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arXiv2013

Experimental investigation of the stability of the floating water bridge

When a high voltage is applied between two beakers filled with deionized water, a bridge of water may be formed in between exceeding the length of 2 cm when the beakers are pulled apart. We construct experiments in which the geometry and the electric field within the bridge are measured and compared with predictions of theories on the floating water bridge. A numerical simulation is used for the measurement of the electric field. Our experimental results approve that two forces of dielectric tension and surface tension are holding the bridge against gravity. These forces have the same order of magnitude. Results show that the stability can be explained by macroscopic forces, regardless of the microscopic changes in water structure.

physics.flu-dyn↗

arXiv2013

Log-normal distribution from a process that is not multiplicative but is additive

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal distribution. Although the sum tends eventually to a Gaussian distribution, the distribution of the sum is always close to a log-normal distribution rather than to any Gaussian distribution if the summands are numerous enough. This is in contrast to the current consensus that any log-normal distribution is due to a product of random variables, i.e., a multiplicative process, or equivalently to nonlinearity of the system. In fact, the log-normal distribution is also observable for a sum, i.e., an additive process that is typical of linear systems. We show conditions for such a sum, an analytical example, and an application to random scalar fields such as of turbulence.

physics.flu-dyn↗

arXiv2013

Nonlinear electrohydrodynamics of a viscous droplet

A classic result due to G.I.Taylor is that a drop placed in a uniform electric field becomes a prolate or oblate spheroid, which is axisymmetrically aligned with the applied field. We report an instability and symmetry-breaking transition to obliquely oriented, steady and unsteady shapes in strong fields. Our experiments reveal novel droplet behaviors such as tumbling, shape oscillations, and chaotic dynamics even under creeping flow conditions. A theoretical model, which includes anisotropy in the polarization relaxation due to drop asphericity and charge convection due to drop fluidity, elucidates the interplay of interfacial flow and charging as the source of the rich nonlinear dynamics.

physics.flu-dyn↗

arXiv2013

Bifurcations and dynamics in convection with temperature-dependent viscosity in the presence of the O(2) symmetry

We focus the study of a convection problem in a 2D setup in the presence of the O(2) symmetry. The viscosity in the fluid depends on the temperature as it changes its value abruptly in an interval around a temperature of transition. The influence of the viscosity law on the morphology of the plumes is examined for several parameter settings, and a variety of shapes ranging from spout to mushroom shaped is found. We explore the impact of the symmetry on the time evolution of this type of fluid, and find solutions which are greatly influenced by its presence: at a large aspect ratio and high Rayleigh numbers, traveling waves, heteroclinic connections and chaotic regimes are found. These solutions, which are due to the symmetry presence, have not been previously described in the context of temperature dependent viscosities. However, similarities are found with solutions described in other contexts such as flame propagation problems or convection problems with constant viscosity also under the presence of the O(2) symmetry, thus confirming the determining role of the symmetry in the dynamics.

physics.flu-dyn↗

arXiv2013

Information Content of Turbulence

We treat a turbulent velocity field as a message in the same way as a book or a picture. All messages can be described by their entropy per symbol $h$, defined as in Shannon's theory of communication. In a turbulent flow, as the Reynolds number $Re$ increases, more correlated degrees of freedom are excited and participate in the turbulent cascade. Experiments in a turbulent soap film suggest that the spatial entropy density $h$ is a decreasing function of $Re$, namely $h \propto -\log Re$ + const. In the logistic map, also analyzed here, increasing the control parameter $r$ increases $h$. A modified logistic map with additional coupling to past iterations suggests the significance of correlations.

nlin.CD↗

arXiv2013

Achieving tunable surface tension in the pseudopotential lattice Boltzmann modeling of multiphase flows

In this paper, we aim to address an important issue about the pseudopotential lattice Boltzmann (LB) model, which has attracted much attention as a mesoscopic model for simulating interfacial dynamics of complex fluids, but suffers from the problem that the surface tension cannot be tuned independently of the density ratio. In the literature, a multi-range potential was devised to adjust the surface tension [Sbragaglia et al., Phys. Rev. E 75, 026702 (2007)]. However, it was recently found that the density ratio of the system will be changed when the multi-range potential is employed to adjust the surface tension. A new approach is therefore proposed in the present work. The basic strategy is to add a source term to the LB equation so as to tune the surface tension of the pseudopotential LB model. The proposed approach can guarantee that the adjustment of the surface tension does not affect the mechanical stability condition of the pseudopotential LB model, and thus provides a separate control of the surface tension and the density ratio. Meanwhile, it still retains the mesoscopic feature and the computational simplicity of the pseudopotential LB model. Numerical simulations are carried out for stationary droplets, capillary waves, and droplet splashing on a thin liquid film. The numerical results demonstrate that the proposed approach is capable of achieving a tunable surface tension over a very wide range and can keep the density ratio unchanged when adjusting the surface tension.

physics.comp-ph↗

arXiv2014

Soft beams: when capillarity induces axial compression

We study the interaction of an elastic beam with a liquid drop in the case where bending and extensional effects are both present. We use a variational approach to derive equilibrium equations and constitutive relation for the beam. This relation is shown to include a term due to surface energy in addition of the classical Young's modulus term, leading to a modification of Hooke's law. At the triple point where solid, liquid, and vapor phases meet we find that the external force applied on the beam is parallel to the liquid-vapor interface. Moreover, in the case where solid-vapor and solid-liquid interface energies do not depend on the extension state of the beam, we show that the extension in the beam is continuous at the triple point and that the wetting angle satisfy the classical Young-Dupré relation.

cond-mat.soft↗

arXiv2013

Identification of Separation Wavenumber between Weak and Strong Turbulence Spectra for Vibrating Plate

A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a statistically steady state of elastic wave turbulence. The analytical representation of the nonlinear frequency is obtained by evaluating the extended self-nonlinear interactions. The {\em critical\/} wavenumbers at which the nonlinear frequencies are comparable with the linear frequencies agree with the {\em separation\/} wavenumbers between the weak and strong turbulence spectra. We also confirm the validity of our analytical representation of the separation wavenumbers through comparison with the results of direct numerical simulations by changing the material parameters of a vibrating plate.

nlin.CD↗

arXiv2013

Transient Growth of Ekman-Couette Flow

Coriolis force effects on shear flows are important in geophysical and astrophysical contexts. We here report a study on the linear stability and the transient energy growth of the plane Couette flow with system rotation perpendicular to the shear direction. External rotation causes linear instability. At small rotation rates, the onset of linear instability scales inversely with the rotation rate and the optimal transient growth in the linearly stable region is slightly enhanced, ~Re^2. The corresponding optimal initial perturbations are characterized by roll structures inclined in the streamwise direction and are twisted under external rotation. At large rotation rates, the transient growth is significantly inhibited and hence linear stability analysis is a reliable indicator for instability.

physics.flu-dyn↗

arXiv2014

Role of roughness on the hydrodynamic homogeneous base state of inelastic spheres

A gas of inelastic rough spheres admits a spatially homogeneous base state which turns into a hydrodynamic state after a finite relaxation time. We show that this relaxation time is hardly dependent on the degree of inelasticity but increases dramatically with decreasing roughness. An accurate description of translational-rotational velocity correlations at all times is also provided. At a given inelasticity, the roughness parameter can be tuned to produce a huge distortion from the Maxwellian distribution function. The results are obtained from a Grad-like solution of the Boltzmann-Enskog equation complemented by Monte Carlo and molecular dynamics simulations.

cond-mat.soft↗

arXiv2013

Energy flux measurement from the dissipated energy in capillary wave turbulence

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a fluid by changing its viscosity. We observe that the frequency power law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the fluid. Here, we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be non constant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.

physics.flu-dyn↗

arXiv2014

Scaling of heat flux and energy spectrum for "very large" Prandtl number convection

Under the limit of infinite Prandtl number, we derive analytical expressions for the large-scale quantities, e.g., Péclet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations $θ_\mathrm{rms}$. We complement the analytical work with direct numerical simulations, and show that $\mathrm{Nu} \sim \mathrm{Ra}^γ$ with $γ\approx (0.30-0.32)$, $\mathrm{Pe} \sim \mathrm{Ra}^η$ with $η\approx (0.57-0.61)$, and $θ_\mathrm{rms} \sim \mathrm{const}$. The Nusselt number is observed to be an intricate function of $\mathrm{Pe}$, $θ_\mathrm{rms}$, and a correlation function between the vertical velocity and temperature. Using the scaling of large-scale fields, we show that the energy spectrum $E_u(k)\sim k^{-13/3}$, which is in a very good agreement with our numerical results. The entropy spectrum $E_θ(k)$ however exhibits dual branches consisting of $k^{-2}$ and $k^0$ spectra; the $k^{-2}$ branch corresponds to the Fourier modes $\hatθ(0,0,2n)$, which are approximately $-1/(2n π)$. The scaling relations for Prandtl number beyond $10^2$ match with those for infinite Prandtl number.

physics.flu-dyn↗

arXiv2014

Entropy and energy spectra in low-Prandtl-number convection with rotation

We present results for entropy and kinetic energy spectra computed from direct numerical simulations for low-Prandtl-number ($Pr < 1$) turbulent flow in Rayleigh-Bénard convection with uniform rotation about a vertical axis. The simulations are performed in a three-dimensional periodic box for a range of Taylor number ($ 0 \leq Ta \leq 10^8$) and reduced Rayleigh number $r = Ra/Ra_{\circ} (Ta, Pr)$ ($1.0 \times 10^2 \le r \le 5.0 \times 10^3$). The Rossby number $Ro$ varies in the range $1.34 \le Ro \le 73$. The entropy spectrum $E_θ(k)$ shows bi-splitting into two branches for lower values of wave number $k$. The entropy in the lower branch scales with $k$ as $k^{-1.4\pm 0.1}$ for $r > 10^3$ for the rotation rates considered here. The entropy in the upper branch also shows scaling behavior with $k$, but the scaling exponent decreases with increasing $Ta$ for all $r$. The energy spectrum $E_v(k)$ is also found to scale with the wave number $k$ as $k^{-1.4\pm 0.1}$ for $r > 10^3$. The scaling exponent for the energy spectrum and the lower branch of the entropy spectrum vary between $-1.7$ to $-2.4$ for lower values of $r$ ($< 10^3$). We also provide some simple arguments based on the variation of the Kolmogorov picture to support the results of simulations.

physics.flu-dyn↗

arXiv2013

Choice of boundary condition for lattice-Boltzmann simulation of moderate Reynolds number flow in complex domains

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlet/outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries (Guo, Zheng and Shi, Phys Fluids (2002); Bouzdi, Firdaouss and Lallemand, Phys. Fluids (2001); Junk and Yang Phys. Rev. E (2005)) in our open-source application \HemeLB{}. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Reynolds (1--300) and Womersley (4--12) numbers and steady flow in a curved pipe at relevant Dean number (100--200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand and Guo-Zheng-Shi methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Reynolds number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs.\ multiple relaxation time) and velocity set (D3Q15 vs.\ D3Q19 vs.\ D3Q27) does not significantly affect the accuracy in the problems studied.

physics.comp-ph↗

arXiv2014

The effect of confinement on the deformation of microfluidic drops

We study the deformation of drops squeezed between the floor and ceiling of a microchannel and subjected to a hyperbolic flow. We observe that the maximum deformation of drops depends on both the drop size and the rate of strain of the external flow and can be described with power laws with exponents 2.59 +/- 0.28 and 0.91 +/- 0.05 respectively. We develop a theoretical model to describe the deformation of squeezed drops based on the Darcy approximation for shallow geometries and the use of complex potentials. The model describes the steady-state deformation of the drops as a function of a non-dimensional parameter Ca d^2, where Ca is the capillary number (proportional to the strain rate and the drop size) and d is a confinement parameter equal to the drop size divided by the channel height. For small deformations, the theoretical model predicts a linear relationship between the deformation of drops and this parameter, in good agreement with the experimental observations.

physics.flu-dyn↗

arXiv2014

The alpha-effect in a turbulent liquid-metal plane Couette flow

We calculate the mean electromotive force in plane Couette flows of a nonrotating conducting fluid under the influence of a large-scale magnetic field for driven turbulence. A vertical stratification of the turbulence intensity results in an alpha effect owing to the presence of horizontal shear. Here we discuss the possibility of an experimental determination of the components of the alpha tensor using both quasilinear theory and nonlinear numerical simulations. For magnetic Prandtl numbers of the order of unity, we find that in the high-conductivity limit the alpha effect in the direction of the flow clearly exceeds the component in spanwise direction. In this limit, alpha runs linearly with the magnetic Reynolds number Rm while in the low-conductivity limit it runs with the product Rm*Re, where Re is the kinetic Reynolds number so that for given Rm the alpha effect grows with decreasing magnetic Prandtl number. For the small magnetic Prandtl numbers of liquid metals, a common value for the horizontal elements of the alpha tensor appears, which makes it unimportant whether the alpha effect is measured in the spanwise or streamwise directions. The resulting effect should lead to an observable voltage in both directions of about 0.5 mV for magnetic fields of 1 kgauss and velocity fluctuations of about 1 m/s in a channel of 50 cm height (independent of its width).

astro-ph.SR↗

arXiv2014

Asymptotic results for backwards two-particle dispersion in a turbulent flow

We derive an exact equation governing two-particle backwards mean-squared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe the consequences of our formula for short times and arrive at approximate expressions for the mean-squared dispersion which involve second order structure functions of the velocity and acceleration fields. For the stochastic trajectories, we analytically compute an exact $t^3$ contribution to the squared separation of stochastic paths. We argue that this contribution appears also for deterministic paths at long times and present direct numerical simulation results for incompressible Navier-Stokes flows to support this claim. We also numerically compute the probability distribution of particle separations for the deterministic paths and the stochastic paths and show their strong self-similar nature.

physics.flu-dyn↗

arXiv2013

Transport-limited water splitting at ion-selective interfaces during concentration polarization

We present an analytical model of salt- and water-ion transport across an ion-selective interface based on an assumption of local equilibrium of the water-dissociation reaction. The model yields current-voltage characteristics and curves of water-ion current versus salt-ion current, which are in qualitative agreement with experimental results published in the literature. The analytical results are furthermore in agreement with direct numerical simulations. As part of the analysis, we find approximate solutions to the classical problem of pure salt transport across an ion-selective interface. These solutions provide closed-form expressions for the current-voltage characteristics, which include the overlimiting current due to the development of an extended space charge region. Finally, we discuss how the addition of an acid or a base affects the transport properties of the system and thus provide predictions accessible to further experimental tests of the model.

physics.flu-dyn↗