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The combination of flow elasticity and inertia has emerged as a viable tool for focusing and manipulating particles using microfluidics. Although there is considerable interest in the field of elasto-inertial microfluidics owing to its potential applications, research on particle focusing has been mostly limited to low Reynolds numbers (Re<1), and particle migration toward equilibrium positions has not been extensively examined. In this work, we thoroughly studied particle focusing on the dynamic range of flow rates and particle migration using straight microchannels with a single inlet high aspect ratio. We initially explored several parameters that had an impact on particle focusing, such as the particle size, channel dimensions, concentration of viscoelastic fluid, and flow rate. Our experimental work covered a wide range of dimensionless numbers (0.05 < Reynolds number < 85, 1.5 < Weissenberg number < 3800, 5 < Elasticity number < 470) using 3, 5, 7, and 10 µm particles. Our results showed that the particle size played a dominant role, and by tuning the parameters, particle focusing could be achieved at Reynolds numbers ranging from 0.2 (1 µL/min) to 85 (250 µL/min). Furthermore, we numerically and experimentally studied particle migration and reported differential particle migration for high-resolution separations of 5 µm, 7 µm and 10 µm particles in a sheathless flow at a throughput of 150 µL/min. Our work elucidates the complex particle transport in elasto-inertial flows and has great potential for the development of high-throughput and high-resolution particle separation for biomedical and environmental applications. [ABSTRACT FROM AUTHOR]

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) for different volume fractions in a wall-bounded, effectively inertialess, small amplitude oscillatory shear (SAOS) flow for a wide range of applied frequencies. The RBCs are modeled as biconcave capsules, whose membrane is an isotropic and hyperelastic material following the Skalak constitutive law. The frequency-dependent viscoelasticity in the bulk suspension is quantified by the complex viscosity, defined by the amplitude of the particle shear stress and the phase difference between the stress and shear. SAOS flow basically impedes the deformation of individual RBCs as well as the magnitude of fluid-membrane interactions, resulting in a lower specific viscosity and first and second normal stress differences than in steady shear flow. Although it is known that the RBC deformation alone is sufficient to give rise to shear-thinning, our results show that the complex viscosity weakly depends on the frequency-modulated deformations or orientations of individual RBCs but rather depends on combinations of the frequency-dependent amplitude and phase difference. The effect of the viscosity ratio between the cytoplasm and plasma and of the capillary number is also assessed. [ABSTRACT FROM AUTHOR]

We study the collision rates of settling spheres and elongated spheroids in homogeneous, isotropic turbulence by means of direct numerical simulations aiming to understand microscale-particle encounters in oceans and lakes. We explore a range of aspect ratios and sizes relevant to the dynamics of plankton and microplastics in water environments. The results presented here confirm that collision rates between elongated particles in a quiescent fluid are more frequent than those among spherical particles in turbulence due to oblique settling. We also demonstrate that turbulence generally enhances collisions among elongated particles as compared to those expected for a random distribution of the same particles settling in a quiescent fluid, although we also find a decrease in collision rates in turbulence for particles of the highest density and moderate aspect ratios (A = 5). The increase in the collision rate due to turbulence is found to quickly decrease with aspect ratio, reach a minimum for aspect ratios approximately equal to 5, and then slowly increase again, with an increase up to 50% for the largest aspect ratios investigated. This non-monotonic trend is explained as the result of two competing effects: the increase in the surface area with aspect ratio (beneficial to increase encounter rates) and the alignment of nearby prolate particles in turbulence (reducing the probability of collision). Turbulence mixing is, therefore, partially balanced by rod alignment at high particle aspect ratios. [ABSTRACT FROM AUTHOR]

We propose an analytical model to estimate the interface temperature $\varTheta _{\varGamma }$ and the Nusselt number $Nu$ for an evaporating two-layer Rayleigh–Bénard configuration in statistically stationary conditions. The model is based on three assumptions: (i) the Oberbeck–Boussinesq approximation can be applied to the liquid phase, while the gas thermophysical properties are generic functions of thermodynamic pressure, local temperature and vapour composition, (ii) the Grossmann–Lohse theory for thermal convection can be applied to the liquid and gas layers separately and (iii) the vapour content in the gas can be taken as the mean value at the gas–liquid interface. We validate this setting using direct numerical simulations in a parameter space composed of the Rayleigh number ($10^6\leq Ra\leq 10^8$) and the temperature differential ($0.05\leq \varepsilon \leq 0.20$), which modulates the variation of state variables in the gas layer. To better disentangle the variable property effects on $\varTheta _\varGamma$ and $Nu$ , simulations are performed in two conditions. First, we consider the case of uniform gas properties except for the gas density and gas–liquid diffusion coefficient. Second, we include the variation of specific heat capacity, dynamic viscosity and thermal conductivity using realistic equations of state. Irrespective of the employed setting, the proposed model agrees very well with the numerical simulations over the entire range of $Ra$ – $\varepsilon$ investigated. [ABSTRACT FROM AUTHOR]

The dynamics of droplet fragmentation in turbulence is described by the Kolmogorov-Hinze framework. Yet, a quantitative theory is lacking at higher concentrations when strong interactions between the phases and coalescence become relevant, which is common in most flows. Here, we address this issue through a fully-coupled numerical study of the droplet dynamics in a turbulent flow at Rλ ≈ 140, the highest attained up to now. By means of time-space spectral statistics, not currently accessible to experiments, we demonstrate that the characteristic scale of the process, the Hinze scale, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than this scale preferentially break up absorbing energy from the flow; smaller droplets, instead, undergo rapid oscillations and tend to coalesce releasing energy to the flow. Further, we link the droplet-size distribution with the probability distribution of the turbulent dissipation. This shows that key in the fragmentation process is the local flux of energy which dominates the process at large scales, vindicating its locality. Dynamics of droplet fragmentation in turbulence is described by the Kolmogorov-Hinze theory, but at higher concentrations common in most flows a quantitative theory is required. The authors use direct numerical simulations of turbulent multiphase flows finding that larger droplets break up absorbing energy from the flow, while smaller droplets undergo rapid oscillations and tend to coalesce releasing energy to the flow. [ABSTRACT FROM AUTHOR]

We present a new and efficient phase‐field solver for viscoelastic fluids with moving contact line based on a dual‐resolution strategy. The interface between two immiscible fluids is tracked by using the Cahn‐Hilliard phase‐field model, and the viscoelasticity incorporated into the phase‐field framework. The main challenge of this approach is to have enough resolution at the interface to approach the sharp‐interface methods. The method presented here addresses this problem by solving the phase field variable on a mesh twice as fine as that used for the velocities, pressure, and polymer‐stress constitutive equations. The method is based on second‐order finite differences for the discretization of the fully coupled Navier–Stokes, polymeric constitutive, and Cahn–Hilliard equations, and it is implemented in a 2D pencil‐like domain decomposition to benefit from existing highly scalable parallel algorithms. An FFT‐based solver is used for the Helmholtz and Poisson equations with different global sizes. A splitting method is used to impose the dynamic contact angle boundary conditions in the case of large density and viscosity ratios. The implementation is validated against experimental data and previous numerical studies in 2D and 3D. The results indicate that the dual‐resolution approach produces nearly identical results while saving computational time for both Newtonian and viscoelastic flows in 3D. [ABSTRACT FROM AUTHOR]

This study presents direct numerical simulations of turbulent Rayleigh–Bénard convection in non-colloidal suspensions, with special focus on the heat transfer modifications in the flow. Adopting a Rayleigh number of $10^8$ and Prandtl number of 7, parametric investigations of the particle volume fraction $0\leq \varPhi \leq 40\,\%$ and particle diameter $1/20\leq d^*_p\leq 1/10$ with respect to the cavity height, are carried out. The particles are neutrally buoyant, rigid spheres with physical properties that match the fluid phase. Up to $\varPhi =25\,\%$ , the Nusselt number increases weakly but steadily, mainly due to the increased thermal agitation that overcomes the decreased kinetic energy of the flow. Beyond $\varPhi =30\,\%$ , the Nusselt number exhibits a substantial drop, down to approximately 1/3 of the single-phase value. This decrease is attributed to the dense particle layering in the near-wall region, confirmed by the time-averaged local volume fraction. The dense particle layer reduces the convection in the near-wall region and negates the formation of any coherent structures within one particle diameter from the wall. Significant differences between $\varPhi \leq 30\,\%$ and 40 % are observed in all statistical quantities, including heat transfer and turbulent kinetic energy budgets, and two-point correlations. Special attention is also given to the role of particle rotation, which is shown to contribute to maintaining high heat transfer rates in moderate volume fractions. Furthermore, decreasing the particle size promotes the particle layering next to the wall, inducing a similar heat transfer reduction as in the highest particle volume fraction case. [ABSTRACT FROM AUTHOR]

We present a numerical study of emulsions in homogeneous and isotropic turbulence (HIT) at Reλ = 137. The problem is addressed via direct numerical simulations, where the volume of fluid is used to represent the complex features of the liquid–liquid interface. We consider a mixture of two iso-density fluids, where fluid properties are varied with the goal of understanding their role in turbulence modulation, in particular the volume fraction (0.03 < α < 0.5), viscosity ratio (0.01 < μd/μc < 100) and large-scale Weber number (10.6 < WeL < 106.5). The analysis, performed by studying integral quantities and spectral scale-by-scale analysis, reveals that energy is transported consistently from large to small scales by the interface, and no inverse cascade is observed. Furthermore, the total surface is found to be directly proportional to the amount of energy transported, while viscosity and surface tension alter the dynamic that regulates energy transport. We also observe the −10/3 and −3/2 scaling on droplet size distributions, suggesting that the dimensional arguments that led to their derivation are verified in HIT conditions. [ABSTRACT FROM AUTHOR]

We perform interface-resolved simulations of finite-size evaporating droplets in weakly compressible homogeneous shear turbulence. The study is conducted by varying three dimensionless physical parameters: the initial gas temperature over the critical temperature Tg,0/Tc, the initial droplet diameter over the Kolmogorov scale d0/η and the surface tension, i.e. the shear-basedWeber number, WeS. For the smallest WeS, we first discuss the impact on the evaporation rate of the three thermodynamic models employed to evaluate the gas thermophysical properties: a constant property model and two variable-properties approaches where either the gas density or all the gas properties are allowed to vary. Taking this last approach as reference, the model assuming constant gas properties and evaluated with the '1/3' rule is shown to predict the evaporation rate better than the model where the only variable property is the gas density. Moreover, we observe that the well-known Frössling/Ranz-Marshall correlation underpredicts the Sherwood number at low temperatures, Tg,0/Tc = 0.75. Next, we show that the ratio between the actual evaporation rate in turbulence and the one computed in stagnant conditions is always much higher than one for weakly deformable droplets: it decreases with Tg,0/Tc without approaching unity at the highest Tg,0/Tc considered. This suggests an evaporation enhancement due to turbulence also in conditions typical of combustion applications. Finally, we examine the overall evaporation rate and the local interfacial mass flux at higher WeS, showing a positive correlation between evaporation rate and interfacial curvature, especially at the lowest Tg,0/Tc. [ABSTRACT FROM AUTHOR]

This review is motivated by the fast progress in our understanding of the physics of particle-laden turbulence in the last decade, partly due to the tremendous advances of measurement and simulation capabilities. The focus is on spherical particles in homogeneous and canonical wall-bounded flows. The analysis of recent data indicates that conclusions drawn in zero gravity should not be extrapolated outside of this condition, and that the particle response time alone cannot completely define the dynamics of finite-size particles. Several breakthroughs have been reported, mostly separately, on the dynamics and turbulence modifications of small inertial particles in dilute conditions and of large weakly buoyant spheres. Measurements at higher concentrations, simulations fully resolving smaller particles, and theoretical tools accounting for both phases are needed to bridge this gap and allow for the exploration of the fluid dynamics of suspensions, from laminar rheology and granular media to particulate turbulence. [ABSTRACT FROM AUTHOR]

Direct numerical simulations are carried out to study the effect of finite Weissenberg number up to $Wi=16$ on laminar and turbulent channel flows of an elastoviscoplastic (EVP) fluid, at a fixed bulk Reynolds number of $2800$. The incompressible flow equations are coupled with the evolution equation for the EVP stress tensor by a modified Saramito model that extends both the Bingham viscoplastic and the finite extensible nonlinear elastic-Peterlin (FENE-P) viscoelastic models. In turbulent flow, we find that drag decreases with both the Bingham and Weissenberg numbers, until the flow laminarises at high enough elastic and yield stresses. Hence, a higher drag reduction is achieved than in the viscoelastic flow at the same Weissenberg number. The drag reduction persists at Bingham numbers up to 20, in contrast to viscoplastic flow, where the drag increases in the laminar regime compared with a Newtonian flow. Moreover, elasticity affects the laminarisation of an EVP flow in a non-monotonic fashion, delaying it at lower and promoting it at higher Weissenberg numbers. A hibernation phenomenon is observed in the EVP flow, leading to large changes in the unyielded regions. Finally, plasticity is observed to affect both low- and high-speed streaks equally, attenuating the turbulent dissipation and the fragmentation of turbulent structures. [ABSTRACT FROM AUTHOR]

We use interface-resolved simulations to study near-wall turbulence modulation by small inertial particles, much denser than the fluid, in dilute/semi-dilute conditions. We considered three bulk solid mass fractions, $\varPsi =0.34\,\%$ , $3.37\,\%$ and $33.7\,\%$ , with only the latter two showing turbulence modulation. The increase of the drag is strong at $\varPsi =3.37\,\%$ , but mild in the densest case. Two distinct regimes of turbulence modulation emerge: for smaller mass fractions, the turbulence statistics are weakly affected and the near-wall particle accumulation increases the drag so the flow appears as a single-phase flow at slightly higher Reynolds number. Conversely, at higher mass fractions, the particles modulate the turbulent dynamics over the entire flow, and the interphase coupling becomes more complex. In this case, fluid Reynolds stresses are attenuated, but the inertial particle dynamics near the wall increases the drag via correlated velocity fluctuations, leading to an overall drag increase. Hence, we conclude that, although particles at high mass fractions reduce the fluid turbulent drag, the solid phase inertial dynamics still increases the overall drag. However, inspection of the streamwise momentum budget in the two-way coupling limit of vanishing volume fraction, but finite mass fraction, indicates that this trend could reverse at even higher particle load. [ABSTRACT FROM AUTHOR]

We perform immersed-boundary-method numerical simulations of small amplitude oscillatory shear flow of suspensions of monodisperse noncolloidal rigid spherical particles in non-Newtonian liquids from the dilute to the concentrated regime. We study the influence of suspending liquid inertia and rheology and particle concentration on the computationally measured storage and loss moduli of the suspensions. In particular, the rheology of the suspending liquid is modeled through the inelastic shear-thinning Carreau–Yasuda constitutive equation and the viscoelastic Giesekus and Oldroyd-B constitutive equations. The role of inertia is quantified by the Stokes number, St, whereas the relevance of the non-Newtonian effects of the suspension matrix is measured through the Carreau number, Cu, for the Carreau–Yasuda liquid and the Deborah number, De, for the viscoelastic liquids. In suspensions with a Carreau–Yasuda matrix, both the storage and the loss modulus increase with St and decrease with Cu, yet the order of magnitude of Cu has to be greater than unity for these effects to be visible. In suspensions with a viscoelastic matrix, both the moduli increase with St and have a nonmonotonic trend with De, showing a maximum with no quantitative differences between the results pertaining suspensions with Giesekus and Oldroyd-B constitutive equations. [ABSTRACT FROM AUTHOR]

We study the effect of droplet coalescence on turbulent wall-bounded flows by means of direct numerical simulations. In particular, the volume-of-fluid and front-tracking methods are used to simulate turbulent channel flows containing coalescing and non-coalescing droplets, respectively. We find that coalescing droplets have a negligible effect on the drag, whereas the non-coalescing ones steadily increase drag as the volume fraction of the dispersed phase increases: indeed, at 10% volume fraction, the non-coalescing droplets show a 30% increase in drag, whereas the coalescing droplets show less than 4% increase. We explain this by looking at the wall-normal location of droplets in the channel and show that non-coalescing droplets enter the viscous sublayer, generating an interfacial shear stress, which reduces the budget for viscous stress in the channel. On the other hand, coalescing droplets migrate toward the bulk of the channel forming large aggregates, which hardly affect the viscous shear stress while damping the Reynolds shear stress. We prove this by relating the mean viscous shear stress integrated in the wall-normal direction to the centerline velocity. [ABSTRACT FROM AUTHOR]

We analyze a suspension of deformable particles in a pressure-driven flow. The suspension is composed of neutrally buoyant initially spherical particles and a Newtonian carrier fluid, and the flow is solved by means of direct numerical simulations, using a fully Eulerian method based on a one-continuum formulation. The solid phase is modeled with an incompressible viscous hyperelastic constitutive relation, and the flow is characterized by three main dimensionless parameters, namely the solid volume fraction, the Reynolds and capillary numbers. The dependency of the effective viscosity on these three quantities is investigated to study the inertial effects on a suspension of deformable particles. It can be observed that the suspension has a shear-thinning behavior, and the reduction in effective viscosity for high shear rates is emphasized in denser configurations. The separate analysis of the Reynolds and capillary numbers reveal that the effective viscosity depends more on the capillary than on the Reynolds number. In addition, our simulations exhibit a consistent tendency for deformable particles to move toward the center of the channel, where the shear rate is low. This phenomenon is particularly marked for very dilute suspensions, where a whole region near the wall is empty of particles. Furthermore, when the volume fraction is increased this near-wall region is gradually occupied, because of higher mutual particle interactions. Deformability also plays an important role in the process. Indeed, at high capillary numbers, particles are more sensitive to shear rate variations and can modify their shape more easily to accommodate a greater number of particles in the central region of the channel. Finally, the total stress budgets show that the relative particle-induced stress contribution increases with the volume fraction and Reynolds number, and decreases with the particle deformability. [ABSTRACT FROM AUTHOR]

We perform interface-resolved simulations to study the modulation of statistically steady-state homogeneous shear turbulence by neutrally buoyant finite-size particles. We consider two shapes, spheres and oblates, and various solid volume fractions, up to 20%. The results show that a statistically steady state is not exclusive to single-phase homogeneous shear turbulence as the production and dissipation rates of the turbulent kinetic energy are also statistically in balance in particle-laden cases. The turbulent kinetic energy shows a non-monotonic behaviour with increasing solid volume fraction: increasing turbulence attenuation up to a certain concentration of solid particles and then enhancement of the turbulent kinetic energy at higher concentrations. This behaviour is observed at lower volume fractions for oblate particles than for spheres. The attenuation of the turbulence activity at lower volume fractions is explained through the enhancement of the dissipation rate close to the surface of particles. At higher volume fractions, however, particle pair interactions induce regions of high Reynolds shear stress, resulting in the enhancement of the turbulence activity. We show that the oblate particles of the considered size have larger rotational rates than spheres with no preferential orientation. This is in contrast to previous studies in wall-bounded flows where preferential orientation close to the wall and reduced rotation rates result in turbulence attenuation and thus drag reduction. Our results shed some light on the effect of rigid particles, smaller than the near-wall turbulent structures but still comparable to the viscous length scale, on the dynamics of the equilibrium logarithmic layer in wall-bounded flows. [ABSTRACT FROM AUTHOR]

We perform three-dimensional numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross-shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross-shear flow is a secondary flow with amplitude 10 % of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modelled using the elastoviscoplastic constitutive laws proposed by Saramito (J. Non-Newtonian Fluid Mech., vol. 158 (1–3), 2009, pp. 154–161). The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary method. Our results show that the fore–aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross-shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross-shear flow cannot be derived from the pure sedimentation drag law owing to the nonlinear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction. [ABSTRACT FROM AUTHOR]

We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, in turn, amplify the turbulent Reynolds stresses in the fluid. At a very low Reynolds number, the only production term is due to the energy input from the elastic wall, which increases with the wall elasticity. This mechanism may be exploited to passively enhance mixing in microfluidic devices. [ABSTRACT FROM AUTHOR]

We use interface-resolved direct numerical simulations to study the dynamics of a single sediment particle in a turbulent open channel flow over a fixed porous bed. The relative strength of the gravitational acceleration, quantified by the Galileo number, is varied so as to reproduce the different modes of sediment transport – resuspension, saltation and rolling. The results show that the sediment dynamics at lower Galileo numbers (i.e. resuspension and saltation) are mainly governed by the mean flow. Here, the regime of motion can be predicted by the ratio between the gravity and the shear-induced boundary force. In these cases, the sediment particle rapidly takes off when exposed to the flow, and proceeds with an oscillatory motion. Increasing the Galileo number, the frequency of these oscillations increases and their amplitude decreases, until the transport mode switches from resuspension to saltation. In this case, the sediment travels by short successive collisions with the bed. Further increasing the Galileo number, the particle rolls without detaching from the bed. Differently from the previous modes, the motion is triggered by extreme turbulent events, and the particle response depends on the specific initial conditions, at fixed Reynolds number. The results reveal that close to the onset of sediment motion, only turbulent sweeps can effectively trigger the particle motion by increasing the stagnation pressure upstream. We show that for the parameters in this study, a criterion based on the streamwise flow-induced force can successfully predict the incipient movement. [ABSTRACT FROM AUTHOR]

In the present study, a simple method is developed to apply astigmatism particle tracking velocimetry (APTV) to transparent particles utilizing backlight illumination. Here, a particle acts as ball lens and bundles the light to a focal point, which is used to determine the particle's out-of-plane position. Due to the distance between focal point and particle, additional features have to be considered in ball lens astigmatism particle tracking velocimetry (BLAPTV) compared to conventional APTV. We describe required calibration steps and perform parameter studies to show how the autocorrelation coefficient and the light exposure affect the accuracy of the method. It is found that the accuracy and robustness of the Euclidean calibration approach as also used in conventional APTV (Cierpka et al. in Meas Sci Technol 22(1):015401, 2010a) can be increased if an additional calibration curve for the light intensity of the particle's focal point is considered. In addition, we study the influence of the particle diameter and the refractive index jump between liquid and particles on the calibration curves and the accuracy. In this way, particles of the same size, but different material, can be distinguished by their calibration curve. Furthermore, an approach is presented to account for shape changes of the calibration curve along the depth of the measurement volume. Overall, BLAPTV provides high out-of-plane particle reconstruction accuracies with respect to the particle diameter. In test cases, position uncertainties down to 1.8% of the particle diameter are achieved for particles of d p = 124 μ m . The measurement technique is validated for a laminar flow in a straight rectangular channel with a cross-sectional area of 2.3 × 30 mm 2 . Uncertainties of 0.75% for the in-plane and 2.29% for out-of-plane velocity with respect to the maximum streamwise velocity are achieved. Graphic abstract [ABSTRACT FROM AUTHOR]

The flapping states of a flexible fiber fully coupled to a three-dimensional turbulent flow are investigated via state-of-the-art numerical methods. Two distinct flapping regimes are predicted by the phenomenological theory recently proposed by Rosti et al. (Phys. Rev. Lett. 121:044501, 2018) the under-damped regime, where the elasticity strongly affects the fiber dynamics, and the over-damped regime, where the elastic effects are strongly inhibited. In both cases we can identify a critical value of the bending rigidity of the fiber by a resonance condition, which further provides a distinction between different flapping behaviors, especially in the under-damped case. We validate the theory by means of direct numerical simulations and find that, both for the over-damped regime and for the under-damped one, fibers are effectively slaved to the turbulent fluctuations and can therefore be used as a proxy to measure various two-point statistics of turbulence. Finally, we show that this holds true also in the case of a passive fiber, without any feedback force on the fluid. [ABSTRACT FROM AUTHOR]

A numerical and theoretical study of yield-stress fluid flows in two types of model porous media is presented. We focus on viscoplastic and elastoviscoplastic flows to reveal some differences and similarities between these two classes of flows. Small elastic effects increase the pressure drop and also the size of unyielded regions in the flow which is the consequence of different stress solutions compare to viscoplastic flows. Yet, the velocity fields in the viscoplastic and elastoviscoplastic flows are comparable for small elastic effects. By increasing the yield stress, the difference in the pressure drops between the two classes of flows becomes smaller and smaller for both considered geometries. When the elastic effects increase, the elastoviscoplastic flow becomes time-dependent and some oscillations in the flow can be observed. Focusing on the regime of very large yield stress effects in the viscoplastic flow, we address in detail the interesting limit of 'flow/no flow': yield-stress fluids can resist small imposed pressure gradients and remain quiescent. The critical pressure gradient which should be exceeded to guarantee a continuous flow in the porous media will be reported. Finally, we propose a theoretical framework for studying the 'yield limit' in the porous media. [ABSTRACT FROM AUTHOR]

We perform immersed-boundary-method numerical simulations of oscillatory shear flow of suspensions of mono-disperse non-colloidal rigid spherical particles in a Newtonian liquid from the dilute to the concentrated regime. Both small and large amplitude oscillatory shear flow (SAOS and LAOS, respectively) are studied and the effects of particle concentration, fluid inertia, particle-to-fluid density ratio, and deformation amplitude on the measured apparent viscoelastic moduli of the suspensions are quantified. In the SAOS regime, a non-zero storage modulus G ′ is always detected: inertia acts as an apparent elasticity. G ′ -values significantly change with inertia, but depend on the volume fraction of the solid phase only for suspensions of particles denser than the fluid. On the other hand, the loss modulus G ′ ′ increases with both inertia and particle concentration. In the LAOS regime, the moduli are only weakly dependent on the deformation amplitude for a dilute suspension, whereas non-monotonic variations are observed at high concentrations. [ABSTRACT FROM AUTHOR]

We study the settling of finite-size rigid spheres in quiescent fluid and in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We consider semi-dilute and dense suspensions of rigid spheres with solid volume fractions ϕ=0.5-10%, solid-to-fluid density ratio R=1.02, and Galileo number (i.e., the ratio between buoyancy and viscous forces) Ga=145. In HIT, the nominal Reynolds number based on the Taylor microscale is Reλ≃90, and the ratio between the particle diameter and the nominal Kolmogorov scale is (2a)/η≃12 (being a the particle radius). We find that in HIT the mean settling speed is less than that in quiescent fluid for all ϕ. For ϕ=0.5%, the mean settling speed in HIT is 8% less than in quiescent fluid. However, by increasing the volume fraction the difference in the mean settling speed between quiescent fluid and HIT cases reduces, being only 1.7% for ϕ=10%. Indeed, while at low ϕ the settling speed is strongly altered by the interaction with turbulence, at large ϕ this is mainly determined by the (strong) hindering effect. This is similar in quiescent fluid and in HIT, leading to similar mean settling speeds. On the contrary, particle angular velocities are always found to increase with ϕ. These are enhanced by the interaction with turbulence, especially at low ϕ. In HIT, the correlations of particle lateral velocity fluctuations oscillate around zero before decorrelating completely. The time period of the oscillation seems proportional to the ratio between the integral lengthscale of turbulence and the particle characteristic terminal velocity. Regarding the mean square particle displacement, we find that it is strongly enhanced by turbulence in the direction perpendicular to gravity, even at the largest ϕ. Finally, we investigate the collision statistics for all cases and find the interesting result that the collision frequency is larger in quiescent fluid than in HIT for ϕ=0.5-1%. This is due to frequent drafting-kissing-tumbling events in quiescent fluid. The collision frequency becomes instead larger in HIT than in still fluid for ϕ=5-10%, due to the larger relative approaching velocities in HIT, and to the less intense drafting-kissing-tumbling events in quiescent fluid. The collision frequency also appears to be almost proportional to the estimate for small inertial particles uniformly distributed in space, though much smaller. Concerning the turbulence modulation, we find that the mean energy dissipation increases almost linearly with ϕ, leading to a large reduction of Reλ. [ABSTRACT FROM AUTHOR]

We present a modification of a recently developed volume of fluid method for multiphase problems (Ii et al. in J Comput Phys 231(5):2328-2358, 2012), so that it can be used in conjunction with a fractional-step method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity μ on the volume fraction Φ (from 10 to 30%) and the Capillary number Ca (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decreases with the deformation and the applied shear (shear-thinning) while exhibiting a non-monotonic behavior with respect to the volume fraction. We report the appearance of a maximum in the effective viscosity curve and compare the results with those of suspensions of rigid and deformable particles and capsules. We show that the flow in the solvent is mostly a shear flow, while it is mostly rotational in the suspended phase; moreover, this behavior tends to reverse as the volume fraction increases. Finally, we evaluate the contributions to the total shear stress of the viscous stresses in the two fluids and of the interfacial force between them. [ABSTRACT FROM AUTHOR]

We have performed direct numerical simulation of the turbulent flow of a polymer solution in a square duct, with the FENE-P model used to simulate the presence of polymers. First, a simulation at a fixed moderate Reynolds number is performed and its results compared with those of a Newtonian fluid to understand the mechanism of drag reduction and how the secondary motion, typical of the turbulent flow in non-axisymmetric ducts, is affected by polymer additives. Our study shows that the Prandtl's secondary flow is modified by the polymers: the circulation of the streamwise main vortices increases and the location of the maximum vorticity moves towards the centre of the duct. In-plane fluctuations are reduced while the streamwise ones are enhanced in the centre of the duct and dumped in the corners due to a substantial modification of the quasi-streamwise vortices and the associated near-wall low- and high-speed streaks; these grow in size and depart from the walls, their streamwise coherence increasing. Finally, we investigated the effect of the parameters defining the viscoelastic behaviour of the flow and found that the Weissenberg number strongly influences the flow, with the cross-stream vortical structures growing in size and the in-plane velocity fluctuations reducing for increasing flow elasticity. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a three‐dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time three‐dimensional simulations of inertial and turbulent EVP fluids with a large number particles and droplets. This is achieved by combining fast and highly scalable methods such as an FFT‐based pressure solver, with the evolution equation for non‐Newtonian (including EVP) stresses. In this flexible computational framework, the fluid can be modeled by either Oldroyd‐B, neo‐Hookean, FENE‐P, or Saramito EVP models, and the additional equations for the non‐Newtonian stresses are fully coupled with the flow. The rigid particles are discretized on a moving Lagrangian grid, whereas the flow equations are solved on a fixed Eulerian grid. The solid particles are represented by an immersed boundary method with a computationally efficient direct forcing method, allowing simulations of a large numbers of particles. The immersed boundary force is computed at the particle surface and then included in the momentum equations as a body force. The droplets and soft particles on the other hand are simulated in a fully Eulerian framework, the former with a level‐set method to capture the moving interface and the latter with an indicator function. The solver is first validated for various benchmark single‐phase and two‐phase EVP flow problems through comparison with data from the literature. Finally, we present new results on the dynamics of a buoyancy‐driven drop in an EVP fluid. We develop an efficient solver for the direct numerical simulations of viscoelastic and elastoviscoplastic multiphase flows. The solver is validated for various benchmark single‐phase and two‐phase elastoviscoplastic flow problems. We study a Newtonian droplet rising in an elastoviscoplastic fluid and show the appearance of a negative wake. [ABSTRACT FROM AUTHOR]

We report experimental observations of turbulent flow with spherical particles in a square duct. Three particle sizes, namely 2H=dp D 40, 16 and 9 (2H being the duct full height and dp being the particle diameter), are investigated. The particles are nearly neutrally buoyant with a density ratio of 1.0035 and 1.01 with respect to the suspending fluid. Refractive index matched--particle image velocimetry (RIM--PIV) is used for fluid velocity measurement even at the highest particle volume fraction (20 %) and particle tracking velocimetry (PTV) for the particle velocity statistics for the flows seeded with particles of the two largest sizes, whereas only pressure measurements are reported for the smallest particles. Settling effects are seen at the lowest bulk Reynolds number Re2H ≈ 10 000, whereas, at the highest Re2H ≈ 27 000, particles are in almost full suspension. The friction factor of the suspensions is found to be significantly larger than that of single-phase duct flow at the lower Re2H investigated; however, the difference decreases when increasing the flow rate and the total drag approaches the values of the single-phase flow at the higher Reynolds number considered, Re2H = 27 000. The pressure drop is found to decrease with the particle diameter for volume fractions lower than ϕ = 10% for nearly all Re2H investigated. However, at the highest volume fraction ϕ = 20 %, we report a peculiar non-monotonic behaviour: the pressure drop first decreases and then increases with increasing particle size. The decrease of the turbulent drag with particle size at the lowest volume fractions is related to an attenuation of the turbulence. The drag increase for the two largest particle sizes at ϕ = 20 %, however, occurs despite this large reduction of the turbulent stresses, and it is therefore due to significant particle-induced stresses. At the lowest Reynolds number, the particles reside mostly in the bottom half of the duct, where the mean velocity significantly decreases; the flow is similar to that in a moving porous bed near the bottom wall and to turbulent duct flow with low particle concentration near the top wall. [ABSTRACT FROM AUTHOR]

Keywords: Particle/fluid flows EN Particle/fluid flows 1 3 3 07/25/20 20200525 NES 200525 Equation (2.10) in Costa, Brandt & Picano ([1]) for the lift force model used in the point-particle direct numerical simulations (DNS), and which is derived from the classical lift force of Saffman ([4]), 1 Graph $$\begin{eqnarray}\boldsymbol{F} {l}=1.615J\unicode[STIX]{x1D707}D|\boldsymbol{U} {s}|\sqrt{\frac{D^{2}|\unicode[STIX]{x1D74E}|}{\unicode[STIX]{x1D708}}}\frac{\unicode[STIX]{x1D74E}\times \boldsymbol{U} {s}}{|\unicode[STIX]{x1D74E}|\,|\boldsymbol{U} {s}|},\end{eqnarray}$$ does not correspond to the force model actually used in the point-particle DNS with lift force presented in the manuscript. Instead, the following equation was used: 2 Graph $$\begin{eqnarray}\boldsymbol{F} {l}=1.615J\unicode[STIX]{x1D707}|\unicode[STIX]{x1D74E}|D^{2}\sqrt{\frac{D^{2}|\unicode[STIX]{x1D74E}|}{\unicode[STIX]{x1D708}}}\frac{\unicode[STIX]{x1D74E}\times \boldsymbol{U} {s}}{|\unicode[STIX]{x1D74E}|\,|\boldsymbol{U} {s}|},\end{eqnarray}$$ which replaces the first occurrence of the term Graph $|\boldsymbol{U} {s}|$ on the right-hand-side of (1) with Graph $|\unicode[STIX]{x1D74E}|D$. We recall that two cases were considered in the manuscript depending on the value of Graph $J$ in the lift force equation: Graph $J=1$ in the case denoted PP-Saffman; and Graph $J$ given by 3 Graph $$\begin{eqnarray}J=0.3\left(1+\tanh \left[{\textstyle \frac{5}{2}}\left(\log {10}\unicode[STIX]{x1D700}+0.191\right)\right]\right)\left({\textstyle \frac{2}{3}}+\tanh (6\unicode[STIX]{x1D700}-1.92)\right),\end{eqnarray}$$ with Graph $\unicode[STIX]{x1D700}=\sqrt{|\unicode[STIX]{x1D74E}|\unicode[STIX]{x1D708}}/|\boldsymbol{U} {s}|$, in the case denoted PP-McLaughlin. [Extracted from the article]

We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions (0.1 ≤ Φ ≤ 0.4) and particle Reynolds numbers (0.1 ≤ Rep ≤ 10). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal Φ. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter's mean value with the values estimated from the homogenisation theory of Chateau et al. (J. Rheol., vol. 52, 2008, pp. 489-506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the Rep. The wide spectrum of the local shear rate and its dependency on Φ and Rep point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, O(Rep) ~ 10. [ABSTRACT FROM AUTHOR]

We study the turbulent square duct flow of dense suspensions of neutrally buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions φ = 0-0.2, using the immersed boundary method (IBM) to account for the dispersed phase. Based on the hydraulic diameter a Reynolds number of 5600 is considered. We observe that for φ = 0.05 and 0.1, particles preferentially accumulate on the corner bisectors, close to the corners, as also observed for laminar square duct flows of the same duct-to-particle size ratio. At the highest volume fraction, particles preferentially accumulate in the core region. For plane channel flows, in the absence of lateral confinement, particles are found instead to be uniformly distributed across the channel. The intensity of the cross-stream secondary flows increases (with respect to the unladen case) with the volume fraction up to φ = 0.1, as a consequence of the high concentration of particles along the corner bisector. For φ = 0.2 the turbulence activity is reduced and the intensity of the secondary flows reduces to below that of the unladen case. The friction Reynolds number increases with φ in dilute conditions, as observed for channel flows. However, for φ = 0.2 the mean friction Reynolds number is similar to that for φ = 0.1. By performing the turbulent kinetic energy budget, we see that the turbulence production is enhanced up to φ = 0.1, while for φ = 0.2 the production decreases below the values for φ = 0.05. On the other hand, the dissipation and the transport monotonically increase with φ. The interphase interaction term also contributes positively to the turbulent kinetic energy budget and increases monotonically with φ, in a similar way as the mean transport. Finally, we show that particles move on average faster than the fluid. However, there are regions close to the walls and at the corners where they lag behind it. In particular, for φ = 0.05, 0.1, the slip velocity distribution at the corner bisectors seems correlated to the locations of maximum concentration: the concentration is higher where the slip velocity vanishes. The wall-normal hydrodynamic and collision forces acting on the particles push them away from the corners. The combination of these forces vanishes around the locations of maximum concentration. The total mean forces are generally low along the corner bisectors and at the core, also explaining the concentration distribution for φ = 0.2. [ABSTRACT FROM AUTHOR]

Subglacial discharges have been observed to generate buoyant plumes along the ice face of Greenland tidewater glaciers. These plumes have been traditionally modeled using classical plume theory, and their characteristic parameters (e.g., velocity) are employed in the widely used three-equation melt parameterization. However, the applicability of plume theory for three-dimensional turbulent wall plumes is questionable because of the complex near-wall plume dynamics. In this study, corrections to the classical plume theory are introduced to account for the presence of a wall. In particular, the drag and entrainment coefficients are quantified for a three-dimensional turbulent wall plume using data fromdirect numerical simulations. The drag coefficient is found to be an order of magnitude larger than that for a boundary layer flow over a flat plate at a similar Reynolds number. This result suggests a significant increase in the melting estimates by the current parameterization. However, the volume flux in a wall plume is found to be one-half that of a conical plume that has 2 times the buoyancy flux. This finding suggests that the total entrainment (per unit area) of ambient water is the same and that the plume scalar characteristics (i.e., temperature and salinity) can be predicted reasonably well using classical plume theory. [ABSTRACT FROM AUTHOR]

We study the settling of rigid oblates in a quiescent fluid using interface-resolved direct numerical simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication correction and collision models to account for short-range particle-particle interactions. We consider semi-dilute suspensions of oblate particles with aspect ratio AR D 1=3 and solid volume fractions ϕ D 0:5-10 %. The solid-to-fluid density ratio R D 1:02 and the Galileo number (i.e. the ratio between buoyancy and viscous forces) based on the diameter of a sphere with equivalent volume Ga D 60. With this choice of parameters, an isolated oblate falls vertically with a steady wake with its broad side perpendicular to the gravity direction. At this Ga, the mean settling speed of spheres is a decreasing function of the volume ϕ and is always smaller than the terminal velocity of the isolated particle, Vt. On the contrary, in dilute suspensions of oblate particles (with ϕ ≤ 1 %), the mean settling speed is approximately 33% larger than Vt. At higher concentrations, the mean settling speed decreases becoming smaller than the terminal velocity Vt between ϕ D 5% and 10 %. The increase of the mean settling speed is due to the formation of particle clusters that for ϕ D0:5-1% appear as columnar-like structures. From the pair distribution function we observe that it is most probable to find particle pairs almost vertically aligned. However, the pair distribution function is non-negligible all around the reference particle indicating that there is a substantial amount of clustering at radial distances between 2 and 6c (with c the polar radius of the oblate). Above ϕ D5 %, the hindrance becomes the dominant effect, and the mean settling speed decreases below Vt. As the particle concentration increases, the mean particle orientation changes and the mean pitch angle (the angle between the particle axis of symmetry and gravity) increases from 23° to 47°. Finally, we increase Ga from 60 to 140 for the case with ϕ D 0:5% and find that the mean settling speed (normalized by Vt) decreases by less than 1% with respect to GaD60. However, the fluctuations of the settling speed around the mean are reduced and the probability of finding vertically aligned particle pairs increases. [ABSTRACT FROM AUTHOR]

The authors study the condensational growth of cloud droplets in homogeneous isotropic turbulence by means of a large-eddy simulation (LES) approach. The authors investigate the role of a mean updraft velocity and of the chemical composition of the cloud condensation nuclei (CCN) on droplet growth. The results show that a mean constant updraft velocity superimposed onto a turbulent field reduces the broadening of the droplet size spectra induced by the turbulent fluctuations alone. Extending the authors' previous results regarding stochastic condensation, the authors introduce a new theoretical estimation of the droplet size spectrum broadening that accounts for this updraft velocity effect. A similar reduction of the spectra broadening is observed when the droplets reach their critical size, which depends on the chemical composition of CCN. The analysis of the square of the droplet radius distribution, proportional to the droplet surface, shows that for large particles the distribution is purely Gaussian, while it becomes strongly non-Gaussian for smaller particles, with the left tail characterized by a peak around the haze activation radius. This kind of distribution can significantly affect the later stages of the droplet growth involving turbulent collisions, since the collision probability kernel depends on the droplet size, implying the need for new specific closure models to capture this effect. [ABSTRACT FROM AUTHOR]

We perform numerical simulations of a turbulent channel flow over an hyper-elastic wall. In the fluid region the flow is governed by the incompressible Navier-Stokes (NS) equations, while the solid is a neo-Hookean material satisfying the incompressible Mooney-Rivlin law. The multiphase flow is solved with a one-continuum formulation, using a monolithic velocity field for both the fluid and solid phase, which allows the use of a fully Eulerian formulation. The simulations are carried out at Reynolds bulk Re = 2800 and examine the effect of different elasticity and viscosity of the deformable wall. We show that the skin friction increases monotonically with the material elastic modulus. The turbulent flow in the channel is affected by the moving wall even at low values of elasticity since non-zero fluctuations of vertical velocity at the interface influence the flow dynamics. The near-wall streaks and the associated quasi-streamwise vortices are strongly reduced near a highly elastic wall while the flow becomes more correlated in the spanwise direction, similarly to what happens for flows over rough and porous walls. As a consequence, the mean velocity profile in wall units is shifted downwards when shown in logarithmic scale, and the slope of the inertial range increases in comparison to that for the flow over a rigid wall. We propose a correlation between the downward shift of the inertial range, its slope and the wall-normal velocity fluctuations at the wall, extending results for the flow over rough walls. We finally show that the interface deformation is determined by the fluid fluctuations when the viscosity of the elastic layer is low, while when this is high the deformation is limited by the solid properties. [ABSTRACT FROM AUTHOR]

This study reports the results of large-eddy simulations of an axisymmetric turbulent buoyant plume in a stratified fluid. The configuration used is an idealized model of the plume generated by a subglacial discharge at the base of a tidewater glacier with an ambient stratification typical of Greenland fjords. The plume is discharged from a round source of various diameters and characteristic stratifications for summer and winter are considered. The classical theory for the integral parameters of a turbulent plume in a homogeneous fluid gives accurate predictions in the weakly stratified lower layer up to the pycnocline, and the plume dynamics are not sensitive to changes in the source diameter. In winter, when the stratification is similar to an idealized two-layer case, turbulent entrainment and generation of internal waves by the plume top are in agreement with the theoretical and numerical results obtained for turbulent jets in a two-layer stratification. In summer, instead, the stratification is more complex and turbulent entrainment by the plume top is significantly reduced. The subsurface layer in summer is characterized by a strong density gradient and the oscillating plume generates internal waves that might serve as an indicator of submerged plumes not penetrating to the surface. [ABSTRACT FROM AUTHOR]

We study numerically the inertial migration of a single rigid sphere and an oblate spheroid in straight square and rectangular ducts. A highly accurate interface-resolved numerical algorithm is employed to analyse the entire migration dynamics of the oblate particle and compare it with that of the sphere. Similarly to the inertial focusing of spheres, the oblate particle reaches one of the four face-centred equilibrium positions, however they are vertically aligned with the axis of symmetry in the spanwise direction. In addition, the lateral trajectories of spheres and oblates collapse into an equilibrium manifold before ending at the equilibrium positions, with the equilibrium manifold tangential to lines of constant background shear for both sphere and oblate particles. The differences between the migration of the oblate and sphere are also presented, in particular the oblate may focus on the diagonal symmetry line of the duct cross-section, close to one of the corners, if its diameter is larger than a certain threshold. Moreover, we show that the final orientation and rotation of the oblate exhibit chaotic behaviour for Reynolds numbers beyond a critical value. Finally, we document that the lateral motion of the oblate particle is less uniform than that of the spherical particle due to its evident tumbling motion throughout the migration. In a square duct, the strong tumbling motion of the oblate in the first stage of the migration results in a lower lateral velocity and consequently longer focusing length with respect to that of the spherical particle. The opposite is true in a rectangular duct where the higher lateral velocity of the oblate in the second stage of the migration, with negligible tumbling, gives rise to shorter focusing lengths. These results can help the design of microfluidic systems for bioapplications. [ABSTRACT FROM AUTHOR]

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, Ga. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio ρp=ρf. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6%-60% with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations u0 is decreased. Analysing the fluid-particle relative motion, we find that the mean settling speed is progressively reduced while reducing ρp=ρf due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6%-10%. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all Ga if time is scaled by .2a/=u' (where 2a is the particle diameter and u0 is the turbulence velocity root mean square). [ABSTRACT FROM AUTHOR]

The behavior of an axisymmetric vertical turbulent jet in an unconfined stratified environment is studied by means of well-resolved, large-eddy simulations. The stratification is two uniform layers separated by a thermocline. This study considers two cases: when the thermocline thickness is small and on the order of the jet diameter at the thermocline entrance. The Froude number of the jet at the thermocline varies from 0.6 to 1.9, corresponding to the class of weak fountains. The mean jet penetration, stratified turbulent entrainment, jet oscillations, and the generation of internal waves are examined. The mean jet penetration is predicted well by a simple model based on the conservation of the source energy in the thermocline. The entrainment coefficient for the thin thermocline is consistent with the theoretical model for a two-layer stratification with a sharp interface, while for the thick thermocline entrainment is larger at low Froude numbers. The data reveal the presence of a secondary horizontal flow in the upper part of the thick thermocline, resulting in the entrainment of fluid from the thermocline rather than from the upper stratification layer. The spectra of the jet oscillations in the thermocline display two peaks, at the same frequencies for both stratifications at fixed Froude number. For the thick thermocline, internal waves are generated only at the lower frequency, since the higher peak exceeds the maximal buoyancy frequency. For the thin thermocline, conversely, the spectra of the internal waves show the two peaks at low Froude numbers, whereas only one peak at the lower frequency is observed at higher Froude numbers. [ABSTRACT FROM AUTHOR]

Direct numerical simulations (DNS) of particle-laden turbulent flow in straight, mildly curved and strongly bent pipes are performed in which the solid phase is modelled as small heavy spherical particles. A total of seven populations of dilute particles with different Stokes numbers, one-way coupled with their carrier phase, are simulated. The objective is to examine the effect of the curvature on micro-particle transport and accumulation. It is shown that even a slight non-zero curvature in the flow configuration strongly impact the particle concentration map such that the concentration of inertial particles with bulk Stokes number 0:45 (based on bulk velocity and pipe radius) at the inner bend wall of mildly curved pipe becomes 12:8 times larger than that in the viscous sublayer of the straight pipe. Near-wall helicoidal particle streaks are observed in the curved configurations with their inclination varying with the strength of the secondary motion of the carrier phase. A reflection layer, as previously observed in particle laden turbulent S-shaped channels, is also apparent in the strongly curved pipe with heavy particles. In addition, depending on the curvature, the central regions of the mean Dean vortices appear to be completely depleted of particles, as observed also in the partially relaminarised region at the inner bend. The turbophoretic drift of the particles is shown to be affected by weak and strong secondary motions of the carrier phase and geometry-induced centrifugal forces. The first- and second-order moments of the velocity and acceleration of the particulate phase in the same configurations are addressed in a companion paper by the same authors. The current data set will be useful for modelling particles advected in wall-bounded turbulent flows where the effects of the curvature are not negligible. [ABSTRACT FROM AUTHOR]

We study the dynamics of dilute micro-size inertial particles in turbulent curved pipe flows of different curvature by means of direct numerical simulations with one-way coupled Lagrangian particle tracking. The focus of this work is on the first and second order moments of the velocity and acceleration of the particulate phase, relevant statistics for any modelling effort, whereas the particle distribution is analysed in a previous companion paper. The aim is to understand the role of the cross-stream secondary motions (Dean vortices) on the particle dynamics. We identify the mean Dean vortices associated to the motion of the particles and show that these are moved towards the side-walls and, interestingly, more intense than those of the mean flow. Analysis of the streamwise particle flux reveals a substantial increase due to the secondary motions that brings particles towards the pipe core while moving them towards the outer bend. The in-plane particle flux, most intense in the flow viscous sub-layer along the side walls, increases with particle inertia and pipe curvature. The particle reflections at the outer bend, previously observed also in other strongly curved configurations, locally alter the particle axial and wall-normal velocity and increase turbulent kinetic energy. [ABSTRACT FROM AUTHOR]

The motion of an initially spherical capsule in a wall-bounded oscillating shear flow is investigated via an accelerated boundary integral implementation. The neo-Hookean model is used as the constitutive law of the capsule membrane. The maximum wallnormal migration is observed when the oscillation period of the imposed shear is of the order of the relaxation time of the elastic membrane; hence, the optimal capillary number scales with the inverse of the oscillation frequency and the ratio agrees well with the theoretical prediction in the limit of high-frequency oscillation. The migration velocity decreases monotonically with the frequency of the applied shear and the capsule-wall distance. We report a significant correlation between the capsule lateral migration and the normal stress difference induced in the flow. The periodic variation of the capsule deformation is roughly in phase with that of the migration velocity and normal stress difference, with twice the frequency of the imposed shear. The maximum deformation increases linearly with the membrane elasticity before reaching a plateau at higher capillary numbers when the deformation is limited by the time over which shear is applied in the same direction and not by the membrane deformability. The maximum membrane deformation scales as the distance to the wall to the power 1/3 as observed for capsules and droplets in near-wall steady shear flows. [ABSTRACT FROM AUTHOR]

We study the motion of an elastic capsule through a microchannel characterized by a localized constriction. We consider a capsule with a stress-free spherical shape and impose its steady-state configuration in an infinitely long straight channel as the initial condition for our calculations. We report how the capsule deformation, velocity, retention time, and maximum stress of the membrane are affected by the capillary number, Ca , and the constriction shape. We estimate the deformation by measuring the variation of the three-dimensional surface area and a series of alternative quantities easier to extract from experiments. These are the Taylor parameter, the perimeter and the area of the capsule in the spanwise plane. We find that the perimeter is the quantity that best reproduces the behavior of the three-dimensional surface area. This is maximum at the centre of the constriction and shows a second peak after it, whose location depends on the Ca number. We observe that, in general, area-deformation-correlated quantities grow linearly with Ca , while velocity-correlated quantities saturate for large Ca but display a steeper increase for small Ca . The velocity of the capsule divided by the velocity of the flow displays, surprisingly, two different qualitative behaviors for small and large capillary numbers. Finally, we report that longer constrictions and spanwise wall bounded ( versus spanwise periodic) domains cause larger deformations and velocities. If the deformation and velocity in the spanwise wall bounded domains are rescaled by the initial equilibrium deformation and velocity, their behavior is undistinguishable from that in a periodic domain. In contrast, a remarkably different behavior is reported in sinusoidally shaped and smoothed rectangular constrictions indicating that the capsule dynamics is particularly sensitive to abrupt changes in the cross section. In a smoothed rectangular constriction larger deformations and velocities occur over a larger distance. Graphical abstract: [ABSTRACT FROM AUTHOR]