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arXiv2013

Leaking Chaotic Systems

There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. In this paper we provide an unified treatment of leaking systems and we review applications to different physical problems, both in the classical and quantum pictures. Our treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows, to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption/transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the lima .con family of billiards illustrate the main text. Regarding billiard dynamics, we emphasize that a correct discrete time representation can only be given in terms of the so- called true-time maps, while traditional Poincar é maps lead to erroneous results. We generalize Perron-Frobenius-type operators so that they describe true-time maps with partial leaks.

nlin.CD↗

arXiv2012

How can macroscopic models reveal self-organization in traffic flow?

In this paper we propose a new modeling technique for vehicular traffic flow, designed for capturing at a macroscopic level some effects, due to the microscopic granularity of the flow of cars, which would be lost with a purely continuous approach. The starting point is a multiscale method for pedestrian modeling, recently introduced in Cristiani et al., Multiscale Model. Simul., 2011, in which measure-theoretic tools are used to manage the microscopic and the macroscopic scales under a unique framework. In the resulting coupled model the two scales coexist and share information, in the sense that the same system is simultaneously described from both a discrete (microscopic) and a continuous (macroscopic) perspective. This way it is possible to perform numerical simulations in which the single trajectories and the average density of the moving agents affect each other. Such a method is here revisited in order to deal with multi-population traffic flow on networks. For illustrative purposes, we focus on the simple case of the intersection of two roads. By exploiting one of the main features of the multiscale method, namely its dimension-independence, we treat one-dimensional roads and two-dimensional junctions in a natural way, without referring to classical network theory. Furthermore, thanks to the coupling between the microscopic and the macroscopic scales, we model the continuous flow of cars without losing the right amount of granularity, which characterizes the real physical system and triggers self-organization effects, such as, for example, the oscillatory patterns visible at jammed uncontrolled crossroads.

math-ph↗

arXiv2014

Experimental and computational studies of water drops falling through model oil with surfactant and subjected to an electric field

The behaviour of a single sub-millimetre-size water drop falling through a viscous oil while subjected to an electric field is of fundamental importance to industrial applications such as crude oil electrocoalescers. Detailed studies, both experimental and computational, have been performed previously, but an often challenging issue has been the characterization of the fluids. As numerous authors have noted, it is very difficult to have a perfectly clean water-oil system even for very pure model oils, and the presence of trace chemicals may significantly alter the interface behaviour. In this work, we consider a well- characterized water-oil system where controlled amounts of a surface active agent (Span 80) have been added to the oil. This addition dominates any trace contaminants in the oil, such that the interface behaviour can also be well-characterized. We present the results of experiments and corresponding two-phase- flow simulations of a falling water drop covered in surfactant and subjected to a monopolar square voltage pulse. The results are compared and good agreement is found for surfactant concentrations below the critical micelle concentration.

physics.flu-dyn↗

arXiv2013

Study of the cavitating instability on a grooved Venturi profile

Cavitation is a limiting phenomenon in many domains of fluid mechanics. Instabilities of a partial cavity developed on an hydrofoil, a converging-diverging step or in an inter-blade channel in turbomachinery, have already been investigated and described in many previous works. The aim of this study is to evaluate a passive control method of the sheet cavity. According to operating conditions, cavitation can be described by two different regimes: an unstable regime with a cloud cavitation shedding and a stable regime with only a pulsating sheet cavity. Avoiding cloud cavitation can limit structure damages since a pulsating sheet cavity is less agressive. The surface condition of a converging-diverging step, like a Venturi-type obstacle, is here studied as a solution for a passive control of the cavitation. This study discusses the effect of an organized roughness, in the shape of longitudinal grooves, on the developed sheet cavity. Analyzes conducted with Laser Doppler Velocimetry, visualisations and pressure measurements show that the grooves geometry, and especially the groove depth, acts on the sheet cavity dynamics. Results show that modifying the surface condition, by varying the grooves geometry, can reduce cavity sheet length and even suppress the cloud cavitation shedding.

physics.flu-dyn↗

arXiv2014

Irreversibility in an ideal fluid

When a real fluid is expelled quickly from a tube, it forms a jet separated from the surrounding fluid by a thin, turbulent layer. On the other hand, when the same fluid is sucked into the tube, it comes in from all directions, forming a sink-like flow. We show that, even for the ideal flow described by the time-reversible Euler equation, an experimenter who only controls the pressure in a pump attached to the tube would see jets form in one direction exclusively. The asymmetry between outflow and inflow therefore does not depend on viscous dissipation, but rather on the experimenter's limited control of initial and boundary conditions. This illustrates, in a rather different context from the usual one of thermal physics, how irreversibility may arise in systems whose microscopic dynamics are fully reversible.

physics.flu-dyn↗

arXiv2013

Interacting bubble clouds and their sonochemical production

Acoustically driven air pockets trapped in artificial crevices on a sur- face can emit bubbles which organize in (interacting) bubble clusters. With increasing driving power Fernandez Rivas et al. [Angew. Chem. Int. Ed., 2010] observed three different behaviors: clusters close to the very pits out of which they had been created, clusters pointing toward each other, and merging clusters. The latter behavior is highly undesired for technological purposes as it is associated with a reduction of the radical production and an enhancement of the erosion of the reactor walls. The dependence on the control parameters such as the distance of the pits and the conditions for cluster-merging are examined. The underlying mechanism, governed by the secondary Bjerknes forces, turns out to be strongly influenced by the nonlinearity of the bubble oscillations and not directly by the number of nucleated bubbles. The Bjerknes forces are found to dampen the bubble oscillations, thus reducing the radical production. Therefore, the increased number of bubbles at high power could be the key to understand the experimental observation that, after a certain power threshold, any further increase of the driving does not improve the sonochemical efficiency.

physics.flu-dyn↗

arXiv2017

On the use of a Stress-Impedance Model to describe sound propagation in a lined duct with grazing flow

With flow, the acoustical effect of a lined wall cannot be described by a single quantity like the wall impedance. At least two quantities are required. In addition to the impedance, the unsteady tangential force exerted by the wall on the flow has to be taken into account. This force is due either to viscous effects or to the unsteady transfer of axial momentum from the flow into the lined wall. The paper describes a Stress--Impedance model where the two variables used are the impedance and the friction factor that links the pressure to a tangential stress at the wall. The use of a wall stress helps to better understand the mechanisms of momentum transfer between the flow and the wall in the vicinity of an acoustic treatment.

physics.flu-dyn↗

arXiv2014

Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions

Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article (R. Seto, R. Mari, J. F. Morris, and M. M. Denn., Phys. Rev. Lett., 111:218301, 2013) we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including Discontinuous Shear Thickening (DST). We have found frictional contact forces to be essential, and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: as the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition.

cond-mat.soft↗

arXiv2025

X-ray particle tracking velocimetry for steady-state rheological characterization: Case study of a complex polymer melt flow in material extrusion additive manufacturing

We introduce X-ray Particle Tracking Velocimetry (XPTV) as a promising method to quantitatively resolve the velocity field and associated rheological information of polymer melt flow within the nozzle of a fused filament fabrication (FFF) printer. Employing tungsten powder as tracer particles embedded within a polymer filament, we investigate melt flow dynamics through an aluminum nozzle in a custom setup comparable to commercial printers. The velocity profiles obtained via XPTV reveal significant deviations from classical Newtonian flow, highlighting complex heterogeneous and non-isothermal behavior within the melt. From these measurements, we determine the local infinitesimal strain rate tensor and correlate flow-induced non-Newtonian effects to spatially varying temperature distributions, reflecting incomplete thermal homogenization within the nozzle. We complement the experiments with computational fluid dynamics simulations of the flow inside the printing nozzle, incorporating filament melting through an enthalpy-porosity formulation and treating the air-polymer melt interface using a two-phase approach. The simulated velocity profiles agree closely with the XPTV measurements across the investigated operating conditions, supporting the experimental interpretation. Our findings demonstrate the capability of XPTV to quantify both velocity fields and rheological properties, underscoring its potential as a tool for investigating opaque polymer melt flows in additive manufacturing, industrial processing, and rheology. To our knowledge, this is the first application of XPTV to polymer melt rheology. It enables measurements that are inaccessible to conventional optical methods.

cond-mat.soft↗

arXiv2014

Precise and ultrafast molecular sieving through graphene oxide membranes

There has been intense interest in filtration and separation properties of graphene-based materials that can have well-defined nanometer pores and exhibit low frictional water flow inside them. Here we investigate molecular permeation through graphene oxide laminates. They are vacuum-tight in the dry state but, if immersed in water, act as molecular sieves blocking all solutes with hydrated radii larger than 4.5A. Smaller ions permeate through the membranes with little impedance, many orders of magnitude faster than the diffusion mechanism can account for. We explain this behavior by a network of nanocapillaries that open up in the hydrated state and accept only species that fit in. The ultrafast separation of small salts is attributed to an 'ion sponge' effect that results in highly concentrated salt solutions inside graphene capillaries.

cond-mat.mtrl-sci↗

arXiv2013

Universal power law for the energy spectrum of breaking Riemann waves

The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation. The spectrum of spatial amplitudes at the breaking time $t = t_b$ has an asymptotic decay of $k^{-4/3}$, with corresponding energy spectrum decaying as $k^{-8/3}$. This spectrum is formed by the singularity of the form $(x-x_b)^{1/3}$ in the wave shape at the breaking time. This result remains valid for arbitrary nonlinear wave speed. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wave numbers if small dissipation or dispersion is accounted in the viscous Burgers or Korteweg-de Vries equations.

math-ph↗

arXiv2013

The complex singularity of a Stokes wave

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase of the scaled wave height $H/λ$ from the linear limit $H/λ=0$ to the critical value $H_{max}/λ$ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave. Here $H$ is the wave height and $λ$ is the wavelength. We simulated fully nonlinear Euler equations, reformulated in terms of conformal variables, to find Stokes waves for different wave heights. Analyzing spectra of these solutions we found in conformal variables, at each Stokes wave height, the distance $v_c$ from the lowest singularity in the upper half-plane to the real line which corresponds to the fluid free surface. We also identified that this singularity is the square-root branch point. The limiting Stokes wave emerges as the singularity reaches the fluid surface. From the analysis of data for $v_c\to 0$ we suggest a new power law scaling $v_c\propto (H_{max}-H)^{3/2}$ as well as new estimate $H_{max}/λ\simeq 0.1410633$.

physics.flu-dyn↗

arXiv2013

Computer simulation of effective viscosity of fluid-proppant mixture used in hydraulic fracturing

The paper presents results of numerical experiments performed to evaluate the effective viscosity of a fluid-proppant mixture, used in hydraulic fracturing. The results, obtained by two complimenting methods (the particle dynamics and the smoothed particle hydrodynamics), coincide to the accuracy of standard deviation. They provide an analytical equation for the dependence of effective viscosity on the proppant concentration, needed for numerical simulation of the hydraulic fracture propagation.

physics.flu-dyn↗

arXiv2014

Collective Dynamics of Interacting Particles in Unsteady Flows

We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive potential field known as Morse potential. We assume Stokesian drag force between particles and their carrier fluid, and find analytic single-peaked traveling solutions for the spatial density of particles in the catastrophic phase. In steady flow conditions the streaming velocity of particles is identical to their carrier fluid, but we show that particle streaming is asynchronous with an unsteady carrier fluid. Using linear perturbation analysis, the stability of traveling solutions is investigated in unsteady conditions. It is shown that the resulting dispersion relation is an integral equation of the Fredholm type, and yields two general families of stable modes: singular modes whose eigenvalues form a continuous spectrum, and a finite number of discrete global modes. Depending on the value of drag coefficient, stable modes can be over-damped, critically damped, or decaying oscillatory waves. The results of linear perturbation analysis are confirmed through the numerical solution of the fully nonlinear Fokker-Planck equation.

physics.flu-dyn↗

arXiv2014

A Study in Three-Dimensional Chaotic Dynamics: Granular Flow and Transport in a Bi-Axial Spherical Tumbler

We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (in the absence of stochasticity) particle trajectories are restricted to 2D surfaces consisting of a portion of a hemispherical shell closed by a "cap"; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of the granular material, and their dependence on the protocol parameters (rates and durations of rotations). Exploiting the restriction of trajectories to 2D surfaces in the case of equal rotation rates about the axes, a method is proposed for identifying and constructing 3D Kolmogorov-Arnold-Moser (KAM) tubes around the normally elliptic period-one curves. The invariant manifold structure arising from the normally hyperbolic period-one curves is also examined. When the motion is restricted to 2D surfaces, the structure of manifolds of the hyperbolic points in the bulk differs from that corresponding to hyperbolic points in the flowing layer. Each is reminiscent of a template provided by a non-integrable perturbation to a Hamiltonian system, though the governing LTM is not. This highlights the novel 3D chaotic behaviors observed in this model dynamical system.

math.DS↗

arXiv2012

Non-extensive statistics, relativistic kinetic theory and fluid dynamics

Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to Rényi's or Tsallis' entropy formula - over a wide range of energies, colliding system sizes, and produced hadron sorts. In order to derive its evolution one needs a corresponding dynamical description of the system which results in such final state observables. The equations of relativistic fluid dynamics are obtained from a non-extensive Boltzmann equation consistent with Tsallis' non-extensive $q$-entropy formula. The transport coefficients like shear viscosity, bulk viscosity, and heat conductivity are evaluate based on a linearized collision integral.

nucl-th↗

arXiv2014

Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems

We study a liquid film that is deposited onto a flat plate that is inclined at a constant angle to the horizontal and is extracted from a liquid bath at a constant speed. We additionally assume that there is a constant temperature gradient along the plate that induces a Marangoni shear stress. We analyse steady-state solutions of a long-wave evolution equation for the film thickness. Using centre manifold theory, we first obtain an asymptotic expansion of solutions in the bath region. The presence of the temperature gradient significantly changes these expansions and leads to the presence of logarithmic terms that are absent otherwise. Next, we obtain numerical solutions of the steady-state equation and analyse the behaviour of the solutions as the plate velocity is changed. We observe that the bifurcation curve exhibits snaking behaviour when the plate inclination angle is beyond a certain critical value. Otherwise, the bifurcation curve is monotonic. The solutions along these curves are characterised by a foot-like structure that is formed close to the meniscus and is preceded by a thin precursor film further up the plate. The length of the foot increases along the bifurcation curve. Finally, we explain that the snaking behaviour of the bifurcation curves is caused by the existence of an infinite number of heteroclinic orbits close to a heteroclinic chain that connects in an appropriate three-dimensional phase space the fixed point corresponding to the precursor film with the fixed point corresponding to the foot and then with the fixed point corresponding to the bath.

physics.flu-dyn↗

arXiv2014

Boiling of the Interface between Two Immiscible Liquids below the Bulk Boiling Temperatures of Both Components

We consider the problem of boiling of the direct contact of two immiscible liquids. An intense vapour formation at such a direct contact is possible below the bulk boiling points of both components, meaning an effective decrease of the boiling temperature of the system. Although the phenomenon is known in science and widely employed in technology, the direct contact boiling process was thoroughly studied (both experimentally and theoretically) only for the case where one of liquids is becoming heated above its bulk boiling point. On the contrary, we address the case where both liquids remain below their bulk boiling points. In this paper we construct the theoretical description of the boiling process and discuss the actualisation of the case we consider for real systems.

cond-mat.soft↗