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At least 811 records · Page 45Linked to original sources
arXiv2011

A low-Reynolds-number treadmilling swimmer near a semi-infinite wall

We investigate the behavior of a treadmilling microswimmer in a two-dimensional unbounded domain with a semi-infinite no-slip wall. The wall can also be regarded as a probe or pipette inserted into the flow. We solve the governing evolution equations in an analytical form and numerically calculate trajectories of the swimmer for several different initial positions and orientations. We then compute the probability that the treadmilling organism can escape the vicinity of the wall. We find that many trajectories in a 'wedge' around the wall are likely to escape. This suggests that inserting a probe or pipette in a suspension of organism may push away treadmilling swimmers.

physics.bio-ph↗
arXiv2012

Survey of analogue spacetimes

Analogue spacetimes, (and more boldly, analogue models both of and for gravity), have attracted significant and increasing attention over the last decade and a half. Perhaps the most straightforward physical example, which serves as a template for most of the others, is Bill Unruh's model for a dumb hole, (mute black hole, acoustic black hole), wherein sound is dragged along by a moving fluid --- and can even be trapped behind an acoustic horizon. This and related analogue models for curved spacetimes are useful in many ways: Analogue spacetimes provide general relativists with extremely concrete physical models to help focus their thinking, and conversely the techniques of curved spacetime can sometimes help improve our understanding of condensed matter and/or optical systems by providing an unexpected and countervailing viewpoint. In this introductory chapter, I shall provide a few simple examples of analogue spacetimes as general background for the rest of the contributions.

gr-qc↗
arXiv2012

Some aspects of dispersive horizons: lessons from surface waves

Hydrodynamic surface waves propagating on a moving background flow experience an effective curved space-time. We discuss experiments with gravity waves and capillary-gravity waves in which we study hydrodynamic black/white-hole horizons and the possibility of penetrating across them. Such possibility of penetration is due to the interaction with an additional "blue" horizon, which results from the inclusion of surface tension in the low-frequency gravity-wave theory. This interaction leads to a dispersive cusp beyond which both horizons completely disappear. We speculate the appearance of high-frequency "superluminal" corrections to be a universal characteristic of analogue gravity systems, and discuss their relevance for the trans-Planckian problem. We also discuss the role of Airy interference in hybridising the incoming waves with the flowing background (the effective spacetime) and blurring the position of the black/white-hole horizon.

physics.flu-dyn↗
arXiv2014

Curvature calculations for the level-set method

The present work illustrates a difficulty with the level-set method to accurately capture the curvature of interfaces in regions that are of equal distance to two or more interfaces. Such regions are characterized by kinks in the level-set function where the derivative is discontinuous. Thus the standard discretization scheme is not suitable. Three discretization schemes are outlined that are shown to perform better than the standard discretization on two selected test cases.

physics.flu-dyn↗
arXiv2017

On the surface of superfluids

Developing on a recent work on localized bubbles of ordinary relativistic fluids, we study the comparatively richer leading order surface physics of relativistic superfluids, coupled to an arbitrary stationary background metric and gauge field in $3+1$ and $2+1$ dimensions. The analysis is performed with the help of a Euclidean effective action in one lower dimension, written in terms of the superfluid Goldstone mode, the shape-field (characterizing the surface of the superfluid bubble) and the background fields. We find new terms in the ideal order constitutive relations of the superfluid surface, in both the parity-even and parity-odd sectors, with the corresponding transport coefficients entirely fixed in terms of the first order bulk transport coefficients. Some bulk transport coefficients even enter and modify the surface thermodynamics. In the process, we also evaluate the stationary first order parity-odd bulk currents in $2+1$ dimensions, which follows from four independent terms in the superfluid effective action in that sector. In the second part of the paper, we extend our analysis to stationary surfaces in $3+1$ dimensional Galilean superfluids via the null reduction of null superfluids in $4+1$ dimensions. The ideal order constitutive relations in the Galilean case also exhibit some new terms similar to their relativistic counterparts. Finally, in the relativistic context, we turn on slow but arbitrary time dependence and answer some of the key questions regarding the time-dependent dynamics of the shape-field using the second law of thermodynamics. A linearized fluctuation analysis in $2+1$ dimensions about a toy equilibrium configuration reveals some new surface modes, including parity-odd ones. Our framework can be easily applied to model more general interfaces between distinct fluid-phases.

hep-th↗
arXiv2013

Singular Casimir Elements of the Euler Equation and Equilibrium Points

The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the context of the Euler equation for an incompressible inviscid fluid. The problem is traced to a Casimir deficit, where Casimir elements constitute the center of the Lie-Poisson algebra underlying the Hamiltonian formulation, and this leads to a study of the symplectic operator defining the Poisson bracket. The kernel of the symplectic operator, for this typical example of an infinite-dimensional Hamiltonian system for media in terms of Eulerian variables, is analyzed. For two-dimensional flows, a rigorously solvable system is formulated. The nonlinearity of the Euler equation makes the symplectic operator inhomogeneous on phase space (the function space of the state variable), and it is seen that this creates a singularity where the nullity of the symplectic operator (the "dimension" of the center) changes. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket.

math-ph↗
arXiv2017

A Floating Cylinder on An Unbounded Bath

In this paper, we reconsider a circular cylinder horizontally floating on an unbounded reservoir in a gravitational field directed downwards, which was studied by Bhatnargar and Finn in 2006. We follow their approach but with some modifications. We establish the relation between the total energy relative to the undisturbed state and the total force. There is a monotone relation between the height of the centre and the wetting angle. We study the number of equilibria, the floating configurations and their stability for all parameter values. We find that the system admits at most two equilibrium points for arbitrary contact angle, the one with smaller wetting angle is stable and the one with larger wetting angle is unstable. The initial model has a limitation that the fluid interfaces may intersect. We show that the stable equilibrium point never lies in the intersection region, while the unstable equilibrium point may lie in the intersection region.

math.CA↗
arXiv2018

Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics

Reformulating constitutive relation in terms of gradient dynamics (being derivative of a dissipation potential) brings additional information on stability, metastability and instability of the dynamics with respect to perturbations of the constitutive relation, called CR-stability. CR-instability is connected to the loss of convexity of the dissipation potential, which makes the Legendre-conjugate dissipation potential multivalued and causes dissipative phase transitions, that are not induced by non-convexity of free energy, but by non-convexity of the dissipation potential. CR-stability of the constitutive relation with respect to perturbations is then manifested by constructing evolution equations for the perturbations in a thermodynamically sound way. As a result, interesting experimental observations of behavior of complex fluids under shear flow and supercritical boiling curve can be explained.

physics.flu-dyn↗
arXiv2012

Cloud microphysical effects of turbulent mixing and entrainment

Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence time scales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.

physics.flu-dyn↗
arXiv2013

Hamiltonian dynamics of several rigid bodies interacting with point vortices

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the Hamiltonian formulation via symplectic reduction from a canonical Hamiltonian system. The reduced system is described by a non-canonical symplectic form, which has previously been derived for a single, circular disk using heavy differential-geometric machinery in an infinite-dimensional setting. In contrast, our derivation makes use of the fact that the dynamics of the fluid, and thus the point vortex dynamics, is determined from first principles. Using this knowledge we can directly determine the dynamics on the reduced, finite-dimensional phase space, using only classical mechanics. Furthermore, our approach easily handles several bodies of arbitrary shapes. From the Hamiltonian description we derive a Lagrangian formulation, which enables the system for variational time integrators. We briefly describe how to implement such a numerical scheme and simulate different configurations for validation.

physics.flu-dyn↗
arXiv2013

Shock waves in dispersive Eulerian fluids

The long time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (convex or concave) and a general pressure law. Two mechanisms leading to the breakdown of this simple wave DSW theory for sufficiently large jumps are identified: a change in the sign of dispersion, leading to gradient catastrophe in the modulation equations, and the loss of genuine nonlinearity in the modulation equations. Large amplitude DSWs are constructed for several particular dispersive fluids with differing pressure laws modeled by the generalized nonlinear Schrodinger equation. These include superfluids (Bose-Einstein condensates and ultracold Fermions) and "optical fluids". Estimates of breaking times for smooth initial data and the long time behavior of the shock tube problem are presented. Numerical simulations compare favorably with the asymptotic results in the weak to moderate amplitude regimes. Deviations in the large amplitude regime are identified with breakdown of the simple wave DSW theory.

nlin.PS↗
arXiv2014

On a regularized family of models for homogeneous incompressible two-phase flows

We consider a general family of regularized models for incompressible two-phase flows based on the Allen-Cahn formulation in n-dimensional compact Riemannian manifolds for n=2,3. The system we consider consists of a regularized family of Navier-Stokes equations (including the Navier-Stokes-α-like model, the Leray-α model, the Modified Leray-α model, the Simplified Bardina model, the Navier-Stokes-Voight model and the Navier-Stokes model) for the fluid velocity suitably coupled with a convective Allen-Cahn equation for the (phase) order parameter. We give a unified analysis of the entire three-parameter family of two-phase models using only abstract mapping properties of the principal dissipation and smoothing operators, and then use assumptions about the specific form of the parametrizations, leading to specific models, only when necessary to obtain the sharpest results. We establish existence, stability and regularity results, and some results for singular perturbations, which as special cases include the inviscid limit of viscous models and the α->0 limit in α-models. Then, we also show the existence of a global attractor and exponential attractor for our general model, and then establish precise conditions under which each trajectory converges to a single equilibrium by means of a LS inequality. We also derive new results on the existence of global and exponential attractors for the regularized family of Navier-Stokes equations and magnetohydrodynamics models which improve and complement the results of Holst et. al. [J. Nonlinear Science 20, 2010, 523-567]. Finally, our analysis is applied to certain regularized Ericksen-Leslie (RSEL) models for the hydrodynamics of liquid crystals in n-dimensional compact Riemannian manifolds.

math.AP↗
arXiv2021

On the motion of gravity-capillary waves with odd viscosity

We develop three asymptotic models of surface waves in a non-newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applications such as quantum Hall fluids or chiral active fluids. Besides the odd viscosity effects, these models capture both gravity and capillary forces up to quadratic interactions and take the form of nonlinear and nonlocal wave equations. Two of these models describe bidirectional waves while the third PDE studies the case of unidirectional propagation. We also prove the well-posedness of these asymptotic models in spaces of analytic functions and in Sobolev spaces. Finally, we present a number of numerical simulations for the unidirectional model.

math.AP↗
arXiv2013

Velocity measurements in the liquid metal flow driven by a two-phase inductor

We present the results of velocity measurements obtained by ultrasonic Doppler velocimetry and local potential probes in the flow of GaInSn eutectic melt driven by a two-phase inductor in a cylindrical container. This type of flow is expected in a recent modification to the floating zone technique for the growth of small-diameter single intermetallic compound crystals. We show that the flow structure can be changed from the typical two toroidal vortices to a single vortex by increasing the phase shift between the currents in the two coils from 0 to 90 degrees. The latter configuration is thought to be favourable for the growth of single crystals. The flow is also computed numerically and a reasonable agreement with the experimental results is found. The obtained results may be useful for the design of combined two-phase electromagnetic stirrers and induction heaters for metal or semiconductor melts.

physics.flu-dyn↗
arXiv2014

Toward compressed DMD: spectral analysis of fluid flows using sub-Nyquist-rate PIV data

Dynamic mode decomposition (DMD) is a powerful and increasingly popular tool for performing spectral analysis of fluid flows. However, it requires data that satisfy the Nyquist-Shannon sampling criterion. In many fluid flow experiments, such data are impossible to capture. We propose a new approach that combines ideas from DMD and compressed sensing. Given a vector-valued signal, we take measurements randomly in time (at a sub-Nyquist rate) and project the data onto a low-dimensional subspace. We then use compressed sensing to identify the dominant frequencies in the signal and their corresponding modes. We demonstrate this method using two examples, analyzing both an artificially constructed test dataset and particle image velocimetry data collected from the flow past a cylinder. In each case, our method correctly identifies the characteristic frequencies and oscillatory modes dominating the signal, proving the proposed method to be a capable tool for spectral analysis using sub-Nyquist-rate sampling.

physics.flu-dyn↗
arXiv2013

Aperiodic tumbling of microrods advected in a microchannel flow

We report on an experimental investigation of the tumbling of microrods in the shear flow of a microchannel (40 x 2.5 x 0.4 mm). The rods are 20 to 30 microns long and their diameters are of the order of 1 micron. Images of the centre-of-mass motion and the orientational dynamics of the rods are recorded using a microscope equipped with a CCD camera. A motorised microscope stage is used to track individual rods as they move along the channel. Automated image analysis determines the position and orientation of a tracked rods in each video frame. We find different behaviours, depending on the particle shape, its initial position, and orientation. First, we observe periodic as well as aperiodic tumbling. Second, the data show that different tumbling trajectories exhibit different sensitivities to external perturbations. These observations can be explained by slight asymmetries of the rods. Third we observe that after some time, initially periodic trajectories lose their phase. We attribute this to drift of the centre of mass of the rod from one to another stream line of the channel flow.

physics.flu-dyn↗
arXiv2014

Liquid soap film generates electricity

We have observed that a rotating liquid soap film generates electricity when placed between two non-contact electrodes with a sufficiently large potential difference. In our experiments suspended liquid film (water + soap film) is formed on the surface of a circular frame, which is forced to rotate in the $x-y$ horizontal plane by a motor. This system is located at the center of two capacitor-like vertical plates to apply an external electric voltage difference in the $x-$direction. The produced electric current is collected from the liquid film using two conducting electrodes that are separated in the $y-$direction. We previously reported that a liquid film in an external electric field rotates when an electric current passes through it, naming it the liquid film motor (LFM). In this paper we report a novel technique, in which a similar device can be used as an electric generator, converting the rotating mechanical energy to electrical energy. The liquid film electric generator (LFEG) is in stark contrast to the LFM, both of which could be designed similarly in very small scales like micro scales with different applications. Although the device is comparable to commercial electric motors or electric generators, there is a significant difference in their working principles. Usually in an electric motor or generator the magnetic field causes the driving force, while in a LFM or LFEG the Coulomb force is the driving force. This fact is also interesting from the Bio-science point of view and brings a similarity to bio motors. Here we have investigated the electrical characteristics of such a generator for the first time experimentally and modelled the phenomenon with electroconvection governing equations. A numerical simulation is performed using the local approximation for the charge-potential relation and results are in qualitative agreement with experiments.

cond-mat.soft↗