Shaping liquid drops by vibration

Pototsky, Andrey; Bestehorn, Michael

doi:10.1209/0295-5075/121/46001

Cited by 13 publications

(23 citation statements)

References 33 publications

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“…A reduced hydrodynamic model describing the dynamics of liquid drop an non-zero Reynolds numbers under the action of external vertical vibration was developed in Ref. [25]. Here, we adopt a simplified version of the model [25] that captures all essential features of the flow field, but has a more simple expression for the nonlinear terms.…”

Section: Hydrodynamic Model Of a Vibrated Liquid Dropmentioning

confidence: 99%

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Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Maksymov

Pototsky

2019

Phys. Rev. E

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Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at 70 Hz are in qualitative agreement with the predictions of our modelling. * Electronic address: apototskyy@swin.edu.au

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Section: Hydrodynamic Model Of a Vibrated Liquid Dropmentioning

confidence: 99%

“…(8) with the drop profile h(x,t) and fluid flux q(x,t). Following [25], we numerically solve Eqs. (8) in a periodic domain x ∈ [−L, L] using a semi-implicit spectral method with the time step ∆t ≈ 10 −3 and the spatial discretization step ∆x of the order of β .…”

Section: Vibrated Pancake Shaped Dropmentioning

confidence: 99%

Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Maksymov

Pototsky

2019

Phys. Rev. E

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“…The study of the generic effects of nonlinear stripe patterns in deformable domains undertaken here shares many similarities with the specific example of Faraday waves emerging on top of shaken liquid droplets [15,16,32]. However, Faraday waves on droplet surfaces are a three-dimensional situation.…”

Section: Discussionmentioning

confidence: 67%

“…If-naturally very deformable-liquid drops are placed on a surface and are shaken vertically, the so-called Faraday instability causes oscillating, spatially periodic stripe patterns at the drop's free surface [8]. Experiments [15,16] and simulations [32] show that with increasing amplitude of the Faraday waves, the liquid drops of originally circular cross-section (their three-dimensional shape being a spherical cap) deform to elliptical and finally even worm-like shapes. Is this a general effect for patterns in deformable domains?…”

Section: Introductionmentioning

confidence: 99%

Nonlinear patterns shaping the domain on which they live

2020

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Nonlinear stripe patterns in two spatial dimensions break the rotational symmetry and generically show a preferred orientation near domain boundaries, as described by the famous Newell-Whitehead-Segel (NWS) equation. We first demonstrate that, as a consequence, stripes favour rectangular over quadratic domains. We then investigate the effects of patterns 'living' in deformable domains by introducing a model coupling a generalized Swift-Hohenberg model to a generic phase field model describing the domain boundaries. If either the control parameter inside the domain (and therefore the pattern amplitude) or the coupling strength ('anchoring energy' at the boundary) are increased, the stripe pattern self-organizes the domain on which it 'lives' into anisotropic shapes. For smooth phase field variations at the domain boundaries, we simultaneously find a selection of the domain shape and the wave number of the stripe pattern. This selection shows further interesting dynamical behavior for rather steep variations of the phase field across the domain boundaries. The here-discovered feedback between the anisotropy of a pattern and its orientation at boundaries is relevant e.g. for shaken drops or biological pattern formation during development.

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“…Parametrically excited vibrations and surface waves have also been observed in isolated liquid drops subjected to external mechanical forcing [30][31][32][33][34][35][36][37][38]. In response to vibration, the drop can either adopt a regular star shape [30][31][32][33] or exhibit a more dramatic transformation by spontaneously elongating in horizontal direction to form a worm-like structure of gradually increasing length [34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Excitation of Faraday-like body waves in vibrated living earthworms

Maksymov

Pototsky

2019

Preprint

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Biological cells and many living organisms are mostly made of liquids and therefore, by analogy with liquid drops, they should exhibit a range of fundamental nonlinear phenomena such as the onset of standing surface waves. Here, we test four common species of earthworm to demonstrate that vertical vibration of living worms lying horizontally of a flat solid surface results in the onset of subharmonic Faraday-like body waves, which is possible because earthworms have a hydrostatic skeleton with a flexible skin and a liquid-filled body cavity. Our findings are supported by theoretical analysis based on a model of parametrically excited vibrations in liquid-filled elastic cylinders using material parameters of the worm's body reported in the literature. The ability to excite nonlinear subharmonic body waves in a living organism could be used to probe, and potentially to control, important biophysical processes such as the propagation of nerve impulses, thereby opening up avenues for addressing biological questions of fundamental impact.

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Shaping liquid drops by vibration

Cited by 13 publications

References 33 publications

Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Nonlinear patterns shaping the domain on which they live

Excitation of Faraday-like body waves in vibrated living earthworms

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