The outwardly propagating spherical flames in premixed gas containing water droplets are theoretically studied in this work. The correlations between the flame propagation speed, droplet distribution and flame radius are derived, based on the large activation energy and quasi-planar flame assumptions. With this, flame bifurcation and multiplicity are analysed, focusing on the effects of initial droplet mass loading, evaporative heat loss and Lewis number. Meanwhile, the model can predict different gaseous flame types and liquid droplet distributions, as well as the bifurcations and transitions between them. It is shown that the spherical flame propagation is strongly affected by water droplet properties. When initial loading and/or heat loss coefficient are small, there is only one normal stable flame. Two stable flames arise when they increase, i.e. normal and weak flames. Increased droplet loading mainly affects the weak flame, resulting in decreased propagation speed, increased values of evaporation onset and completion fronts. However, increased heat loss affects both normal and weak flames, and flame bifurcation is observed for large heat loss. Droplet properties also greatly influence the weak flame transition between different regimes. Our results also show that Lewis number has significant influence on droplet-laden spherical flame propagation, in terms of flame bifurcation and regime transition. The Lewis number would affect the flame propagation jointly with the positive stretch rate and/or the evolving temperature gradients near the flame front through the interactions with the dispersed evaporating droplets. Furthermore, the magnitudes of Markstein length of the normal flames decrease when Lewis number approaches unity. However, those of the weak flames are mostly negative, indicating the enchantment over the shown Lewis number range. The larger magnitudes of Markstein length of weak flames show stronger sensitivity to stretch than those of normal flames. Finally, different flame types seen from our theoretical analysis are summarised.

A linear stability analysis for the onset of mixed convection in a saturated porous medium through an absolute instability of both two- and three-dimensional disturbances is performed. Relevant control parameters associated with the inclined temperature gradient and the vertical throughflow are the vertical and horizontal Rayleigh numbers, \(R_{\mathrm{v}}\) and \(R_{\mathrm{h}}\), and the vertical Péclet number, \(Q_{\mathrm{v}}\), respectively. This work extends previous studies on the very same problem in two fronts. For two-dimensional disturbances, the present results do not agree with the literature for a few of the parametric conditions reported. This is caused by the collision of the convectively unstable downstream propagating branch with multiple upstream propagating branches, which generates several saddle points and, hence, makes the identification of the correct pinching point more difficult. In other words, literature results are all saddle points but not always pinching points. For three-dimensional disturbances, this issue is not present and the current results agree with the literature. On the other hand, due to the inherent difficulties associated with a three-dimensional absolute instability analysis, literature results have only been able to report the group velocities at the onset of convective instability. When their real parts are zero, transition occurs directly from stable to absolutely unstable. Otherwise, transition occurs from stable to convectively unstable first and nothing can be said about the onset of absolute instability. In this work, a novel technique recently developed by the authors allowed the identification of the onset of absolute instability under all parametric conditions investigated in the literature, extending earlier results. Doing so confirmed the dichotomy already observed in these earlier studies, i.e., the onset of absolute instability for two- and three-dimensional longitudinal modes indeed differs.

In many simulations of turbulent flows, the viscous forces $\nu\nabla^2 \bu$ are replaced by a hyper-viscous term $-\nu_p(-\nabla^2)^{p}\bu$ in order to suppress the effect of viscosity at the large scales. In this work we examine the effect of hyper-viscosity on decaying turbulence for values of p ranging from p=1 (ordinary viscosity) up to p=100. Our study is based on direct numerical simulations of the Taylor-Green vortex for resolutions from 5123 to 20483. Our results demonstrate that the evolution of the total energy E and the energy dissipation ϵ remain almost unaffected by the order of the hyper-viscosity used. However, as the order of the hyper-viscosity is increased, the energy spectrum develops a more pronounced bottleneck that contaminates the inertial range. At the largest values of p examined, the spectrum at the bottleneck range has a positive power-law behavior E(k)∝kα with the power-law exponent α approaching the value obtained in flows at thermal equilibrium α=2. This agrees with the prediction of Frisch et al. [Phys. Rev. Lett. 101, 144501 (2008)] who suggested that at high values of p, the flow should behave like the truncated Euler equations (TEE). Nonetheless, despite the thermalization of the spectrum, the flow retains a finite dissipation rate up to the examined order, which disagrees with the predictions of the TEE system implying suppression of energy dissipation. We reconcile the two apparently contradictory results, predicting the value of p for which the hyper-viscous Navier-Stokes goes over to the TEE system and we discuss why thermalization appears at smaller values of p.

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of quantum computing to statistical modeling by establishing a connection between point processes and Gaussian Boson Sampling, an algorithm for photonic quantum computers. We show that Gaussian Boson Sampling can be used to implement a class of point processes based on hard-to-compute matrix functions which, in general, are intractable to simulate classically. We also discuss situations where polynomial-time classical methods exist. This leads to a family of efficient quantum-inspired point processes, including a new fast classical algorithm for permanental point processes. We investigate the statistical properties of point processes based on Gaussian Boson Sampling and reveal their defining property: like bosons that bunch together, they generate collections of points that form clusters. Finally, we analyze properties of these point processes for homogeneous and inhomogeneous state spaces, describe methods to control cluster location, and illustrate how to encode correlation matrices.

Self-assembly and force generation are two central processes in biological systems that usually are considered in separation. However, the signals that activate non-muscle myosin II molecular motors simultaneously lead to self-assembly into myosin II minifilaments as well as progression of the motor heads through the crossbridge cycle. Here we investigate theoretically the possible effects of coupling these two processes. Our assembly model, which builds upon a consensus architecture of the minifilament, predicts a critical aggregation concentration at which the assembly kinetics slows down dramatically. The combined model predicts that increasing actin filament concentration and force both lead to a decrease in the critical aggregation concentration. We suggest that due to these effects, myosin II minifilaments in a filamentous context might be in a critical state that reacts faster to varying conditions than in solution. We finally compare our model to experiments by simulating fluorescence recovery after photobleaching.

The effective one component plasma (EOCP) model has provided an efficient approach to obtaining many important thermophysical parameters of hot dense matter [{Phys. Rev. Lett. 116, 115003 (2016)}}]. In this paper, we perform extensive quantum molecular dynamics (QMD) simulations to determine the equations of state, ionic structures, and ionic transport properties of neon and krypton within the warm dense matter (WDM) regime where the density ({ρ}) is up to 12 g/cm$ ^{3} $ and the temperature (T) is up to 100 kK. The simulated data are then used as a benchmark to explicitly evaluate the EOCP and Yukawa models. It is found that, within present {ρ-T} regime, the EOCP model can excellently reproduce the diffusion and viscosity coefficients of neon and krypton due to the fact that this model defines a system which nearly reproduces the actual physical states of WDM. Therefore, the EOCP model may be a promising alternative approach to reasonably predicting the transport behaviors of matter in WDM regime at lower QMD computational cost. The evaluation of Yukawa model shows that the consideration of the energy level broadening effect in the average atom model is necessary. Finally, with the help of EOCP model, the Stokes-Einstein relationships about neon and krypton are discussed, and fruitful plasma parameters as well as a practical {ρ-T}-dependent formula of the effective coupling parameter are obtained. These results not only provide valuable information for future theoretical and experimental studies on dense neon and krypton, but also reveal the applicability of the EOCP model and the limitation of the Yukawa model in WDM regime, and further support the continuing search for a unified description of ionic transport in dense plasma.

Recently, we have reported the discovery of enormous negative viscosity of a nematic liquid crystal in the presence of turbulence induced by ac electric fields, which enabled us to observe novel phenomena related to the negative viscosity, such as spontaneous shear flow, hysteresis in flow curves, and self-oscillation [H. Orihara et al., Phys. Rev. E 99, 012701 (2019)]. In the present paper, we report the rheological properties of another nematic liquid crystal, which is a homologue of the previous one. The properties of the present liquid crystal are strongly dependent on electrical conductivity. Three samples with different conductivities were prepared by changing the amount of an ionic dopant. It was found that the lowest-conductivity sample without dopant shows no negative viscosity whereas the other ion-doped samples exhibit negative viscosity with strong dependence on the frequency of the ac electric field, consistent with microscopic observations. Phase diagrams of the negative- and positive-viscosity states in the amplitude and frequency plane are constructed to show the conductivity effect. Furthermore, we propose a model to reproduce another type of self-oscillation found in the present study. {I. Introduction} We recently discovered enormous negative viscosity of the nematic liquid crystal MBBA (p-methoxybenzylidene-{p$$n-}butylaniline) in the presence of turbulence induced by electric fields [1]. The viscosity of a fluid is a measure of its resistance to flow. Therefore, in the case of negative viscosity, the flow is amplified by negative resistance, even in the absence of external stress, resulting in spontaneous flow. Numerous experimental [2-9] and theoretical [10-20] studies have attempted to observe negative viscosity, mainly in magnetic fluids [7, 8, 16, 17], electro-rheological suspension [9, 18-20] and active suspensions of bacteria [2-6, 10-15, 21-23]. Recently, active suspensions exhibit liquid crystalline order at high concentrations, have attracted much attention [13, 15, 21-23] and are theoretically predicted to show intriguing nonlinear rheological properties [13, 15]. In suspensions of Escherichia coli, negative viscosity was first measured, although it was very low (approximately −10−1 mPa s) [5]. In contrast, MBBA exhibited much larger negative viscosity of −40 mPa s [1]. Taking advantage of the enormous negative viscosity of MBBA, we successfully observed several characteristic phenomena with a conventional rheometer [1]. We observed a spontaneous shear flow that rotated the upper disk of the rheometer, as well as reversal of the rotational direction upon application of an external torque in the opposite direction. The rotation speed ($$ shear rate) was proportional to the square of the electric field amplitude. Hysteresis loops were also observed in the shear rate–shear stress curves under controlled shear stress, which were quite similar to those seen for ferroic materials such as ferromagnetics. As the frequency of the applied ac electric field was increased, the hysteresis loop or the negative viscosity vanished, indicating that a phase transition took place from a negative- to positive-viscosity state. In this case, the frequency can be regarded as the temperature for ferroic materials. Thus, we …

We pose an engineering challenge of controlling an via coordinated, implementation-light and randomized on/off switching as a problem in . We show that with nonlinear feedback on the cumulative consumption, assumed available to the aggregator via direct physical measurements of the energy flow, allows the ensemble to recover from its use in the regime, i.e. transition to a statistical steady state, significantly faster than in the case of the fixed feedback. Moreover when the nonlinearity is sufficiently strong, one observes the phenomenon of ``super-relaxation" – where the total instantaneous energy consumption of the ensemble transitions to the steady state much faster than the underlying probability distribution of the devices over their state space, while also leaving almost no devices outside of the comfort zone.

Weak turbulence has been investigated in nonlinear-nonequilibrium physics to understand universal characteristics near the transition point of order to disorder states. Here the one-dimensional Nikolaevskii turbulence, which is a mathematical model of weak turbulence, was studied theoretically. We calculated the velocity field of the Nikolaevskii turbulence assuming convective structure and carried out tagged-particle simulations in the flow to clarify the Nikolaevskii turbulence from the Lagrangian description. The tagged-particle diffuses in the disturbed flow, and the diffusion was superdiffusive in an intermediate timescale between ballistic and normal-diffusive scale. The diffusion of the slow structure is characterized by the power-law for the control parameter near the transition point of the Nikolaevskii turbulence, suggesting that the diffusive characteristics of the slow structure hold scale-invariance. We proposed a simplified model named two-scale Brownian motion, which reveals a hierarchy in the Nikolaevskii turbulence.

In this paper, we investigate designing a new type of high-order finite difference multi-resolution trigonometric weighted essentially non-oscillatory (TWENO) schemes for solving hyperbolic conservation laws and some benchmark highly oscillatory problems. We only use the information defined on a hierarchy of nested central spatial stencils in a trigonometric polynomial reconstruction framework without introducing any equivalent multi-resolution representations. These new finite difference trigonometric WENO schemes use the same large stencils as the classical WENO schemes [26, 41], could obtain the optimal order of accuracy in smooth regions, and simultaneously suppress spurious oscillations near strong discontinuities. The linear weights of such multi-resolution trigonometric WENO schemes can be any positive numbers on condition that their summation is one. This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finite difference trigonometric WENO schemes. These new trigonometric WENO schemes are simple to construct and can be easily implemented to arbitrary high-order accuracy in multi-dimensions. Some benchmark examples including some highly oscillatory problems are given to demonstrate the robustness and good performance of these new trigonometric WENO schemes.

An extensive experimental study using Particle Image Velocimetry (PIV) on synthetic jets issuing from different orifice shapes is reported. All data are phase and time averaged to derive mean velocity, half-velocity width and rms velocity profiles in the near field of the jet (0 < X/D < 7), at a Reynolds number around 10,000. Different non-circular orifice shapes as rectangular, square, elliptic and triangular are considered and results are compared to those of the circular orifice in order to investigate the effect of asymmetry on the turbulent flow field in view of mixing enhancement. The measurements are carried out on two orthogonal planes to capture three dimensional features of non-circular jets. Results show highest velocity decay rate for elongated orifices, especially the rectangular one, in comparison to the circular one, both in phase and time-averaged plots. Time averaged results show higher velocity decay rate of synthetic jets in comparison to those of continuous ones. It is also observed that, for X/D > 5, only profiles of circular and square jets become partially self-similar. For synthetic jets, higher turbulence content is measured for all orifice shapes at the centerline and close to the orifice exit in comparison to continuous jets.

Most treatments of electron-electron correlations in dense plasmas either ignore them entirely (random phase approximation) or neglect the role of ions (jellium approximation). In this work, we go beyond both these approximations to derive a new formula for the electron-electron static structure factor which properly accounts for the contributions of both ionic structure and quantum-mechanical dynamic response in the electrons. The result can be viewed as a natural extension of the quantum Ornstein-Zernike theory of ionic and electronic correlations, and it is suitable for dense plasmas in which the ions are classical and the conduction electrons are quantum-mechanical. The corresponding electron-electron pair distribution functions are compared with the results of path integral Monte Carlo simulations, showing good agreement whenever no strong electron resonance states are present. We construct approximate potentials of mean force which describe the effective screened interaction between electrons. Significant deviations from Debye-H"uckel screening are present at temperatures and densities relevant to high energy density experiments involving warm and hot dense plasmas. The presence of correlations between conduction electrons is likely to influence the electron-electron contribution to the electrical and thermal conductivity. It is expected that excitation processes involving the conduction electrons (e.g., free-free absorption) will also be affected.

Anisotropic prismatic/strand meshes are often used to capture viscous boundary layer effects in Reynolds Averaged Navier Stokes (RANS) simulations of high Reynolds number flows. This paper describes a new algorithm for generation of prismatic meshes using the minimum distance field of the surface tessellation. The algorithm starts with initial point placement using both the direction of best visibility and the direction to the closest point on the minimum distance iso-surface. Initial point placement is followed by a constrained smoothing operation based on an elastic spring analogy. The constraints ensure movement of nodes is restricted to the iso-surface of the distance field and within the region of visibility. Simulations are performed using a dual-mesh infrastructure, where the prismatic meshes transition to a Cartesian background mesh a short distance from the wall. This overset mesh system is processed by a domain connectivity method to establish connections between self-intersecting strand meshes and strand/Cartesian mesh systems. Mesh and flow simulation results are presented for test cases of varying complexity.

Evaporation rates of low-density water aerosols in a cylindrical acoustic resonator were investigated experimentally, motivated by the potential use of water droplet aerosols in two-phase thermoacoustic devices. Measurements of water aerosol evaporation rates were conducted using a novel direct visualization method combining mass balance quantification based on the light scattering from water droplets and two-dimensional PIV measurements with the droplets acting as the flow visualization particles. Water droplet aerosol evaporation was monitored at a location between the resonator pressure and velocity anti-nodes, while being subjected to a low frequency (110 [Hz]) acoustic standing wave with various acoustic pressure amplitude (APA) values. Application of the acoustic field was found to significantly increase water droplet evaporation rates, exhibiting a linear dependency on the applied APA in the range 600[Pa]

Abstract Understanding mechanism of transmitted and stored heat in porous materials was extremely important for improving thermal protective performance of clothing. A coupled heat and moisture transfer model in a three-layer fabric system while exposing to a low-level thermal radiation was developed in this study. The model simulated the transmitted and stored heat in porous materials, and considered the effect of moisture transport on the transmitted and stored heat. The predicted results from the coupled model were validated with the experimental results, and compared with the predicted results from the previous model without considering the moisture effect. It was found that the prediction accuracies in skin burn and skin temperature through the coupled model were further improved. The coupled model was used to examine the moisture effect on heat transport and storage in porous materials. The results demonstrated that the moisture within porous materials increased the heat storage and discharge, but decreased the heat transport. The increases in initial moisture content and fiber moisture regain, while increasing the thermal hazardous effect, greatly enhanced the thermal protective performance of clothing. Therefore, it suggested that the moisture management in porous materials was a key consideration for thermal functional design of fabric.

Suspension flow through porous medium was studied using the Stokesian dynamics simulation method. Stokesian dynamics is an efficient tool to carry out numerical simulations for suspension of rigid particles interacting through hydrodynamic and non-hydrodynamic forces. After validating the simulation method for a single particle flowing through an array of fixed grain particles, we have analysed the suspension transport through porous medium. It was observed that the hydrodynamic interactions and the inter-particle non-hydrodynamic forces between the moving and fixed grain particles have a strong influence on the particle trajectories. This was apparent from the change in particle flux with the fractional channel width in the presence of non-hydrodynamic forces. Hydrodynamic interaction between the suspension and grain particles was also studied for large-scale porous system that was generated by a random arrangement of the particles in a periodic cell. It was found that the change in porosity leads to change in the average fluctuation velocity of the suspension. The fluctuation velocity was observed to vary linearly with the particle concentration and average suspension velocity. Finally, a comparative study was performed with suspension flow in a straight channel and it was observed that the shear-induced particle migration in porous medium is altered by the presence of grain particles.

Abstract We address the problem of initiation of convective motion in the case of a fluid saturated porous layer, containing a salt in solution, which is heated and salted below. We amplify the very interesting recent results of Nield and Kuznetsov and examine in detail a whole range of temperature and salt boundary conditions allowing for a combination of prescribed heat flux and temperature. The behaviour of the transition from stationary to oscillatory convection is examined in detail as the boundary conditions vary from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux.

Abstract The 4th order Darcy–Bénard eigenvalue problem for the onset of thermal convection in a 3D rectangular porous box is investigated. We start from a recent 2D model Tyvand et al. (Transp Porous Med 128:633–651, 2019) for a rectangle with handpicked boundary conditions defying separation of variables so that the eigenfunctions are of non-normal mode type. In this paper, the previous 2D model (Tyvand et al. 2019) is extended to 3D by a Fourier component with wave number k in the horizontal y direction, due to insulating and impermeable sidewalls. As a result, the eigenvalue problem is 2D in the vertical xz-plane, with k as a parameter. The transition from a preferred 2D mode to 3D mode of convection onset is studied with a 2D non-normal mode eigenfunction. We study the 2D eigenfunctions for a unit width in the lateral y direction to compare the four lowest modes \(k_m = m \pi ~(m=0,1,2,3)\), to see whether the 2D mode \((m=0)\) or a 3D mode \((m\ge 1)\) is preferred. Further, a continuous spectrum is allowed for the lateral wave number k, searching for the global minimum Rayleigh number at \(k=k_c\) and the transition between 2D and 3D flow at \(k=k^*\). Finally, these wave numbers \(k_c\) and \(k^*\) are studied as functions of the aspect ratio.

Abstract The concept of the representative elementary volume (REV) is often associated with the notion of hydrodynamic dispersion and Fickian transport. However, it has been frequently observed experimentally and in numerical pore-scale simulations that transport is non-Fickian and cannot be characterized by hydrodynamic dispersion. Does this mean that the concept of the REV is invalid? We investigate this question by a comparative analysis of the advective mechanisms of Fickian and non-Fickian dispersions and their representation in large-scale transport models. Specifically, we focus on the microscopic foundations for the modeling of pore-scale fluctuations of Lagrangian velocity in terms of Brownian dynamics (hydrodynamic dispersion) and in terms of continuous-time random walks, which account for non-Fickian transport through broad distributions of advection times. We find that both approaches require the existence of an REV that, however, is defined in terms of the representativeness of Eulerian flow properties. This is in contrast to classical definitions in terms of medium properties such as porosity, for example.

Abstract The RANS modelling of turbulence across fluid-porous interface regions within ribbed channels has been investigated by applying double (both volume and Reynolds) averaging to the Navier–Stokes equations. In this study, turbulence is represented by using the Launder and Sharma (Lett Heat Mass Transf 1:131–137, 1974) low-Reynolds-number \(k-\varepsilon \) turbulence model, modified via proposals by either Nakayama and Kuwahara (J Fluids Eng 130:101205, 2008) or Pedras and de Lemos (Int Commun Heat Mass Transf 27:211–220, 2000), for extra source terms in turbulent transport equations to account for the porous structure. One important region of the flow, for modelling purposes, is the interface region between the porous medium and clear fluid regions. Here, corrections have been proposed to the above porous drag/source terms in the k and \(\varepsilon \) transport equations that are designed to account for the effective increase in porosity across a thin near-interface region of the porous medium, and which bring about significant improvements in predictive accuracy. These terms are based on proposals put forward by Kuwata and Suga (Int J Heat Fluid Flow 43:35–51, 2013), for second-moment closures. Two types of porous channel flows have been considered. The first case is a fully developed turbulent porous channel flow, where the results are compared with DNS predictions obtained by Breugem et al. (J Fluid Mech 562:35–72, 2006) and experimental data produced by Suga et al. (Int J Heat Fluid Flow 31:974–984, 2010). The second case is a turbulent solid/porous rib channel flow to examine the behaviour of flow through and around the solid/porous rib, which is validated against experimental work carried out by Suga et al. (Flow Turbul Combust 91:19–40, 2013). Cases are simulated covering a range of porous properties, such as permeability and porosity. Through the comparisons with the available data, it is demonstrated that the extended model proposed here shows generally satisfactory accuracy, except for some predictive weaknesses in regions of either impingement or adverse pressure gradients, associated with the underlying eddy-viscosity turbulence model formulation.

Abstract Carbon dioxide injection into deep saline aquifers is governed by a number of physico-chemical processes including mineral dissolution and precipitation, multiphase fluid flow, and capillary trapping. These processes can be coupled; however, the impact of fluid–rock reaction on the multiphase flow properties is difficult to study and is not simply correlated with variations in porosity. We observed the impact of rock mineral dissolution on multiphase flow properties in two carbonate rocks with distinct pore structures. Observations of steady-state \(\hbox {N}_2\)–water relative permeability and residual trapping were obtained, along with mercury injection capillary pressure characteristics. These tests alternated with eight stages in which 0.5% of the mineral volume was uniformly dissolved into solution from the rock cores using an aqueous solution with a temperature-controlled acid. Variations in the multiphase flow properties did not relate simply to changes in porosity, but corresponded to the changes in the underlying pore structure. In the Ketton carbonate, dissolution resulted in an increase in the fraction of pore volume made up by the smallest pores and a decrease in the fraction made up by the largest pores. This resulted in an increase in the relative permeability to the nonwetting phase, a decrease in the relative permeability to the wetting phase, and a modest, but systematic decrease in residual trapping. In the Estaillades carbonate, dissolution resulted in an increase in the fraction of pore volume made up by pores in the central range of the initial pore size distribution, and a corresponding decrease in the fraction made up by both the smallest and largest pores. This resulted in a decrease in the relative permeability to both the wetting and nonwetting fluid phases and no discernible impact on the residual trapping. In summary, the impact of rock matrix dissolution will be strongly dependent on the impact of that dissolution on the underlying pore structure of the rock. However, if the variation in pore structure can be observed or estimated with modelling, then it should be possible to estimate the impacts on multiphase flow properties.

The diffusive behavior of nanoparticles inside porous materials is attracting a lot of interest in the context of understanding, modeling, and optimization of many technical processes. A very powerful technique for characterizing the diffusive behavior of particles in free media is dynamic light scattering (DLS). The applicability of the method in porous media is considered, however, to be rather difficult due to the presence of multiple sources of scattering. In contrast to most of the previous approaches, the DLS method was applied without ensuring matching refractive indices of solvent and porous matrix in the present study. To test the capabilities of the method, the diffusion of spherical gold nanoparticles within the interconnected, periodic nanopores of inverse opals was analyzed. Despite the complexity of this system, which involves many interfaces and different refractive indices, a clear signal related to the motion of particles inside the porous media was obtained. As expected, the diffusive process inside the porous sample slowed down compared to the particle diffusion in free media. The obtained effective diffusion coefficients were found to be wave vector-dependent. They increased linearly with increasing spatial extension of the probed particle concentration fluctuations. On average, the slowing-down factor measured in this work agrees within combined uncertainties with literature data.

Abstract Flow, transport, mechanical, and fracture properties of porous media depend on their morphology and are usually estimated by experimental and/or computational methods. The precision of the computational approaches depends on the accuracy of the model that represents the morphology. If high accuracy is required, the computations and even experiments can be quite time-consuming. At the same time, linking the morphology directly to the permeability, as well as other important flow and transport properties, has been a long-standing problem. In this paper, we develop a new network that utilizes a deep learning (DL) algorithm to link the morphology of porous media to their permeability. The network is neither a purely traditional artificial neural network (ANN), nor is it a purely DL algorithm, but, rather, it is a hybrid of both. The input data include three-dimensional images of sandstones, hundreds of their stochastic realizations generated by a reconstruction method, and synthetic unconsolidated porous media produced by a Boolean method. To develop the network, we first extract important features of the images using a DL algorithm and then feed them to an ANN to estimate the permeabilities. We demonstrate that the network is successfully trained, such that it can develop accurate correlations between the morphology of porous media and their effective permeability. The high accuracy of the network is demonstrated by its predictions for the permeability of a variety of porous media.

Abstract The emergence of hydrocarbons within shale as a major recoverable resource has sparked interest in fluid transport through these tight mudstones. Recent studies suggest the importance to recovery of microfracture networks that connect localized zones with large organic content to the inorganic matrix. This paper presents a joint modeling and experimental study to examine the onset, formation, and evolution of microfracture networks as shale matures. Both the stress field and fractures are simulated and imaged. A novel laboratory-scale, phase-field fracture propagation model was developed to characterize the material failure mechanisms that play a significant role during the shale maturation process. The numerical model developed consists of coupled solid deformation, pore pressure, and fracture propagation mechanisms. Benchmark tests were conducted to validate model accuracy. Laboratory-grade gelatins with varying Young’s modulus were used as scaled-rock analogs in a two-dimensional Hele-Shaw cell apparatus. Yeast within the gelatin generates gas in a fashion analogous to hydrocarbon formation as shale matures. These setups allow study and visualization of host rock elastic-brittle fracture and fracture network propagation mechanisms. The experimental setup was fitted to utilize photoelasticity principles coupled with birefringence properties of gelatin to explore visually the stress field of the gelatin as the fracture network developed. Stress optics image analysis and linear elastic fracture mechanics (LEFM) principles for crack propagation were used to monitor fracture growth for each gelatin type. Observed and simulated responses suggest gas diffusion within and deformation of the gelatin matrix as predominant mechanisms for energy dissipation depending on gelatin strength. LEFM, an experimental estimation of principal stress development with fracture growth, at different stages was determined for each gelatin rheology. The interplay of gas diffusion and material deformation determines the resulting frequency and pattern of fractures. Results correlate with Young’s modulus. Experimental and computed stress fields reveal that fractures resulting from internal gas generation are similar to, but not identical to, type 1 opening mode.

Abstract New experimental and numerical techniques constitute the major recent advancements in the study of flow through porous media. However, a model that duly links the micro- and macroscales of this phenomenon is still lacking. Therefore, the present work describes a new, analytical model suitable for both Darcian and post-Darcian flow. Unlike its predecessors, most of which are based on empirical assessments or on some derivation of the Navier–Stokes equations, the presented model employed the principle of maximum entropy, along with a reduced number of premises. Nevertheless, it is compatible with classic expressions, such as Darcy’s and Forchheimer’s laws. Also, great adherence to previously published experimental results was observed. Moreover, the developed model allows for the delimitation of Darcian and post-Darcian regimes. It enabled the determination of a probabilistic distribution function of flow velocities within the pore space. Further, it bestowed richer interpretations of the physical meanings of principal flow parameters. Finally, through a new quantity called the entropy parameter, the proposed model may serve as a bridge between experimental and numerical findings both at the micro- and macroscales. Therefore, the present research yielded an analytical, entropy-based model for flow through porous media that is sufficiently general and robust to be applied in several fields of knowledge. Graphic Abstract

The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through a notional actuator disk that is stationary in the streamwise direction. The present derivation relaxes the assumptions of steady flow and streamwise actuator disk stationarity, which expands the physically realizable parameter space of flow conditions upstream and downstream of the actuator disk. A key consequence of this generalization is the existence of unsteady motions that can, in principle, lead to energy conversion efficiencies that exceed the Betz limit not only transiently, but also in time-averaged performance. Potential physical implementations of those unsteady motions are speculated.

Depending on the reflectional and rotational symmetries of annular combustors for aeroengines and gas turbines, self-sustained azimuthal thermoacoustic eigenmodes can be standing, spinning or mix of these two types of waves. These thermoacoustic limit cycles are unwanted because the resulting intense acoustic fields induce high-cycle fatigue of the combustor components. This paper presents a new theoretical framework for phenomenologically describing the dynamics of the slow-flow variables, which define the state of an eigenmode, i.e. if the latter is standing, spinning or mixed. The acoustic pressure is expressed as a hypercomplex field and this ansatz is inserted into a one dimensional wave equation that describes the thermoacoustics of a thin annulus. Slow-flow averaging of this wave equation is performed by adapting the classic Krylov-Bogoliubov method to the quaternion field in order to derive a system of coupled first order differential equations for the four slow-flow variables, i.e. the amplitude, the nature angle, the preferential direction and the temporal phase of the azimuthal thermoacoustic mode. The state of the mode can be conveniently depicted by using the first three slow-flow variables as spherical coordinates for a Bloch sphere representation. Stochastic forcing from the turbulence in annular combustors is also accounted for. This new analytical model describes both rotational and reflectional symmetry breaking bifurcations induced by the non-uniform distribution of thermoacoustic sources along the annulus circumference and by the presence of a mean swirl.

We use numerical simulations to study the dynamics of three dimensional vesicles in unconfined and confined Poiseuille flow. Previous numerical studies have shown that when the fluid viscosity inside and outside the vesicle is same (no viscosity contrast), a transition from asymmetric slippers to symmetric parachutes takes place as viscous forcing or capillary number is increased. At higher viscosity contrast, an outward migration tendency has also been observed in unconfined flow simulations. In this paper, we study how the presence of viscosity contrast and confining walls affect the dynamics of vesicles and present phase diagrams for confined Poiseuille flow with and without viscosity contrast. To our knowledge, this is the first study that provides a phase diagram for 3D vesicles with viscosity contrast in confined Poiseuille flow. The confining walls push the vesicle towards the center while the viscosity contrast has the opposite effect. This interplay leads to important differences in the dynamics like bistability at high capillary numbers.

Using mixtures of soap, water, and long chain polymers, free-floating soap bubbles can be formed with volumes approaching 100 m3. Here we investigate how such thin films are created and maintained over time. We show how the extensional rheology is the most important factor in creating the bubble, and how polydispersity in molecular weight of the solvated polymers leads to better performance at lower concentrations. Additionally, using IR absorption, we measure soap film thickness profiles and film lifetimes. Although the initial thickness mostly depends on the choice of detergent, polymers can dramatically increase film lifetime at high molecular weights and high concentrations, although such high concentrations can inhibit the initial film formation. Thus, the ideal concentration of polymer additives for making giant bubbles requires a robust viscoelastic rheology during extension, and is aided by long film lifetimes during gravitational drainage and evaporation.

We study the mixing of a passive scalar in homogeneous turbulent flow with and without anisotropic external force. It is assumed that no scalar source exists and the scalar spectrum at an initial time instant t0 is given by the form Ck2+o(k2) at the wavenumber k→0, where C is independent of k. We have performed direct numerical simulations (DNSs) of the mixing, in which the initial integral length scales of the scalar field are comparable to those of the velocity field and the Schmidt number is unity. The DNSs show that even though the large-scale anisotropy of the velocity field grows with time owing to the external force, its scalar field counterpart remains almost unchanged, i.e., frozen with respect to time, in a state where the scalar field evolves in a self-similar manner. The degree of the anisotropy of each of the velocity and scalar fields is measured by the ratios of the integral length scales in different Cartesian directions. The DNSs also suggest that the scalar spectrum keeps the form Ck2+o(k2) at small k for time t(≥t0), and that C is time-independent.

We study the dynamics of fragmentation for Newtonian and viscoelastic liquids in rotary atomization. In this common industrial process centripetal acceleration destabilizes the liquid torus that forms at the rim of a spinning cup or disk due to the Rayleigh-Taylor instability. The resulting ligaments leave the liquid torus with a remarkably repeatable spacing that scales inversely with the rotation rate. The fluid filaments then follow a well-defined geometrical path-line that is described by the involute of a circle. Knowing the geometry of this phenomenon we derive the detailed kinematics of this process and compare it with the experimental observations. We show that the ligaments elongate tangentially along the involute of the circle and thin radially as they separate from the cup. We use these kinematic conditions to develop an expression for the spatial variation of the filament deformation rate and show that it decays away from the spinning cup. Once the ligaments are sufficiently far from the cup, they are not stretched sufficiently fast to overcome the critical rate of capillary thinning and consequently undergo capillary-driven break up forming droplets. We couple these kinematic considerations with the known properties of several Newtonian and viscoelastic test liquids to develop a quantitative understanding of this commercially-important fragmentation process that can be compared in detail with experimental observations. We also investigate the resulting droplet size distributions and observe that the appearance of satellite droplets during the pinch-off process lead to the emergence of bidisperse droplet size distributions. These binary distributions are well described by the superposition of two separate Gamma distributions that capture the physics of the disintegration process for the main and satellite droplets, respectively. Furthermore, as we consider more viscous Newtonian liquids or weakly viscoelastic test fluids, we show that changes in the liquid viscosity or viscoelasticity have a negligible effect on the average droplet size. However, incorporation of viscous/viscoelastic effects delays the thinning dynamics in the ligaments and thus results in broader droplet size distributions. The ratio of the primary to satellite droplet size increases monotonically with both viscosity and viscoelasticity. We develop a simple physical model that rationalizes the observed experimental trends and provides us a better understanding of the principal dynamical features of rotary fragmentation for both Newtonian and weakly viscoelastic liquids.

Coulomb plasmas crystallize in a number of physical systems, such as dusty plasmas, neutron star crusts, and white dwarf cores. The crystal structure of the one component and binary plasma has received significant attention in the literature, though the less studied multicomponent plasma may be most relevant for many physical systems which contain a large range of particle charges. We report on molecular dynamics simulations of multicomponent plasmas near the melting temperature with mixtures taken to be realistic X-ray burst ash compositions. We quantify the structure of the crystal with the bond order parameters and radial distribution function. Consistent with past work, low charge particles form interstitial defects and we argue that they are in a quasi-liquid state within the lattice. The lattice shows screening effects which preserves long range order despite the large variance in particle charges, which may impact transport properties relevant to astrophysics.

We show that a non-Markovian behavior can appear in a type of Markovian multimeric channels. Such a channel consists of $N_{\thinspace }$independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as M out of N subunits in the open state with $N $> $M $> 0. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can appear a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.

We consider a system of independent point-like particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom that is subjected to a nonequilibrium source of noise, which affects their coupling with the background field. We explore the phase diagram of the system and pinpoint the role of the nonequilibrium drive in producing a nontrivial patterned spatial organization. We are able, by means of a weakly nonlinear analysis, to account for the parameter-dependence of the boundaries of the phase and pattern diagram in the stationary state.