Surface wave pattern formation in a cylindrical container

Shao, Xingchen; Wilson, P.R.; Saylor, J. R.; Bostwick, Joshua

doi:10.1017/jfm.2021.97

Cited by 20 publications

(38 citation statements)

References 51 publications

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“…(1995), while complex patterns originating by the coupling of meniscus and Faraday waves were recently described by Shao et al. (2021 a , b ) for small circular cylinder experiments. A discussion about harmonic Faraday waves disturbed by harmonic meniscus waves (MW) is also outlined in Batson et al.…”

Section: Introductionmentioning

confidence: 80%

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

et al. 2022

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In labscale Faraday experiments, meniscus waves respond harmonically to small-amplitude forcing without threshold, hence potentially cloaking the instability onset of parametric waves. Their suppression can be achieved by imposing a contact line pinned at the container brim with static contact angle $\theta _s=90^{\circ }$ (brimful condition). However, tunable meniscus waves are desired in some applications as those of liquid-based biosensors, where they can be controlled adjusting the shape of the static meniscus by slightly underfilling/overfilling the vessel ( $\theta _s\ne 90^{\circ }$ ) while keeping the contact line fixed at the brim. Here, we refer to this wetting condition as nearly brimful. Although classic inviscid theories based on Floquet analysis have been reformulated for the case of a pinned contact line (Kidambi, J. Fluid Mech., vol. 724, 2013, pp. 671–694), accounting for (i) viscous dissipation and (ii) static contact angle effects, including meniscus waves, makes such analyses practically intractable and a comprehensive theoretical framework is still lacking. Aiming at filling this gap, in this work we formalize a weakly nonlinear analysis via multiple time scale method capable of predicting the impact of (i) and (ii) on the instability onset of viscous subharmonic standing waves in both brimful and nearly brimful circular cylinders. Notwithstanding that the form of the resulting amplitude equation is in fact analogous to that obtained by symmetry arguments (Douady, J. Fluid Mech., vol. 221, 1990, pp. 383–409), the normal form coefficients are here computed numerically from first principles, thus allowing us to rationalize and systematically quantify the modifications on the Faraday tongues and on the associated bifurcation diagrams induced by the interaction of meniscus and subharmonic parametric waves.

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Section: Introductionmentioning

confidence: 80%

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

et al. 2022

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“…In a recent work by Shao et al. (2021), the modes of the mechanical Faraday instability in a circular container of finite size were characterized, demonstrating similar mode forms. By changing the frequency and the amplitude of the excitation, they were able to observe a large range of pure modes.…”

Section: Resultsmentioning

confidence: 82%

“…In addition, Shao et al. (2021) illuminated the role of the boundary meniscus, leading to waves travelling into the domain, which in the case of mechanical actuation stem from a contact angle different from at the container side wall. The superposition of Faraday waves and edge waves leads to complex instability patterns deviating from the modes of .…”

Section: Resultsmentioning

confidence: 99%

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The spatial structure of electrostatically forced Faraday waves

et al. 2022

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The instability of the interface between a dielectric and a conducting liquid, excited by a spatially homogeneous interface-normal time-periodic electric field, is studied based on experiments and theory. Special attention is paid to the spatial structure of the excited Faraday waves. The dominant modes of the instability are extracted using high-speed imaging in combination with an algorithm evaluating light refraction at the liquid–liquid interface. The influence of the liquid viscosities on the critical voltage corresponding to the onset of instability and on the dominant wavelength is studied. Overall, good agreement with theoretical predictions that are based on viscous fluids in an infinite domain is demonstrated. Depending on the relative influence of the domain boundary, the patterns exhibit either discrete modes corresponding to surface harmonics or boundary-independent patterns. The agreement between experiments and theory confirms that the electrostatically forced Faraday instability is sufficiently well understood, which may pave the way to control electrostatically driven instabilities. Last but not least, the analogies to classical Faraday instabilities may enable new approaches to study effects that have so far only been observed for mechanical forcing.

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“…An important feature of complex systems is the emergence of spatiotemporal patterns, which can be observed in numerous physical systems consisting of homogeneous media [1]. Among many examples, the emergence phenomenon can occur as a result of oscillatory kinetics in a chemical reaction [2], self-organization of biological organisms [3], mechanical vibration on liquid surfaces [4], or mineral precipitation on geologic surfaces [5]. In particular, network dynamics of pattern formation is considered to be the key attribute of information processing and memory storage in biological neural networks [6] and, hence, is the main concern in neuroscience.…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation in a RD-MCNN with Locally Active Memristors

Demirkol¹,

Ascoli²,

Messaris³

et al. 2021

Memristor - An Emerging Device for Post-Moore’s Computing and Applications

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This chapter presents the mathematical investigation of the emergence of static patterns in a Reaction–Diffusion Memristor Cellular Nonlinear Network (RD-MCNN) structure via the application of the theory of local activity. The proposed RD-MCNN has a planar grid structure, which consists of identical memristive cells, and the couplings are established in a purely resistive fashion. The single cell has a compact design being composed of a locally active memristor in parallel with a capacitor, besides the bias circuitry, namely a DC voltage source and its series resistor. We first introduce the mathematical model of the locally active memristor and then study the main characteristics of its AC equivalent circuit. Later on, we perform a stability analysis to obtain the stability criteria for the single cell. Consequently, we apply the theory of local activity to extract the parameter space associated with locally active, edge-of-chaos, and sharp-edge-of-chaos domains, performing all the necessary calculations parametrically. The corresponding parameter space domains are represented in terms of intrinsic cell characteristics such as the DC operating point, the capacitance, and the coupling resistance. Finally, we simulate the proposed RD-MCNN structure where we demonstrate the emergence of pattern formation for various values of the design parameters.

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Surface wave pattern formation in a cylindrical container

Abstract: Abstract

Cited by 20 publications

References 51 publications

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

The spatial structure of electrostatically forced Faraday waves

Pattern Formation in a RD-MCNN with Locally Active Memristors

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