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arXiv2013

Nucleation stage in supersaturated vapor with inhomogeneities due to nonstationary diffusion onto growing droplets

An analytical description of nucleation stage in a supersaturated vapor with instantly created supersaturation is given with taking into account the vapor concentration inhomogeneities arising as a result of depletion due to non-stationary diffusion onto growing droplets. This description suggests that the intensity of the nucleation of new droplets is suppressed in spherical diffusion regions of a certain size surrounding previously nucleated droplets, and remains at the initial level in the remaining volume of the vapor-gas medium. The value of volume excluded from nucleation depends on the explicit form of the vapor concentration profile in the space around the growing droplet, and we use for that the unsteady self-similar solution of time-dependent diffusion equation with a convective term describing the flow of the gas-vapor mixture caused by moving surface of single growing droplet. The main characteristics of the phase transition at the end of the nucleation stage are found and compared with those in the theory of nucleation with homogeneous vapor consumption (the theory of mean-field vapor supersaturation).

physics.chem-ph↗

arXiv2013

Guided self-assembly of magnetic beads for biomedical applications

Micromagnetic beads are widely used in biomedical applications for cell separation, drug delivery, and hypothermia cancer treatment. Here we propose to use self-organized magnetic bead structures which accumulate on fixed magnetic seeding points to isolate circulating tumor cells. The analysis of circulating tumor cells is an emerging tool for cancer biology research and clinical cancer management including the detection, diagnosis and monitoring of cancer. Microfluidic chips for isolating circulating tumor cells use either affinity, size or density capturing methods. We combine multiphysics simulation techniques to understand the microscopic behavior of magnetic beads interacting with Nickel accumulation points used in lab-on-chip technologies. Our proposed chip technology offers the possibility to combine affinity and size capturing with special antibody-coated bead arrangements using a magnetic gradient field created by Neodymium Iron Boron permanent magnets. The multiscale simulation environment combines magnetic field computation, fluid dynamics and discrete particle dynamics.

physics.bio-ph↗

arXiv2013

On the coupling between an ideal fluid and immersed particles

In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity interpolation from particle velocities for their principal connection. The consequence of writing evolution equations in terms of interpolation is two-fold. First, it gives estimates on the error incurred when interpolation is used to derive the evolution of the system. Second, this form of the equations of motion can inspire a family of particle and hybrid particle-spectral methods where the error analysis is "built-in". We also discuss the influence of other parameters attached to the particles, such as shape, orientation, or higher-order deformations, and how they can help with conservation of momenta in the sense of Kelvin's circulation theorem.

math.DS↗

arXiv2013

Orientational dynamics of weakly inertial axisymmetric particles in steady viscous flows

The orientational dynamics of weakly inertial axisymmetric particles in a steady flow is investigated. We derive an asymptotic equation of motion for the unit axial vector along the particle symmetry axis, valid for small Stokes number St, and for any axisymmetric particle in any steady linear viscous flow. This reduced dynamics is analysed in two ways, both pertain to the case of a simple shear flow. In this case inertia induces a coupling between precession and nutation. This coupling affects the dynamics of the particle, breaks the degeneracy of the Jeffery orbits, and creates two limiting periodic orbits. We calculate the leading-order Floquet exponents of the limiting periodic orbits and show analytically that prolate objects tend to a tumbling orbit, while oblate objects tend to a log-rolling orbit, in agreement with previous analytical and numerical results. Second, we analyse the role of the limiting orbits when rotational noise is present. We formulate the Fokker-Planck equation describing the orientational distribution of an axisymmetric particle, valid for small St and general Peclet number Pe. Numerical solutions of the Fokker-Planck equation, obtained by means of expansion in spherical harmonics, show that stationary orientational distributions are close to the inertia-free case when Pe St << 1, whereas they are determined by inertial effects, though small, when Pe >> 1/St >> 1.

physics.flu-dyn↗

arXiv2021

Generation of stripe-like vortex flow by noncollinear waves on the water surface

We have studied experimentally the generation of vortex flow by gravity waves with a frequency of 2.34 Hz excited on the water surface at an angle $2 θ= arctan(3/4) \approx 36°$ to each other. The resulting horizontal surface flow has a stripe-like spatial structure. The width of the stripes L = $π$/(2ksin$θ$) is determined by the wave vector k of the surface waves and the angle between them, and the length of the stripes is limited by the system size. It was found that the vertical vorticity $Ω$ of the current on the fluid surface is proportional to the product of wave amplitudes, but its value is much higher than the value corresponding to the Stokes drift and it continues to grow with time even after the wave motion reaches a stationary regime. We demonstrate that the measured dependence $Ω$(t) can be described within the recently developed model that takes into account the Eulerian contribution to the generated vortex flow and the effect of surface contamination. This model contains a free parameter that describes the elastic properties of the contaminated surface, and we also show that the found value of this parameter is in reasonable agreement with the measured decay rate of surface waves.

physics.flu-dyn↗

arXiv2017

Numerical study of wet plastic particle separation using a coupled DEM-SPH method

The separation of different kind of plastic particles is required in the process of waste recycling. For the separation drum processes passed through by a liquid are applicable. Thereby the separation is based on the principle that particles either sink or float in a liquid depending on their densities. In this study the aforementioned process is numerically analysed for the separation of polyethylene terephthalate (PET) from polypropylene (PP) particles. The Discrete Element Method coupled with the Smoothed Particle Hydrodynamics method (DEM-SPH) is used for modelling purposes. The employment of the SPH for the modelling of the liquid let us exploit the strong side of this mesh-less method, namely, the relative easiness to model large movements of the fluid together with free surfaces and moving boundaries. The used theoretical model is presented and validation tests are performed, where a dam-break problem is considered as an example. Simulations of the plastic particle separation in the rotating drum are performed thereafter. The influence of the different operational and design parameters, such as the rotational velocity, the feed rate, the number of lifters etc., on the resultant purity of the plastic is estimated. It is expected that in the future the performed analysis will allow to optimise drum separation processes.

physics.flu-dyn↗

arXiv2018

Effect of wall thermal inertia upon transient thermoacoustic dynamics of a swirl-stabilized flame

This paper shows the importance of considering the thermal state of a combustor to investigate or predict its thermoacoustic stability. This aspect is often neglected or regarded as less important than the effect of the operating parameters, such as thermal power or equivalence ratio, but under certain circumstances it can have a dramatic influence on the development of the instabilities. The paper presents experimental results collected from a combustor featuring a lean swirl-stabilized flame exhibiting thermoacoustic instability at some operating conditions. It is shown that this instability is caused by a change of the flame topology that is induced by the progressive increase of the wall temperature with the thermal power. This dependence of the instability on wall temperature leads to inertial effects and hysteresis when the operating condition is changed dynamically. A low-order model of the system reproducing this remarkable dynamics is proposed and validated against the experimental data.

physics.flu-dyn↗

arXiv2014

A concurrent precursor inflow method for Large Eddy Simulations and applications to finite length wind farms

In order to enable simulations of developing wind turbine array boundary layers with highly realistic inflow conditions a concurrent precursor method for Large Eddy Simulations is proposed. In this method we consider two domains simultaneously, i.e. in one domain a turbulent Atmospheric Boundary Layer (ABL) without wind turbines is simulated in order to generate the turbulent inflow conditions for a second domain in which the wind turbines are placed. The benefit of this approach is that a) it avoids the need for large databases in which the turbulent inflow conditions are stored and the correspondingly slow I/O operations and b) we are sure that the simulations are not negatively affected by statically swept fixed inflow fields or synthetic fields lacking the proper ABL coherent structures. Sample applications are presented, in which, in agreement with field data a strong decrease of the power output of downstream wind-turbines with respect to the first row of wind-turbines is observed for perfectly aligned inflow.

physics.flu-dyn↗

arXiv2014

Temporal behavior of laser induced elastic plate resonances

This paper investigates the dependence on Poisson's ratio of local plate resonances in low attenuating materials. In our experiments, these resonances are generated by a pulse laser source and detected with a heterodyne interferometer measuring surface displacement normal to the plate. The laser impact induces a set of resonances that are dominated by Zero Group Velocity (ZGV) Lamb modes. For some Poisson's ratio, thickness-shear resonances are also detected. These experiments confirm that the temporal decay of ZGV modes follows a $t^{-0.5}$ law and show that the temporal decay of the thickness resonances is much faster. Similar decays are obtained by numerical simulations achieved with a finite difference code. A simple model is proposed to describe the thickness resonances. It predicts that a thickness mode decays as $t^{-1.5}$ for large times and that the resonance amplitude is proportional to $D^{-1.5}$ where $D$ is the curvature of the dispersion curve $ω(k)$ at $k=0$. This curvature depends on the order of the mode and on the Poisson's ratio, and it explains why some thickness resonances are well detected while others are not.

physics.class-ph↗

arXiv2012

The Universal Aspect Ratio of Vortices in Rotating Stratifi?ed Flows: Experiments and Observations

We validate a new law for the aspect ratio $α= H/L$ of vortices in a rotating, stratified flow, where $H$ and $L$ are the vertical half-height and horizontal length scale of the vortices. The aspect ratio depends not only on the Coriolis parameter f and buoyancy (or Brunt-Vaisala) frequency $\bar{N}$ of the background flow, but also on the buoyancy frequency $N_c$ within the vortex and on the Rossby number $Ro$ of the vortex such that $α= f \sqrt{[Ro (1 + Ro)/(N_c^2- \bar{N}^2)]}$. This law for $α$ is obeyed precisely by the exact equilibrium solution of the inviscid Boussinesq equations that we show to be a useful model of our laboratory vortices. The law is valid for both cyclones and anticyclones. Our anticyclones are generated by injecting fluid into a rotating tank filled with linearly-stratified salt water. The vortices are far from the top and bottom boundaries of the tank, so there is no Ekman circulation. In one set of experiments, the vortices viscously decay, but as they do, they continue to obey our law for $α$, which decreases over time. In a second set of experiments, the vortices are sustained by a slow continuous injection after they form, so they evolve more slowly and have larger |Ro|, but they also obey our law for $α$. The law for $α$ is not only validated by our experiments, but is also shown to be consistent with observations of the aspect ratios of Atlantic meddies and Jupiter's Great Red Spot and Oval BA. The relationship for $α$ is derived and examined numerically in a companion paper by Hassanzadeh et al. (2012).

physics.flu-dyn↗

arXiv2012

Longitudinal and transversal flow over a cavity containing a second immiscible fluid

An analytical solution for the flow field of a shear flow over a rectangular cavity containing a second immiscible fluid is derived. While flow of a single-phase fluid over a cavity is a standard case investigated in fluid dynamics, flow over a cavity which is filled with a second immiscible fluid, has received little attention. The flow filed inside the cavity is considered to define a boundary condition for the outer flow which takes the form of a Navier slip condition with locally varying slip length. The slip-length function is determined from the related problem of lid-driven cavity flow. Based on the Stokes equations and complex analysis it is then possible to derive a closed analytical expression for the flow field over the cavity for both the transversal and the longitudinal case. The result is a comparatively simple function, which displays the dependence of the flow field on the cavity geometry and the medium filling the cavity. The analytically computed flow field agrees well with results obtained from a numerical solution of the Navier-Stokes equations. The studies presented in this article are of considerable practical relevance, for example for the flow over superhydrophobic surfaces.

physics.flu-dyn↗

arXiv2012

Libration-induced mean flow in a spherical shell

We investigate the flow in a spherical shell subject to a time harmonic oscillation of its rotation rate, also called longitudinal libration, when the oscillation frequency is larger than twice the mean rotation rate. In this frequency regime, no inertial waves are directly excited by harmonic forcing. We show however that it can generate through non-linear interactions in the Ekman layers a strong mean zonal flow in the interior. An analytical theory is developed using a perturbative approach in the limit of small libration amplitude $ε$ and small Ekman number $E$. The mean flow is found to be at leading order an azimuthal flow which scales as the square of the libration amplitude and only depends on the cylindrical-radius coordinate. The mean flow also exhibits a discontinuity across the cylinder tangent to the inner sphere. We show that this discontinuity can be smoothed through multi-scale Stewartson layers. The mean flow is also found to possess a weak axial flow which scales as $O(ε^2 E^{5/42})$ in the Stewartson layers. The analytical solution is compared to axisymmetric numerical simulations and a good agreement is demonstrated.

physics.flu-dyn↗

arXiv2013

Low-Reynolds number swimming in a capillary tube

We use the boundary element method to study the low-Reynolds number locomotion of a spherical model microorganism in a circular tube. The swimmer propels itself by tangen- tial or normal surface motion in a tube whose radius is on the order of the swimmer size. Hydrodynamic interactions with the tube walls significantly affect the average swimming speed and power consumption of the model microorganism. In the case of swimming parallel to the tube axis, the locomotion speed is always reduced (resp. increased) for swimmers with tangential (resp. normal) deformation. In all cases, the rate of work nec- essary for swimming is increased by confinement. Swimmers with no force-dipoles in the far field generally follow helical trajectories, solely induced by hydrodynamic interactions with the tube walls, and in qualitative agreement with recent experimental observations for Paramecium. Swimmers of the puller type always display stable locomotion at a lo- cation which depends on the strength of their force dipoles: swimmers with weak dipoles (small α) swim in the centre of the tube while those with strong dipoles (large α) swim near the walls. In contrast, pusher swimmers and those employing normal deformation are unstable and end up crashing into the walls of the tube. Similar dynamics is observed for swimming into a curved tube. These results could be relevant for the future design of artificial microswimmers in confined geometries.

physics.flu-dyn↗

arXiv2013

On coherent structure in wall turbulence

A new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier-Stokes equations, under an assumption of a turbulent mean profile. The assumption of the turbulent mean acts as a restriction on the class of possible structures. It is shown that the coherent structure is a manifestation of essentially low-dimensional flow dynamics, arising from a critical layer mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech, 658, 2010), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially-varying travelling waves. By way of example, simple combinations of these modes are offered that predicts hairpins and modulated hairpin packets. The phase interaction also predicts important skewness and correlation results known in the literature. It is also shown that the very large scale motions act to organise hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally varying the shear profile. The relationship between Taylor's hypothesis and coherence is discussed and both are shown to be the consequence of the localisation of the response modes around the critical layer. A pleasing link is made to the classical laminar inviscid theory, whereby the essential mechanism underlying the hairpin vortex is captured by two obliquely interacting Kelvin-Stuart (cat's eye) vortices. Evidence for the theory is presented based on comparison to observations of structure reported in the experimental, transitional flow and turbulent flow numerical simulation literature.

physics.flu-dyn↗

arXiv2013

Modelling spreading dynamics of liquid crystals in three spatial dimensions

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.

physics.flu-dyn↗

arXiv2014

Meridional trapping and zonal propagation of inertial waves in a rotating fluid shell

Inertial waves propagate in homogeneous rotating fluids, and constitute a challenging and simplified case study for the broader class of inertio-gravity waves, present in all geophysical and astrophysical media, and responsible for energetically costly processes as diapycnal and angular momentum mixing. However, a complete analytical description and understanding of internal waves in arbitrarily shaped enclosed domains, such as the ocean, or a planet liquid core, is still missing. In this work, the inviscid, linear inertial wave field is investigated by means of three dimensional ray tracing in spherical shell domains, having in mind possible oceanographic applications. Rays are here classically interpreted as representative of energy paths. But in contrast with previous studies, they are now launched with a non-zero initial zonal component allowing for a more realistic, localized forcing, and the development of azimuthal inhomogeneities. We find that meridional planes generally act in the shell geometry as attractors for ray trajectories. In addition, the existence of trajectories that are not subject to meridional trapping is here observed for the first time. Their dynamics was not captured by the previous purely meridional studies and unveils a new class of possible solutions for inertial motion in the spherical shell. Both observed behaviours shed some new light on possible mechanisms of energy localization, a key process that still deserves further investigation in our ocean, as well as in other stratified, rotating media.

physics.flu-dyn↗

arXiv2013

Spontaneous generation of inertial waves from boundary turbulence in a librating sphere

In this work, we report the excitation of inertial waves in a librating sphere even for libration frequencies where these waves are not directly forced. This spontaneous generation comes from the localized turbulence induced by the centrifugal instabilities in the Ekman boundary layer near the equator and does not depend on the libration frequency. We characterize the key features of these inertial waves in analogy with previous studies of the generation of internal waves in stratified flows from localized turbulent patterns. In particular, the temporal spectrum exhibits preferred values of excited frequency. This first-order phenomenon is generic to any rotating flow in the presence of localized turbulence and is fully relevant for planetary applications.

physics.flu-dyn↗

arXiv2013

Energy cascade and scaling in supersonic isothermal turbulence

Supersonic turbulence plays an important role in a number of extreme astrophysical and terrestrial environments, yet its understanding remains rudimentary. We use data from a three-dimensional simulation of supersonic isothermal turbulence to reconstruct an exact fourth-order relation derived analytically from the Navier-Stokes equations (Galtier and Banerjee, Phys. Rev. Lett., vol. 107, 2011, p. 134501). Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogues of the four-fifths law exist describing fifth- and fourth-order correlations, but only the fourth-order relation remains `universal' in a wide range of Mach numbers from incompressible to highly compressible regimes. A new approximate relation valid in the strongly supersonic regime is derived and verified. We also briefly discuss the origin of bottleneck bumps in simulations of compressible turbulence.

astro-ph.GA↗