Modulation equations for strongly nonlinear oscillations of an incompressible viscous drop

Smith, Warren R.

doi:10.1017/s0022112010000480

Cited by 24 publications

(19 citation statements)

References 19 publications

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“…with n is the mode number and R is the drop radius. However, real situations involve more complex effects, in which several questions remain unanswered [12,[32][33][34][35][36][37][38][39][40][41][42][43][44]. Especially, our situation of a sessile drop shows qualitative and quantitative differences with eq.…”

Section: Droplet Dynamics : a Qualitative Descriptionmentioning

confidence: 97%

Directional motion of vibrated sessile drops: A quantitative study

Costalonga

Brunet

2020

Phys. Rev. Fluids

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The directional motion of sessile drops can be induced by slanted mechanical vibrations of the substrate. As previously evidenced [13][14][15], the mechanical vibrations induce drop deformations which combine axisymmetric and antisymmetric modes. In this paper, we establish quantitative trends from experiments conducted within a large range of parameters, namely the amplitude A and frequency f of the forcing, the liquid viscosity η and the angle between the substrate and the forcing axis α. These experiments are carried out on weak-pinning substrates. For most parameters sets, the averaged velocity < v > grows linearly with A. We extract the mobility, defined as s = ∆ ∆A . It is found that s can show a sharp maximal value close to the resonance frequency of the first axisymmetric mode fp. The value of s tends to be almost independent on η below 50 cSt, while s decreases significantly for higher η. Also, it is found that for peculiar sets of parameters, particularly with f far enough from fp, the drop moves in the reverse direction. Finally, we draw a relationship between < v > and the averaged values of the dynamical contact angles at both sides of the drop over one period of oscillation.

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Section: Droplet Dynamics : a Qualitative Descriptionmentioning

confidence: 97%

Directional motion of vibrated sessile drops: A quantitative study

Costalonga

Brunet

2020

Phys. Rev. Fluids

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“…These oscillations are strongest for small n, and are consistent among the different liquids and substrate temperatures. This phenomenon may be caused by nonlinear effects, e.g., the dependence of the oscillation frequency on the amplitude is stronger for smaller modes [26,27]. Nevertheless, the data suggests a very robust mechanism for selecting either the frequency or wavelength of the modes.…”

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confidence: 89%

Star-shaped oscillations of Leidenfrost drops

Liétor-Santos

Burton

2017

Phys. Rev. Fluids

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We experimentally investigate the self-sustained, star-shaped oscillations of Leidenfrost drops. The drops levitate on a cushion of evaporated vapor over a heated, curved surface. We observe modes with n = 2 − 13 lobes around the drop periphery. We find that the wavelength of the oscillations depends only on the capillary length of the liquid, and is independent of the drop radius and substrate temperature. However, the number of observed modes depends sensitively on the liquid viscosity. The dominant frequency of pressure variations in the vapor layer is approximately twice the drop oscillation frequency, consistent with a parametric forcing mechanism. Our results show that the star-shaped oscillations are driven by capillary waves of a characteristic wavelength beneath the drop, and that the waves are generated by a large shear stress at the liquid-vapor interface.PACS numbers: 47.35.Pq, 47.15.gm, 47.85.mf The Leidenfrost effect can be easily observed by placing a millimeter-scale water drop onto a sufficiently hot pan. The drop will levitate on a thermally-insulating vapor layer and survive for minutes [1][2][3][4]. For small drops, the geometry and dynamics of the vapor layer have been recently characterized [5,6]. The complex interactions between the liquid, vapor, and solid interfaces have led to a broad range of applications such as turbulent dragreduction [7], self-propulsion of drops on ratcheted surfaces [8,9], green nanofabrication [10], fuel combustion [11], and thermal control of nuclear reactors [12].Large Leidenfrost drops are well-known to form selfsustained, star-shaped oscillations (Fig. 1a). Since the 1950's, a number of studies have investigated these oscillations, often with different conclusions as to their physical origin based on the complicated interplay between thermal and hydrodynamic effects in both the liquid and gas phases [13][14][15][16][17][18][19]. A simple underlying mechanism for the onset of star oscillations remains unknown. Drops subjected to external, periodic excitations can form star oscillations with a frequency half that of the external excitation due to a parametric coupling mechanism [20,21]. However, if a parametric mechanism causes Leidenfrost stars, then the source of the periodic excitation is unclear. Recently, Bouwhuis et al. investigated the star oscillations of drops levitated by an air flow over a porous surface [22]. They showed that the onset of star oscillations occurs when the flow rate of air beneath the drop reaches a threshold, suggesting that a hydrodynamic coupling between the gas flow and liquid interface initiates the oscillations.Here we report measurements of star-shaped oscillations of six different liquids on a hot, curved surface. We observe stars with n = 2 − 13 lobes around the drop periphery. Although the number of observed modes depends on the liquid viscosity and substrate temperature, we find that the wavelength and frequency of the modes only depend on the capillary length, l c = γ/ρ l g, where γ and ρ l are the surface tension and ...

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“…X l where l = 2) is 2.5%. [18] Smith [19] has shown that the time-dependent variations in the decay factor of the fundamental mode for oscillation amplitudes as large as 0.3 r 0 can be approximated by an additional component that is quadratic in this amplitude and less than 25% below the linear result, even at this limit.…”

Section: Models For Drop Oscillationmentioning

confidence: 99%

Oscillations of aqueous PEDOT:PSS fluid droplets and the properties of complex fluids in drop-on-demand inkjet printing

Hoath

Hsiao

Martin

et al. 2015

Journal of Non-Newtonian Fluid Mechanics

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a b s t r a c tShear-thinning aqueous poly(3,4-ethylenedioxythiophene): poly(styrene sulphonate) (PEDOT:PSS) fluids were studied under the conditions of drop-on-demand inkjet printing. Ligament retraction caused oscillation of the resulting drops, from which values of surface tension and viscosity were derived. Effective viscosities of <4 mPa s at drop oscillation frequencies of 13-33 kHz were consistent with conventional high-frequency rheometry, with only a small possible contribution from viscoelasticity with a relaxation time of about 6 ls. Strong evidence was found that the viscosity, reduced by shear-thinning in the printhead nozzle, recovered as the drop formed. The low viscosity values measured for the drops in flight were associated with the strong oscillation induced by ligament retraction, while for a weakly perturbed drop the viscosity remained high. Surface tension values in the presence of surfactant were significantly higher than the equilibrium values, and consistent with the surface age of the drops.

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Modulation equations for strongly nonlinear oscillations of an incompressible viscous drop

Cited by 24 publications

References 19 publications

Directional motion of vibrated sessile drops: A quantitative study

Directional motion of vibrated sessile drops: A quantitative study

Star-shaped oscillations of Leidenfrost drops

Oscillations of aqueous PEDOT:PSS fluid droplets and the properties of complex fluids in drop-on-demand inkjet printing

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