Nonlocal Fluid Research Articles

Theory of nonlocal modal hydrodynamic functions for beam and plate vibrations in viscous fluids

In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes (CNTs) are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems. Therefore, the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscous fluid and supported on a nonlinear elastic foundation. The proposed model is based on nonlocal Euler–Bernoulli beam theory. The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation, respectively. A detailed parametric study is reported into how the nonlocal parameter, foundation coefficients, fluid viscosity, and amplitude and frequency of the external force influence the nonlinear dynamics of the system. Subharmonic, quasi-periodic, and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories, frequency-response curves, bifurcation diagrams, phase portraits, power spectra, and Poincaré maps. Also, the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

A unified nonlocal method for capturing discontinuous and multi‐physical behaviors of quasi‐brittle materials

AbstractA unified nonlocal method (UNM) is developed to simulate discontinuous and multi‐physical coupling dynamic behaviors for quasi‐brittle materials. In the proposed method, unified nonlocal momentum equations and constitutive laws are proposed to capture the nonlocal fluid transport effect and loading‐rate effect of quasi‐brittle materials. A general multiscale framework, which couples the proposed nonlocal method and the finite element method (FEM), is presented to accelerate the computational efficiency. The effectiveness and accuracy of this method are verified by comparing its results with experimental observations. Numerical examples show that the proposed model can well simulate the discontinuous and multi‐physical behaviors of quasi‐brittle materials, which can serve an effective numerical method for the simulation of engineering problems such as failure of concrete structures.

Axonemal regulation by curvature explains sperm flagellar waveform modulation.

Flagellar motility is critical to natural and many forms of assisted reproduction. Rhythmic beating and wave propagation by the flagellum propels sperm through fluid and enables modulation between penetrative progressive motion, activated side-to-side yaw and hyperactivated motility associated with detachment from epithelial binding. These motility changes occur in response to the properties of the surrounding fluid environment, biochemical activation state, and physiological ligands, however, a parsimonious mechanistic explanation of flagellar beat generation that can explain motility modulation is lacking. In this paper, we present the Axonemal Regulation of Curvature, Hysteretic model, a curvature control-type theory based on switching of active moment by local curvature, embedded within a geometrically nonlinear elastic model of the flagellum exhibiting planar flagellar beats, together with nonlocal viscous fluid dynamics. The biophysical system is parameterized completely by four dimensionless parameter groupings. The effect of parameter variation is explored through computational simulation, revealing beat patterns that are qualitatively representative of penetrative (straight progressive), activated (highly yawing) and hyperactivated (nonprogressive) modes. Analysis of the flagellar limit cycles and associated swimming velocity reveals a cusp catastrophe between progressive and nonprogressive modes, and hysteresis in the response to changes in critical curvature parameter. Quantitative comparison to experimental data on human sperm exhibiting typical penetrative, activated and hyperactivated beats shows a good fit to the time-average absolute curvature profile along the flagellum, providing evidence that the model is capable of providing a framework for quantitative interpretation of imaging data.

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schrödinger–Newton equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay between the soliton parameter quantum diffusion and the stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensionality.

Reflection/transmission of plane waves at the interface of an ideal fluid and nonlocal piezothermoelastic medium

PurposeThis paper aims to study the variation of energy ratios of different reflected and transmitted waves by calculating the amplitude ratios.Design/methodology/approachThis investigation studied the reflection and transmission of plane waves on an interface of nonlocal orthotropic piezothermoelastic space (NOPHS) and fluid half-space (FHS) in reference to dual-phase-lag theory under three different temperature models, namely, without-two-temperature, classical-two-temperature, and hyperbolic-two-temperature with memory-dependent derivatives (MDDs).FindingsThe primary (P) plane waves propagate through FHS and strike at the interface x3 = 0. The results are one wave reflected in FHS and four waves transmitted in NOPHS. It is noticed that these ratios are observed under the impact of nonlocal, dual-phase-lag (DPL), two-temperature and memory-dependent parameters and are displayed graphically. Some particular cases are also deduced, and the law of conservation of energy across the interface is justified.Research limitations/implicationsAccording to the available literature, there is no substantial research on the considered model incorporating NOPHS and FHS with hyperbolic two-temperature, DPL and memory.Practical implicationsThe current model may be used in various fields, including earthquake engineering, nuclear reactors, high particle accelerators, aeronautics, soil dynamics and so on, where MDDs and conductive temperature play a significant role. Wave propagation in a fluid-piezothermoelastic media with different characteristics such as initial stress, magnetic field, porosity, temperature, etc., provides crucial information about the presence of new and modified waves, which is helpful in a variety of technical and geophysical situations. Experimental seismologists, new material designers and researchers may find this model valuable in revising earthquake estimates.Social implicationsThe researchers may classify the material using the two-temperature parameter and the time-delay operator, where the parameter is a new indication of its capacity to transmit heat in interaction with various materials.Originality/valueThe submitted manuscript is original work done by the team of said authors and each author contributed equally to preparing this manuscript.

Inpatient COVID-19 vaccination rollout: Improving access to vaccination

We were aware of high numbers of inpatients unvaccinated against COVID-19 at Guy's and St Thomas' NHS Foundation Trust (GSTT). Due to this, an inpatient vaccination protocol was set up in July 2021, with initially limited uptake. From October 2021, a multidisciplinary team worked to improve the protocol for inpatient vaccination, with the development of a system that gave ownership to clinical teams. In 4 months (July 2021 to November 2021), 20 inpatients had been vaccinated at GSTT. Following our intervention, rates of uptake increased, and 34 patients were vaccinated in less than 2 months (November 2021 to January 2022). Forty-five patients who had been referred were discharged without vaccination; attempts were made to invite them to receive a vaccine. An improved pathway and referral process increased the number of inpatient vaccinations delivered. Further work is required in order to ensure that more patients who have been referred are vaccinated.

A unified non-local fluid transport model for heterogeneous saturated porous media

A unified non-local fluid transport model is proposed for heterogeneous saturated porous media. First, a non-local governing equation of fluid transport is presented based on the Non-ordinary State-based Peridynamics (NOSB-PD), and a novel flux vector state and a non-local Darcy’s law is proposed to illustrate non-local fluid transport effects in heterogeneous saturated porous media. The proposed flux state vector ensures the non-local governing equation of fluid transport model in heterogeneous saturated porous media degenerates into the local one when the horizon of each material point approaches to zero. A non-local pressure gradient at each material point can be obtained by averaging all the flux state vectors in its horizon, which unifies the weak and strong discontinuities of pressure in heterogeneous saturated porous media in a consistent way. Second, a variational formulation of the unified non-local fluid transport model is developed. This variational formulation enables the proposed model to deal with complex boundary conditions, which is difficult or even impossible for current fluid transport models based on Bond-based Peridynamics (BB-PD) and Ordinary State-based Peridynamics (OSB-PD). Third, a fully implicit algorithm combined with the Newton–Raphson method is introduced to solve the general non-linear problems in the heterogeneous saturated porous media. The penalty function method is employed to eliminate the zero-energy mode oscillation in NOSB-PD. Further, numerical examples demonstrate that the proposed model is accurate and can well capture the weak and strong discontinuities of pressure at the material interfaces and crack surfaces in the heterogeneous saturated porous media. Numerical examples also indicate that the model can effectively eliminate the zero-energy mode oscillation inherently rooted in the NOSB-PD, and thus reaches a stable numerical solution.

A non-local fluid closure for modeling cyclotron resonance in collisionless magnetized plasmas

A fluid description for collisionless magnetized plasmas that takes into account the effect of cyclotron resonance has been developed. Following the same approach as the Landau fluid closure, the heat flux components associated with transverse electromagnetic fluctuations are approximated by a linear combination of lower-order moments in wavenumber space. The closure successfully reproduces the linear cyclotron resonance for electromagnetic waves propagating parallel to the ambient magnetic field. In the presence of finite temperature anisotropy, the model gives approximately correct prediction for an instability destabilized via the cyclotron resonance. A nonlinear simulation demonstrates the wave growth consistent with the linear theory followed by the reduction of initial anisotropy, and finally, the saturation of the instability. The isotropization may be understood in terms of quasilinear theory, which is developed within the framework of the fluid model but very similar to its fully kinetic counterpart. The result indicates that both linear and nonlinear collisionless plasma responses are approximately incorporated in the fluid model.

On nonlocal fractal laminar steady and unsteady flows

In this study, we join the concept of fractality introduced by Li and Ostoja-Starzewski with the concept of nonlocality to produce a new set of nonlocal fractal fluid equations of motion. Both the unsteady and steady laminar flows are discussed. It is revealed that a damped wave equation emerges from the nonlocal fractal Navier–Stokes equation, a result which could lead to a better understanding of fluids turbulence.

A nonlocal variable coefficient KdV equation: Bäcklund transformation and nonlinear waves

A nonlocal two-layer fluid model is constructed through a simple symmetry reduction from the local one. Then, a general variable coefficients nonlocal KdV (VCKdV) equation with shifted space parity and delayed time reversal is derived from it by using multi-scale expansion method, with and without the so-called $$y-$$average method, respectively. A non-auto-Backlund transformation between the VCKdV equation and a constant coefficients KdV (CCKdV) equation is established. By using this transformation, various exact solutions of the VCKdV equation can be obtained from the seed solutions of the CCKdV equation. As some concrete examples, one solitary wave solution and two kinds of periodic wave solutions are given. Due to the inclusion of arbitrary functions in these solutions, they possess abundant dynamical behaviors with some of them analyzed graphically.

Study on Dynamic Characteristics of Microchannel Fluid–Solid Coupling Systems in Nonlocal Stress Fields

Objective of the present work is predicting the dynamic behaviors of fluid-filled microchannels when considering the small-scale effects caused by microchannel and inner fluid. A dynamic Euler–Bernoulli beam model for fluid-filled microchannels is established when applying the nonlocal strain gradient constitutive equation and nonlocal fluid shear stress equation. The scale effects of microtubes are simulated by nonlocality of elastic stress and gradient effect of strain when the fluid nonlocality is applied for predicting the scale effects induced by fluid flow. The dynamic equilibrium equations and boundary conditions for the dynamic tube are derived. By solving the equilibrium equations, different types of scale effects on wave propagation behavior are analyzed. The numerical results indicate that the nonlocal effect induced by microchannels dampens propagation for waves of short wavelengths, whereas the strain gradient effect enhances wave propagation at all wavelengths. The scale effect contributed by fluid flow also leads to decaying of the wave, because the flow velocity is reduced by the nonlocality of the fluid.

A nonlocal variable coefficient modified KdV equation derived from a two-layer fluid system and its exact solutions

A nonlocal form of a two-layer fluid system is proposed by a simple symmetry reduction, then by applying multiple scale method to it a general nonlocal two place variable coefficient modified KdV (VCmKdV) equation with shifted space and delayed time reversal is derived. Various exact solutions of the VCmKdV equation, including elliptic periodic waves, solitary waves and interaction solutions between solitons and periodic waves are obtained and analyzed graphically. As an illustration, an approximate solution of the original nonlocal two-layer fluid system is also given.

Study on the small-scale effect on wave propagation characteristics of fluid-filled carbon nanotubes based on nonlocal fluid theory

In this article, Timoshenko’s beam model is established to investigate the wave propagation behaviors for a fluid-conveying carbon nanotube when employing the nonlocal stress–strain gradient coupled theory and nonlocal fluid theory. The governing equations of motion for the carbon nanotube are derived. The small-scale influences induced by the nanotube are simulated by nonlocal and strain gradient effects, and the scale effect induced by fluid flow is first investigated applying nonlocal fluid theory. Numerical results obtained by solving the governing equations indicate that the nonlocal effect induced by the nanotube leads to wave damping and a decrease in stiffness, while the strain gradient effect contributes to wave promotion and an enhancement in stiffness. The scale effect caused by the inner fluid only leads to a decay for a high-mode wave since there is no influence from fluid flow on the low-mode wave. The numerical solution is validated by comparing with Monte Carlo simulation and interval analysis method.

Jerk in Planetary Systems and Rotational Dynamics, Nonlocal Motion Relative to Earth and Nonlocal Fluid Dynamics in Rotating Earth Frame

Some results following from the implications of nonlocal-in-time kinetic energy approach introduced recently by Suykens in the framework of rotational dynamics and motion in a non-inertial frame are discussed. Their roles in treating aspects concerning the nonlocal motion relative to Earth, the free-fall problem, the Foucault pendulum and the motion of a massive body in a rotating tube are analyzed. Governing nonlocal equations of fluid dynamics in particular the nonlocal-in-time Navier–Stokes equations are constructed under the influence of Earth rotation. Their properties are analyzed and a number of features were revealed and discussed accordingly.

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Cerebral aneurysms and microaneurysms are abnormal vascular dilatations with high risk of rupture. An aneurysmal rupture could cause permanent disability and even death. Finding and treating aneurysms before their rupture is very difficult since symptoms can be easily attributed mistakenly to other common brain diseases. Mathematical models could highlight possible mechanisms of aneurysmal development and suggest specialized biomarkers for aneurysms. Existing mathematical models of intracranial aneurysms focus on mechanical interactions between blood flow and arteries. However, these models cannot be applied to microaneurysms since the anatomy and physiology at the length scale of cerebral microcirculation are different. In this paper, we propose a mechanism for the formation of microaneurysms that involves the chemo-mechanical coupling of blood and endothelial and neuroglial cells. We model the blood as a non-local non-Newtonian incompressible fluid and solve analytically the Poiseuille flow of such a fluid through an axi-symmetric circular rigid and impermeable pipe in the presence of wall slip. The spatial derivatives of the proposed generalization of the rate of deformation tensor are expressed using Caputo fractional derivatives. The wall slip is represented by the classic Navier law and a generalization of this law involving fractional derivatives. Numerical simulations suggest that hypertension could contribute to microaneurysmal formation.

Squeezing in a nonlocal photon fluid

Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information and simulation. However the implications of the quantum nature of light in the nonlinear optical propagation are still missing many features. We theoretically predict classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear medium. By using the so called Gamow vectors, we show that the quadratures of a coherent state get squeezed and that a maximal squeezing power exists. Our analysis holds true for temporal and spatial optical propagation in highly nonlocal regime. These results open a new scenario in quantum photon fluids and may lead to novel applications in fields like metrology and analogues of quantum gravity.

Emergence of long-range phase coherence in nonlocal fluids of light

The emergence of long-range phase coherence among random nonlinear waves is a fascinating effect that characterizes fundamental phenomena such as the condensation of nonlinear waves and the related manifestation of superfluidity of certain turbulent flows. Here we report a previously unrecognized phenomenon of spontaneous emergence of long-range phase coherence among incoherent waves interacting through a nonlocal nonlinearity. The theory reveals that the establishment of long-range phase coherence constitutes a generic property of a conservative (Hamiltonian) system of highly nonlocal random waves that evolve in the strongly nonlinear regime. Aside from phase coherence, the field exhibits intensity fluctuations whose coherence length is shown to increase in a dramatic way during the evolution of the system. The analysis can be transposed to the temporal domain, revealing the emergence of temporal phase coherence among incoherent waves propagating in nonlinear materials featured by a noninstantaneous nonlinear response.

A theory of dielectric fluid films between nanostructures

In this paper a theory of dielectric fluid films between nanostructures is developed by using the theory of nonlocal electromagnetic fluids so that the nonlocal hydrodynamic force, the Lifshitz force and solvation forces can be treated systematically within the realm of continuum mechanics. In order for a continuum model to account for these surface forces of molecular origin without ad hoc assumptions, it should be endowed with a theoretical framework in which not only to represent the inner structures of fluids but to inherently possess a rational basis to merge with the Lifshitz theory without losing its rigor and also to accommodate other types of surface forces. The proposed nonlocal continuum model is formulated as such and can be adapted to all separations for which the Lifshitz theory is valid. It is applied, as an example problem, to the case of a plane-sphere configuration in the non-retarded van der Waals limit where solvation forces manifest themselves.

Role of geometry in the superfluid flow of nonlocal photon fluids

Recent work has unveiled a new class of optical systems that can exhibit the characteristic features of superfluidity. One such system relies on the repulsive photon-photon interaction that is mediated by a thermal optical nonlinearity and is therefore inherently nonlocal due to thermal diffusion. Here we investigate how such a nonlocal interaction, which at a first inspection would not be expected to lead to superfluid behavior, may be tailored by acting upon the geometry of the photon fluid itself. Our models and measurements show that restricting the laser profile and hence the photon fluid to a strongly elliptical geometry modifies thermal diffusion along the major beam axis and reduces the effective nonlocal interaction length by two orders of magnitude. This in turn enables the system to display a characteristic trait of superfluid flow: the nucleation of quantized vortices in the flow past an extended physical obstacle. These results are general and apply to other nonlocal fluids, such as dipolar Bose-Einstein condensates, and show that "thermal" photon superfluids provide an exciting and novel experimental environment for probing the nature of superfluidity, with applications to the study of quantum turbulence and analogue gravity.