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arXiv2011

Debye-Hueckel solution for steady electro-osmotic flow of a micropolar fluid in a cylindrical microcapillary

Analytic expressions for the speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting steady, symmetric and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Hueckel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. As the aciculate particles in a micropolar fluid can rotate without translation, micropolarity influences fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies as the radius increases. The stress tensor is confined to the region near the wall of the microcapillary but the couple stress tensor is uniform across the cross-section.

physics.flu-dyn↗
arXiv2014

Fundamental solutions for micropolar fluids

New fundamental solutions for micropolar fluids are derived in explicit form for two- and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple, including the two-dimensional micropolar Stokeslet, the two- and three-dimensional micropolar Stokes couplet, the three-dimensional micropolar Oseenlet, and the three-dimensional micropolar Oseen couplet. These fundamental solutions do not exist in Newtonian flow due to the absence of microrotation velocity field. The flow due to these singularities is useful for understanding and studying microscale flows. As an application, the drag coefficients for a solid sphere or a circular cylinder that translates in a low-Reynolds-number micropolar flow are determined and compared with those corresponding to Newtonian flow. The drag coefficients in a micropolar fluid are greater than those in a Newtonian fluid.

physics.flu-dyn↗
arXiv2014

Fokker-Planck Theory of Nonequilibrium Systems Governed by Hierarchical Dynamics

Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is studied as an analytically tractable example, and a kinetic theory is formulated for describing the states of the particle. What is peculiar here is that the (inverse) temperature is treated as a dynamical variable. Dynamical hierarchy is introduced in conformity with the adiabatic scheme. Then, a new analytical method is developed to show how the Fokker-Planck equation admits as a stationary solution the Maxwellian distribution modulated by the temperature fluctuations, the distribution of which turns out to be determined by the drift term. A careful comment is also made on so-called superstatistics.

cond-mat.stat-mech↗
arXiv2018

Are Hidden-Variable Theories for Pilot-Wave Systems Possible ?

Recently it was shown that certain fluid-mechanical 'pilot-wave' systems can strikingly mimic a range of quantum properties, including single particle diffraction and interference, quantization of angular momentum etc. How far does this analogy go? The ultimate test of (apparent) quantumness of such systems is a Bell-test. Here the premises of the Bell inequality are re-investigated for particles accompanied by a pilot-wave, or more generally by a resonant 'background' field. We find that two of these premises, namely outcome independence and measurement independence, may not be generally valid when such a background is present. Under this assumption the Bell inequality is possibly (but not necessarily) violated. A class of hydrodynamic Bell experiments is proposed that could test this claim. Such a Bell test on fluid systems could provide a wealth of new insights on the different loopholes for Bell's theorem. Finally, it is shown that certain properties of background-based theories can be illustrated in Ising spin-lattices.

quant-ph↗
arXiv2012

Microfluidic and Nanofluidic Cavities for Quantum Fluids Experiments

The union of quantum fluids research with nanoscience is rich with opportunities for new physics. The relevant length scales in quantum fluids, 3He in particular, are comparable to those possible using microfluidic and nanofluidic devices. In this article, we will briefly review how the physics of quantum fluids depends strongly on confinement on the microscale and nanoscale. Then we present devices fabricated specifically for quantum fluids research, with cavity sizes ranging from 30 nm to 11 microns deep, and the characterization of these devices for low temperature quantum fluids experiments.

cond-mat.mes-hall↗
arXiv2013

A Method for Driving an Oscillator at a Quasi-Uniform Velocity

We describe a simple way to drive an actuator, comprising a superconducting coil moving in a static magnetic field, at a quasi-uniform velocity. The main objective is to avoid oscillations in this system with low damping, as they undermine the uniformity of the velocity. The method consists in calculating the force that should be exerted on the coil from the equation of motion and programming a waveform generator to produce the corresponding current through the coil. The method was tested on a device towing a grid through a closely fitted channel filled with superfluid 4He at temperatures below 100 mK. The motion of the grid over the distance of 4.3 cm at 10 cm/s resulted in oscillations of less than 50 μm in amplitude (or less than 1 mm/s in terms of velocity). The method can be applied to any oscillator.

physics.flu-dyn↗
arXiv2013

Additional Invariants and Statistical Equilibria for the 2D Euler Equations on a spherical domain

The role of the domain geometry for the statistical mechanics of 2D Euler flows is investigated. It is shown that for a spherical domain, there exists invariant subspaces in phase space which yield additional angular momentum, energy and enstrophy invariants. The microcanonical measure taking into account these invariants is built and a mean-field, Robert-Sommeria-Miller theory is developed in the simple case of the energy-enstrophy measure. The variational problem is solved analytically and a partial energy condensation is obtained. The thermodynamic properties of the system are also discussed.

cond-mat.stat-mech↗
arXiv2013

Lyapunov exponents for particles advected in compressible random velocity fields at small and large Kubo numbers

We calculate the Lyapunov exponents describing spatial clustering of particles advected in one- and two-dimensional random velocity fields at finite Kubo numbers Ku (a dimensionless parameter characterising the correlation time of the velocity field). In one dimension we obtain accurate results up to Ku ~ 1 by resummation of a perturbation expansion in Ku. At large Kubo numbers we compute the Lyapunov exponent by taking into account the fact that the particles follow the minima of the potential function corresponding to the velocity field. The Lyapunov exponent is always negative. In two spatial dimensions the sign of the maximal Lyapunov exponent λ_1 may change, depending upon the degree of compressibility of the flow and the Kubo number. For small Kubo numbers we compute the first four non-vanishing terms in the small-Ku expansion of the Lyapunov exponents. By resumming these expansions we obtain a precise estimate of the location of the path-coalescence transition (where λ_1 changes sign) for Kubo numbers up to approximately Ku = 0.5. For large Kubo numbers we estimate the Lyapunov exponents for a partially compressible velocity field by assuming that the particles sample those stagnation points of the velocity field that have a negative real part of the maximal eigenvalue of the matrix of flow-velocity gradients.

physics.flu-dyn↗
arXiv2012

Vortex-density fluctuations, energy spectra and vortical regions in superfluid turbulence

Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.

cond-mat.other↗
arXiv2018

Effects of atrial fibrillation on the arterial fluid dynamics: a modelling perspective

Atrial fibrillation (AF) is the most common form of arrhythmia with accelerated and irregular heart rate (HR), leading to both heart failure and stroke and being responsible for an increase in cardiovascular morbidity and mortality. In spite of its importance, the direct effects of AF on the arterial hemodynamic patterns are not completely known to date. Based on a multiscale modelling approach, the proposed work investigates the effects of AF on the local arterial fluid dynamics. AF and normal sinus rhythm (NSR) conditions are simulated extracting 2000 $\mathrm{RR}$ heartbeats and comparing the most relevant cardiac and vascular parameters at the same HR (75 bpm). Present outcomes evidence that the arterial system is not able to completely absorb the AF-induced variability, which can be even amplified towards the peripheral circulation. AF is also able to locally alter the wave dynamics, by modifying the interplay between forward and backward signals. The sole heart rhythm variation (i.e., from NSR to AF) promotes an alteration of the regular dynamics at the arterial level which, in terms of pressure and peripheral perfusion, suggests a modification of the physiological phenomena ruled by periodicity (e.g., regular organ perfusion)and a possible vascular dysfunction due to the prolonged exposure to irregular and extreme values. The present study represents a first modeling approach to characterize the variability of arterial hemodynamics in presence of AF, which surely deserves further clinical investigation.

physics.flu-dyn↗
arXiv2013

Recent progress and challenges in exploiting graphics processors in computational fluid dynamics

The progress made in accelerating simulations of fluid flow using GPUs, and the challenges that remain, are surveyed. The review first provides an introduction to GPU computing and programming, and discusses various considerations for improved performance. Case studies comparing the performance of CPU- and GPU- based solvers for the Laplace and incompressible Navier-Stokes equations are performed in order to demonstrate the potential improvement even with simple codes. Recent efforts to accelerate CFD simulations using GPUs are reviewed for laminar, turbulent, and reactive flow solvers. Also, GPU implementations of the lattice Boltzmann method are reviewed. Finally, recommendations for implementing CFD codes on GPUs are given and remaining challenges are discussed, such as the need to develop new strategies and redesign algorithms to enable GPU acceleration.

physics.flu-dyn↗
arXiv2017

Numerical Study of Suspension Plasma Spraying

A numerical study of suspension plasma spraying (SPS) is presented in the current work. The liquid suspension jet is replaced with a train of droplets containing the suspension particles injected into the plasma flow. Atomization, evaporation, and melting of different components are considered for droplets and particles as they travel towards the substrate. Effect of different parameters on particle conditions during flight and upon impact on the substrate are investigated. Initially, influence of the torch operating conditions such as inlet flow rate and power are studied. Additionally, effect of injector parameters like injection location, flow rate, and angle are examined. The model used in current study takes high temperature gradients and non-continuum effects into account. Moreover, the important effect of change in physical properties of suspension droplets as a result of evaporation is included in the model. These mainly include variations in heat transfer properties and viscosity. Utilizing this improved model, several test cases have been considered to better evaluate the effect of different parameters on the quality of particles during flight and upon impact on the substrate.

physics.flu-dyn↗
arXiv2018

Relevance of analytical Buckley-Leverett solution for immiscible oil displacement by various gases

In order to generate the valid numerical simulation model, the sufficient amount of gathered data from the oil field is required. However, it is not always possible to acquire such data at the initial stage of project development. Buckley and Leverett (1942) developed the analytical solution allowing to assess the oil displacement efficiency. One of the main assumptions of this model is incompressibility of oil and injected fluid. For slightly compressible water and oil such assumption is rational. However, that is not always the case when the gas is injected. This research aims to identify the conditions at which the usage of the incompressible gas model is appropriate. Likewise, the cases when the model of compressible gas is required are also evaluated. To accomplish the goals of this research, the comparative analysis between the injection of compressible and incompressible gases was undertaken using the numerical solution of the correspondent reservoir engineering problem. The validation of the numerical model was undertaken showing that it matches the analytical Buckley-Leverett solution. The findings of this research indicate that the relative and absolute density change with the pressure of the injected gas has the profound impact on the convergence between two models under consideration. With the increase in the injection pressure, the discrepancy between the models of compressible and incompressible gas raises for all the considered injection fluids (CO2, CH4 and N2). Due to a steep slope of 'density-pressure' curve for CO2 at low initial reservoir pressure, the incompressible model cannot accurately predict the oil displacement efficiency by this gas at any reasonable injection pressure. All 1D results are also representative for 2D simulation. However, the mismatch between two models increases considerably for 2D simulation scenarios.

physics.flu-dyn↗
arXiv2014

Heat transfer in the flow of a cold, two-dimensional vertical liquid jet against a hot, horizontal plate

A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which exploits the hydrodynamic similarity solution for thin film flow. The approximate solution may provide a valuable basis for assessing flow and heat transfer in more complex settings.

physics.flu-dyn↗
arXiv2024

Interaction between corner and bulk flows during drainage in granular porous media

Drainage in porous media can be broken down into two main mechanisms: a primary piston-like displacement of the interfaces through the bulk of pore bodies and throats, and a secondary slow flow through corners and films in the wake of the invasion front. In granular porous media, this secondary drainage mechanism unfolds in connected pathways of pendular structures, such as capillary bridges and liquid rings, formed between liquid clusters. To represent both mechanisms, we proposed a dynamic dual-network model for drainage, considering that a gas displaces a wetting liquid from quasi-2D granular porous media. For this model, dedicated analyses of the capillary bridge shapes and hydraulic conductivity were conducted so that the secondary drainage mechanism could be properly quantified at finite speeds. With the model, an investigation of the wetting-phase connectivity and flow during drainage was carried out, covering a broad range of flow conditions. Results indicate that the span of liquid-connected structures in the unsaturated region, as well as their ability to contribute to flow, varies significantly with Capillary and Bond numbers.

cond-mat.soft↗
arXiv2018

Electromagnetically driven convection suitable for mass transfer enhancement in liquid metal batteries

Liquid metal batteries (LMBs) were recently proposed as cheap large scale energy storage. Such devices are urgently required for balancing highly fluctuating renewable energy sources. During discharge, intermetallic phases tend to form in the cathode of LMBs. These do not only limit the up-scalability, but also the efficiency of the cells. Generating a mild fluid flow in the fully liquid cell will smoothen concentration gradients and minimise the formation of intermetallics. In this context we study electro-vortex flow numerically. We simulate a recent LMB related experiment and discuss how the feeding lines to the cell can be optimised to enhance mass transfer. The Lorentz forces have to overcome the stable thermal stratification in the cathode of the cell; we show that thermal effects may reduce electro-vortex flow velocities considerable. Finally, we study the influence of the Earth magnetic field on the flow.

physics.app-ph↗
arXiv2012

Liquid-gas-solid flows with lattice Boltzmann: Simulation of floating bodies

This paper presents a model for the simulation of liquid-gas-solid flows by means of the lattice Boltzmann method. The approach is built upon previous works for the simulation of liquid-solid particle suspensions on the one hand, and on a liquid-gas free surface model on the other. We show how the two approaches can be unified by a novel set of dynamic cell conversion rules. For evaluation, we concentrate on the rotational stability of non-spherical rigid bodies floating on a plane water surface - a classical hydrostatic problem known from naval architecture. We show the consistency of our method in this kind of flows and obtain convergence towards the ideal solution for the measured heeling stability of a floating box.

cs.CE↗