The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Fabian Denner - One of the best experts on this subject based on the ideXlab platform.
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Capillary Waves with surface viscosity
Journal of Fluid Mechanics, 2018Co-Authors: Li Shen, Fabian Denner, Berend Van Wachem, Neal Morgan, Daniele DiniAbstract:Experiments over the last 50 years have suggested a tentative correlation between the surface (shear) viscosity and the stability of a foam or emulsion. We examine this link theoretically using small-amplitude Capillary Waves in the presence of a surfactant solution of dilute concentration, where the associated Marangoni and surface viscosity effects are modelled via the Boussinesq–Scriven formulation. The resulting integro-differential initial value problem is solved analytically, and surface viscosity is found to contribute an overall damping effect to the amplitude of the Capillary wave with varying degree depending on the length scale of the system. Numerically, we find that the critical damping wavelength increases for increasing surface concentration but the rate of increase remains different for both the surface viscosity and the Marangoni effect.
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marangoni effect on small amplitude Capillary Waves in viscous fluids
Physical Review E, 2017Co-Authors: Li Shen, Fabian Denner, Berend Van Wachem, Neal Morgan, Daniele DiniAbstract:We derive a general integro-differential equation for the transient behavior of small-amplitude Capillary Waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism, and a first-order term correction to the critical wavelength with respect to the surfactant concentration difference and the Schmidt number is proposed.
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Dispersion and viscous attenuation of Capillary Waves with finite amplitude
The European Physical Journal Special Topics, 2017Co-Authors: Fabian Denner, Gounséti Paré, Stéphane ZaleskiAbstract:We present a comprehensive study of the dispersion of Capillary Waves with finite amplitude, based on direct numerical simulations. The presented results show an increase of viscous attenuation and, consequently, a smaller frequency of Capillary Waves with increasing initial wave amplitude. Interestingly, however, the critical wavenumber as well as the wavenumber at which the maximum frequency is observed remain the same for a given two-phase system, irrespective of the wave amplitude. By devising an empirical correlation that describes the effect of the wave amplitude on the viscous attenuation, the dispersion of Capillary Waves with finite initial amplitude is shown to be, in very good approximation, self-similar throughout the entire underdamped regime and independent of the fluid properties. The results also shown that analytical solutions for Capillary Waves with infinitesimal amplitude are applicable with reasonable accuracy for Capillary Waves with moderate amplitude.
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Frequency dispersion of small-amplitude Capillary Waves in viscous fluids.
Physical Review E, 2016Co-Authors: Fabian DennerAbstract:This work presents a detailed study of the dispersion of Capillary Waves with small amplitude in viscous fluids using an analytically derived solution to the initial value problem of a small-amplitude Capillary wave as well as direct numerical simulation. A rational parametrization for the dispersion of Capillary Waves in the underdamped regime is proposed, including predictions for the wave number of critical damping based on a harmonic-oscillator model. The scaling resulting from this parametrization leads to a self-similar solution of the frequency dispersion of Capillary Waves that covers the entire underdamped regime, which allows an accurate evaluation of the frequency at a given wave number, irrespective of the fluid properties. This similarity also reveals characteristic features of Capillary Waves, for instance that critical damping occurs when the characteristic time scales of dispersive and dissipative mechanisms are balanced. In addition, the presented results suggest that the widely adopted hydrodynamic theory for damped Capillary Waves does not accurately predict the dispersion when viscous damping is significant, and an alternative definition of the damping rate, which provides consistent accuracy in the underdamped regime, is presented.
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Numerical time-step restrictions as a result of Capillary Waves
Journal of Computational Physics, 2015Co-Authors: Fabian Denner, Berend Van WachemAbstract:The propagation of Capillary Waves on material interfaces between two fluids imposes a strict constraint on the numerical time-step applied to solve the equations governing this problem and is directly associated with the stability of interfacial flow simulations. The explicit implementation of surface tension is the generally accepted reason for the restrictions on the temporal resolution caused by Capillary Waves. In this article, a fully-coupled numerical framework with an implicit treatment of surface tension is proposed and applied, demonstrating that the Capillary time-step constraint is in fact a constraint imposed by the temporal sampling of Capillary Waves, irrespective of the type of implementation. The presented results show that the Capillary time-step constraint can be exceeded by several orders of magnitude, with the explicit as well as the implicit treatment of surface tension, if Capillary Waves are absent. Furthermore, a revised Capillary time-step constraint is derived by studying the temporal resolution of Capillary Waves based on numerical stability and signal processing theory, including the Doppler shift caused by an underlying fluid motion. The revised Capillary time-step constraint assures a robust, aliasing-free result, as demonstrated by representative numerical experiments, and is in the static case less restrictive than previously proposed time-step limits associated with Capillary Waves.
Daniele Dini - One of the best experts on this subject based on the ideXlab platform.
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Capillary Waves with surface viscosity
Journal of Fluid Mechanics, 2018Co-Authors: Li Shen, Fabian Denner, Berend Van Wachem, Neal Morgan, Daniele DiniAbstract:Experiments over the last 50 years have suggested a tentative correlation between the surface (shear) viscosity and the stability of a foam or emulsion. We examine this link theoretically using small-amplitude Capillary Waves in the presence of a surfactant solution of dilute concentration, where the associated Marangoni and surface viscosity effects are modelled via the Boussinesq–Scriven formulation. The resulting integro-differential initial value problem is solved analytically, and surface viscosity is found to contribute an overall damping effect to the amplitude of the Capillary wave with varying degree depending on the length scale of the system. Numerically, we find that the critical damping wavelength increases for increasing surface concentration but the rate of increase remains different for both the surface viscosity and the Marangoni effect.
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marangoni effect on small amplitude Capillary Waves in viscous fluids
Physical Review E, 2017Co-Authors: Li Shen, Fabian Denner, Berend Van Wachem, Neal Morgan, Daniele DiniAbstract:We derive a general integro-differential equation for the transient behavior of small-amplitude Capillary Waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism, and a first-order term correction to the critical wavelength with respect to the surfactant concentration difference and the Schmidt number is proposed.
Luc Deike - One of the best experts on this subject based on the ideXlab platform.
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Turbulence of Capillary Waves forced by steep gravity Waves
Journal of Fluid Mechanics, 2018Co-Authors: Michael Berhanu, Eric Falcon, Luc DeikeAbstract:We study experimentally the dynamics and statistics of Capillary Waves forced by random steep gravity Waves mechanically generated in the laboratory. Capillary Waves are produced here by gravity Waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free surface, we characterize statistically the random regimes of Capillary Waves in the spatial and temporal Fourier spaces. For a significant wave steepness (0.2–0.3), power-law spectra are observed both in space and time, defining a turbulent regime of Capillary Waves transferring energy from the large scale to the small scale. Analysis of temporal fluctuations of the spatial spectrum demonstrates that the Capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to the small scale in a fast time scale, when Capillary wave trains are generated in a way similar to the parasitic Capillary wave generation mechanism. The frequency and wavenumber power-law exponents of the wave spectra are found to be in agreement with those of the weakly nonlinear wave turbulence theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with wave turbulence theory. These results suggest that theoretical developments beyond the classic wave turbulence theory are necessary to describe the dynamics and statistics of Capillary Waves in a natural environment. In particular, in the presence of broad-scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions should be reconsidered.
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Turbulence of Capillary Waves forced by steep gravity Waves
Journal of Fluid Mechanics, 2018Co-Authors: Michael Berhanu, Eric Falcon, Luc DeikeAbstract:We study experimentally the dynamics and statistics of Capillary Waves forced by random steep gravity Waves mechanically generated in laboratory. Capillary Waves are produced here by gravity Waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free-surface, we characterize statistically the random regimes of Capillary Waves in the spatial and temporal Fourier spaces. For a significant wave steepness ($0.2-0.3$), power-law spectra are observed both in space and time, defining a turbulent regime of Capillary Waves transferring energy from large scale to small scale. Analysis of temporal fluctuations of spatial spectrum demonstrates that the Capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to small scale in a fast time scale, when Capillary wave trains are generated in a way similar to the parasitic Capillary wave generation mechanism. The frequency and wavenumber power-law exponents of wave spectrum are found to be in agreement with those of the weakly nonlinear Wave Turbulence Theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with Wave Turbulence Theory. These results suggest that theoretical developments beyond the classic Wave Turbulence Theory are necessary to describe the dynamics and statistics of Capillary Waves in natural environment. In particular, in presence of broad scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions could be reconsidered.
Jonathan S Chapman - One of the best experts on this subject based on the ideXlab platform.
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three dimensional Capillary Waves due to a submerged source with small surface tension
Journal of Fluid Mechanics, 2019Co-Authors: Christopher J Lustri, Ravindra Pethiyagoda, Jonathan S ChapmanAbstract:Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface Capillary Waves generated are exponentially small in the surface tension, and are determined using the theory of exponential asymptotics. In the steady problem, Capillary Waves are found to extend upstream from the source, switching on across curves on the free surface known as Stokes lines. Asymptotic predictions are compared with computational solutions for the position of the free surface. In the unsteady problem, transient effects cause the solution to display more complicated asymptotic behaviour, such as higher-order Stokes lines. The theory of exponential asymptotics is applied to show how the Capillary Waves evolve over time, and eventually tend to the steady solution.
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three dimensional Capillary Waves due to a submerged source with small surface tension
arXiv: Fluid Dynamics, 2018Co-Authors: Christopher J Lustri, Ravindra Pethiyagoda, Jonathan S ChapmanAbstract:Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface Capillary Waves generated are exponentially small in the surface tension, and are determined using the theory of exponential asymptotics. In the steady problem, Capillary Waves are found to extend upstream from the source, switching on across curves on the free surface known as Stokes lines. Asymptotic predictions and compared with computational solutions for the position of the free surface. In the unsteady problem, transient effects cause the solution to display more complicated asymptotic behaviour, such as higher-order Stokes lines. The theory of exponential asymptotics is applied to show how the Capillary Waves evolve over time, and eventually tend to the steady solution.
Li Shen - One of the best experts on this subject based on the ideXlab platform.
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Capillary Waves with surface viscosity
Journal of Fluid Mechanics, 2018Co-Authors: Li Shen, Fabian Denner, Berend Van Wachem, Neal Morgan, Daniele DiniAbstract:Experiments over the last 50 years have suggested a tentative correlation between the surface (shear) viscosity and the stability of a foam or emulsion. We examine this link theoretically using small-amplitude Capillary Waves in the presence of a surfactant solution of dilute concentration, where the associated Marangoni and surface viscosity effects are modelled via the Boussinesq–Scriven formulation. The resulting integro-differential initial value problem is solved analytically, and surface viscosity is found to contribute an overall damping effect to the amplitude of the Capillary wave with varying degree depending on the length scale of the system. Numerically, we find that the critical damping wavelength increases for increasing surface concentration but the rate of increase remains different for both the surface viscosity and the Marangoni effect.
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marangoni effect on small amplitude Capillary Waves in viscous fluids
Physical Review E, 2017Co-Authors: Li Shen, Fabian Denner, Berend Van Wachem, Neal Morgan, Daniele DiniAbstract:We derive a general integro-differential equation for the transient behavior of small-amplitude Capillary Waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism, and a first-order term correction to the critical wavelength with respect to the surfactant concentration difference and the Schmidt number is proposed.
