Classical Fluid Research Articles

Emergence of an Ising critical regime in the clustering of one-dimensional soft matter revealed through string variables.

Soft matter systems are renowned for being able to display complex emerging phenomena such as clustering phases. Recently, a surprising quantum phase transition has been revealed in a one-dimensional (1D) system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model. In this work we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we study the low-temperature behavior of three different classical models of 1D soft matter, whose interparticle interactions allow for clustering. The same string variables highlight that, at the commensurate density for the two-particle cluster phase, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, namely the presence of an anomalous peak in the low-temperature specific heat, thus indicating the emergence of Schottky phenomenology in a nonmagnetic fluid.

Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity

One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler–Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e., the principle of least action on a Finsler manifold.

Irreversible Dynamics of Vortex Reconnections in Quantum Fluids.

We statistically study vortex reconnections in quantum fluids by evolving different realizations of vortex Hopf links using the Gross-Pitaevskii model. Despite the time reversibility of the model, we report clear evidence that the dynamics of the reconnection process is time irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently by Proment and Krstulovic [Phys. Rev. Fluids 5, 104701 (2020)PLFHBR2469-990X10.1103/PhysRevFluids.5.104701], we quantitatively relate the origin of this asymmetry to the generation of a sound pulse after the reconnection event. Our results have the prospect of being tested in several quantum fluid experiments and, theoretically, may shed new light on the energy transfer mechanisms in both classical and quantum turbulent fluids.

On Schwarzschild’s Interior Solution and Perfect Fluid Star Model

We solve the boundary value problem for Einstein’s gravitational field equations in the presence of matter in the form of an incompressible perfect fluid of density ρ and pressure field p(r) located in a ball r≤r0. We find a 1-parameter family of time-independent and radially symmetric solutions ga,ρa,pa:−2m<a<a1 satisfying the boundary conditions g=gS and p=0 on r=r0, where gS is the exterior Schwarzschild solution (solving the gravitational field equations for a point mass M concentrated at r=0) and containing (for a=0) the interior Schwarzschild solution, i.e., the classical perfect fluid star model. We show that Schwarzschild’s requirement r0>9κM/(4c2) identifies the “physical” (i.e., such that pa(r)≥0 and pa(r) is bounded in 0≤r≤r0) solutions {pa:a∈U0} for some neighbourhood U0⊂(−2m,+∞) of a=0. For every star model {ga:a0<a<a1}, we compute the volume V(a) of the region r≤r0 in terms of abelian integrals of the first, second, and third kind in Legendre form.

The K number, a new analogy criterion number to connect pressure drop and heat transfer of sCO2 in vertical tubes

Pressure drop and heat transfer are important for design and operation of power plant using supercritical fluid, but they were investigated independently previously. The objective of this paper is to make a connection between pressure drop and heat transfer for supercritical carbon dioxide (sCO2). Experimental data of pressure drop and heat transfer were obtained in our sCO2 convective test loop, covering pressures, mass fluxes and heat fluxes in the ranges of 7.5–23 MPa, 500–1500 kg/m2s and 15–400 kW/m2, respectively. Different from classical single-phase fluid assumption for supercritical fluid, pseudo-boiling is introduced to deal with flow and heat transfer in supercritical domain, including a wall-attached gas-like layer and a liquid-like fluid in tube core. Supercritical boiling number SBO and K number are developed to characterize the gas-like layer thickness. Friction factors and heat transfer are found to display the two regimes distribution: a normal heat transfer (NHT) regime with smaller friction factors at smaller SBO, and a heat transfer deterioration (HTD) regime accompanying sharply increased pressure drops beyond a critical SBO. We conclude an orifice contraction effect due to the strong vapor expansion, explaining the HTD induced rise of pressure drops. We show that K can be the similarity criterion number to connect pressure drops and heat transfer. A new correlation of friction factors is developed for sCO2, which is suitable for NHT and HTD, having mean relative error, mean absolute relative error and root-mean-square relative error of −6.2%, 18.1% and 21.2%, respectively, which are significantly smaller than those predicted by the correlations in the literature.

Electron hydrodynamics in anisotropic materials

Rotational invariance strongly constrains the viscosity tensor of classical fluids. When this symmetry is broken in anisotropic materials a wide array of novel phenomena become possible. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only thermodynamics and crystal symmetries. We find nontrivial behaviors in both two- and three-dimensional materials, including imprints of the crystal symmetry on the large-scale flow pattern. Breaking time-reversal symmetry introduces a non-dissipative Hall component to the viscosity tensor, and while this vanishes for 3D isotropic systems we show it need not for anisotropic materials. Further, for such systems we find that the electronic fluid stress can couple to the vorticity without breaking time-reversal symmetry. Our work demonstrates the anomalous landscape for electron hydrodynamics in systems beyond graphene, and presents experimental geometries to quantify the effects of electronic viscosity.

Bénard-von Kármán vortex street in a spin-orbit-coupled Bose-Einstein condensate.

The dynamics of pseudo-spin-1/2 Bose-Einstein condensates with weak spin-orbit coupling through a moving obstacle potential are studied numerically. Four types of wakes are observed and the phase diagrams are determined for different spin-orbit coupling strengths. The conditions to form Bénard-von Kármán vortex street are rather rigorous, and we investigate in detail the dynamical characteristics of the vortex streets. The two point vortices in a pair rotate around their center, and the angular velocity and their distance oscillate periodically. The oscillation intensifies with increasing spin-orbit coupling strengths, and it makes part of the vortex pairs dissociate into separate vortices or combine into single ones and destroys the vortex street in the end. The width b of the street and the distance l between two consecutive vortex pairs of the same circulation are determined by the potential radius and its moving velocity, respectively. The b/l ratios are independent of the spin-orbit coupling strength and fall in the range 0.19-0.27, which is a little smaller than the stability criterion 0.28 for classical fluids. Proper b/l ratios are necessary to form Bénard-von Kármán vortex street, but the spin-orbit coupling strength affects the stability of the street patterns. Finally, we propose a protocol to experimentally realize the vortex street in ^{87}Rb spin-orbit-coupling Bose-Einstein condensates.

Entropy Multiparticle Correlation Expansion for a Crystal.

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded in theoretical arguments, that both entropies are extensive quantities.

What can bouncing oil droplets tell us about quantum mechanics?

A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be distinctly quantum. To explain this correspondence it has been suggested that the fluid mechanical system provides a single-particle classical model of de Broglie’s idiosyncratic ‘double solution’ pilot wave theory of quantum mechanics. In this paper we assess the epistemic function of the bouncing oil droplet experiments in relation to quantum mechanics. We find that the bouncing oil droplets are best conceived as an analogue illustration of quantum phenomena, rather than an analogue simulation, and, furthermore, that their epistemic value should be understood in terms of how-possibly explanation, rather than confirmation. Analogue illustration, unlike analogue simulation, is not a form of ‘material surrogacy’, in which source empirical phenomena in a system of one kind can be understood as ‘standing in for’ target phenomena in a system of another kind. Rather, analogue illustration leverages a correspondence between certain empirical phenomena displayed by a source system and aspects of the ontology of a target system. On the one hand, this limits the potential inferential power of analogue illustrations, but, on the other, it widens their potential inferential scope. In particular, through analogue illustration we can learn, in the sense of gaining how-possibly understanding, about the putative ontology of a target system via an experiment. As such, the potential scientific value of these extraordinary experiments is undoubtedly a significant one.

Impact and lifecycle of superfluid helium drops on a solid surface

Superfluid helium droplets impacting on a solid surface behave much differently than any other fluid. After a short period of initial spreading that is similar to classical fluids, superfluid helium drops quickly shrink and disappear as the superfluid drains out through a thin adsorbed layer of helium on the surface. The lifetime and contact angle of these drops is strongly temperature-dependent, and colder drops (with high superfluid fractions) maintain a constant contact angle throughout the contraction. Above ${T}_{l\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}b\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}a}$, helium spreads slowly like other classical fluids.

Quantum paracrystalline shear modes of the electron liquid

Unlike classical fluids, a quantum Fermi liquid can support a long-lived and propagating shear sound wave at arbitrarily small wave vectors and frequencies, reminiscent of the transverse sound in crystals, despite lacking any form of long-range crystalline order. This mode is expected to be present in moderately interacting metals where the quasiparticle mass is renormalized to be more than twice the bare mass in two dimensions (2D), but it has remained undetected because it is hard to excite since it does not involve charge density fluctuations, in contrast to the conventional plasma mode. In this work we propose a strategy to excite and detect this unconventional mode in clean metallic channels. We show that the shear sound is responsible for the appearance of sharp dips in the ac conductance of narrow channels at resonant frequencies matching its dispersion. The liquid resonates while minimizing its dissipation in an analogous fashion to a sliding crystal. Ultra-clean 2D materials that can be tuned towards the Wigner crystallization transition such as silicon metal-oxide-semiconductor field-effect transistors, MgZnO/ZnO, p-GaAs, and AlAs quantum wells are promising platforms to experimentally discover the shear sound.

Fluid and kinetic aspects of magnetic reconnection and some related magnetospheric phenomena

Magnetic field reconnection plays a key role in determining the magnetic field topology and in the conversion of magnetic energy into kinetic energy in cosmic plasmas. Magnetic reconnection was proposed by solar physicists in an attempt to explain solar flares. The concept of magnetic reconnection was extended to Earth’s magnetosphere to explain auroral substorms. In this review, we first briefly review the classical fluid steady models with small separatrix angle. We then report magnetic reconnection with a large separatrix angle, and the time-dependent multiple X line reconnection (MXR) associated with flux transfer events. The transition from a single X line reconnection to MXR is examined. Global three-dimensional (3-D) magnetic reconnection is reviewed. The particle pressure gradient associated mainly with the electron (ion) off-diagonal pressure tensor terms, $$P_{xy}$$ and $$P_{zy}$$ , is shown to play an important role for electron (ion) dynamics to balance the reconnection electric field ( $$E_{y}$$ ) near the X line. In addition, various plasma waves and instabilities may occur near the ion diffusion and electron diffusion regions, including the upper hybrid drift waves, lower hybrid drift waves, ion-ion beam instability, electron beam instability, whistler waves and kinetic Alfven waves. The layered structure of outflow region of magnetic reconnection is examined. These layered structures include slow shocks, rotation discontinuities, expansion waves and plasma jets. Recent satellite observations of magnetic reconnection in the Earth and planetary magnetospheres are also discussed. The polar cap electric field associated with magnetic reconnection at the Earth's magnetopause and the energy flow in the polar cap region are examined.

Modeling and theoretical analysis of SDBD plasma actuators driven by fast-rise–slow-decay pulsed-DC voltages

Surface dielectric barrier discharge (SDBD) actuators driven by the pulsed-DC voltages are analyzed. The pulsed-DC SDBD studied in this work is equivalent to a classical SDBD driven by a tailored fast-rise–slow-decay (FRSD) voltage waveform. The plasma channel formation and charge production process in the voltage rising stage are studied at different slopes using a classical 2D fluid model, the thrust generated in the voltage decaying stage is studied based on an analytical approach taking 2D model results as the input. A thrust pulse is generated in the trailing edge of the voltage waveform and reaches maximum when the voltage decreases by approximately the value of cathode voltage fall (≈ 600 V). The time duration of the rising and trailing edge, the decay rate and the amplitude of applied voltage are the main factors affecting the performance of the actuator. Analytical expressions are formulated for the value and time moment of peak thrust, the upper limit of thrust is also estimated. Higher voltage rising rate leads to higher charge density in the voltage rising stage thus higher thrust. Shorter voltage trailing edge, in general, results in higher value and earlier appearance of the peak thrust. The detailed profile of the trailing edge also affects the performance. Results in this work allow us to flexibly design the FRSD waveforms for an SDBD actuator according to the requirements of active flow control in different application conditions.

Stochastic Lagrangian dynamics of vorticity. Part 2. Application to near-wall channel-flow turbulence

Abstract

Statistical properties of homogeneous and isotropic turbulence in He II measured via particle tracking velocimetry

Despite being a quantum two-fluid system, superfluid helium-4 (He II) is observed to behave similarly to classical fluids when a flow is generated by mechanical forcing. This similarity has brought up the feasibility of utilizing He II for high Reynolds number classical turbulence research, considering the small kinematic viscosity of He II. However, it has been suggested that the non-classical dissipation mechanism in He II at small scales may alter its turbulent statistics and intermittency. In this work, we report our study of a nearly homogeneous and isotropic turbulence (HIT) generated by a towed grid in He II. We measure the velocity field using particle tracking velocimetry with solidified deuterium particles as the tracers. By correlating the velocities measured simultaneously on different particle trajectories or at different times along the same particle trajectory, we are able to conduct both Eulerian and Lagrangian flow analyses. Spatial velocity structure functions obtained through the Eulerian analysis show scaling behaviors in the inertial subrange similar to that for classical HIT but with enhanced intermittency. The Lagrangian analysis allows us to examine the flow statistics down to below the dissipation length scale. Interestingly, strong deviations from the classical scaling behaviors are observed in this regime. We discuss how these deviations may relate to the motion of quantized vortices in the superfluid component in He II.

Separation scaling for viscous vortex reconnection

Abstract

Universal dynamics in the expansion of vortex clusters in a dissipative two-dimensional superfluid

A large ensemble of quantum vortices in a superfluid may itself be treated as a novel kind of fluid that exhibits anomalous hydrodynamics. Here we consider the dynamics of vortex clusters with thermal friction, and present an analytic solution that uncovers a new universality class in the out-of-equilibrium dynamics of dissipative superfluids. We find that the long-time dynamics of the vorticity distribution is an expanding Rankine vortex (i.e.~top-hat distribution) independent of initial conditions. This highlights a fundamentally different decay process to classical fluids, where the Rankine vortex is forbidden by viscous diffusion. Numerical simulations of large ensembles of point vortices confirm the universal expansion dynamics, and further reveal the emergence of a frustrated lattice structure marked by strong correlations. We present experimental results in a quasi-two-dimensional Bose-Einstein condensate that are in excellent agreement with the vortex fluid theory predictions, demonstrating that the signatures of vortex fluid theory can be observed with as few as $N\sim 11$ vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems.

Infinitesimal quantum group from helicity in fluid mechanics

Arnold showed that the Euler equations of an ideal fluid describe geodesics in the Lie algebra of incompressible vector fields. We will show that helicity induces a splitting of the Lie algebra into two isotropic subspaces, forming a Manin triple. Viewed another way, this shows that there is an infinitesimal quantum group (a.k.a. Lie bi-algebra) underlying classical fluid mechanics.

Classical analogies for the force acting on an impurity in a Bose–Einstein condensate

We study the hydrodynamic forces acting on a small impurity moving in a two-dimensional Bose–Einstein condensate at non-zero temperature. The condensate is modelled by the damped-Gross Pitaevskii (dGPE) equation and the impurity by a Gaussian repulsive potential coupled to the condensate. For weak coupling, we obtain analytical expressions for the forces acting on the impurity, and compare them with those computed through direct numerical simulations of the dGPE and with the corresponding expressions for classical forces. For non-steady flows, there is a time-dependent force dominated by inertial effects and which has a correspondence in the Maxey–Riley theory for particles in classical fluids. In the steady-state regime, the force is dominated by a self-induced drag. Unlike at zero temperature, where the drag force vanishes below a critical velocity, at low temperatures the impurity experiences a net drag even at small velocities, as a consequence of the energy dissipation through interactions of the condensate with the thermal cloud. This dissipative force due to thermal drag is similar to the classical Stokes’ drag. There is still a critical velocity above which steady-state drag is dominated by acoustic excitations and behaves non-monotonically with impurity’s speed.

Influences of sub-atmospheric pressure on downward flame spread over typical insulation material with parallel glass curtain wall structure in underground buildings

Downward flame spread over insulation materials by restriction of parallel glass curtain wall is an important potential scenario in modern underground building fire accidents. Meanwhile, considering the continuous challenge of research efforts in low pressure fire behavior, experimental investigation was conducted for the individual and coupling effects of pressure and curtain wall spacing on flexible polyurethane (FPU) downward flame spreading characteristics. Three pressures (70/85/100 kPa) below or near atmospheric pressure, and six kinds of spacings (4.5/6.0/8.5/11.0/14.0 cm and non-curtain wall) were applied to give a phenomenological study on the complicated variations of pyrolysis front, melting and dripping process, burning rate, flame spread velocity, flame height and pulsation frequency. First, evolution of vertex angle in pyrolysis front was observed to be stable and insensitive to both ambient pressure and interlayer spacing. Also, three dripping formations of molten fuel were found, and enhanced by decreasing pressure and spacing. Second, comprehensive understandings of coupling effects on burning rate, spread velocity and various heat transfer components were performed and formulated with semi-quantitative correlations theoretically. Finally, nonmonotonic tendencies of spacing vs. flame height or pulsation frequency were interpreted based on classical fluid and fire dynamic theory. This work could be valuable for fire hazardous analysis of modern building under sub-atmospheric environment.