a fluid in the vicinity of its critical point, we demonstrate that in perfect wetting this length scale is neither the wavelength nor the capillary length but a much shorter one, the thickness of the boundary layer. Above this crossover length scale, the resonance frequency remains roughly constant while dissipation significantly increases. We also show that dynamical wetting is involved in both linear and nonlinear dissipative processes.

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Measurements of surface-wave damping in a container

Cited by 40 publications

References 12 publications

Scaling behaviour of the maximal growth rate in the Rosensweig instability

Scaling behaviour of the maximal growth rate in the Rosensweig instability

Faraday instability threshold in large-aspect-ratio containers

Observation of nonlinear sloshing induced by wetting dynamics

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