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Due to its capability of duplicating the deformation scenario of erythrocytes (red blood cells), in in vivo time scales, passing through interendothelial slits in the spleen, the understanding of the dynamic response of erythrocytes in oscillatory shear flows is of critical importance to the development of an effective in vitro methodology to study the mechanics, metabolism, and aging procedure in vivo [R. Asaro et al., "Erythrocyte aging, protection via vesiculation: An analysis methodology via oscillatory flow," Front. Physiol. 9, 1607 (2018)]. Accordingly, we conducted a systematic computational investigation of the dynamics of erythrocytes in high-frequency oscillatory shear flows by using a fluid-cell interaction model based on the Stokes-flow framework and a multiscale structural depiction of the cell. Within the range of parameters we consider, we identify five different response modes (wheeling, tilted wheeling, tank treading mode 1, tank treading mode 2, and irregular). The occurrence and stability of these response modes depend on the frequency of the flow, the peak capillary number, the viscosity ratio, the initial orientation of the cell, and the stress-free state of the protein skeleton. Through long-term simulations [ O (1 0 2 ) periods], mode switching events have been discovered, during which the cell transfers from one mode to another, often via an intermediate transient mode. The deformation of the skeleton and the contact stress between the skeleton and the lipid bilayer are computed since these are of direct importance to describing vital cell phenomena such as vesiculation by which the cell protects itself from premature elimination. [ABSTRACT FROM AUTHOR]

Among droplet generation technologies, the flow focusing technique is a major process due to its control, stability, and reproducibility. In this process, one fluid (the continuous phase) interacts with another one (the dispersed phase) to create small droplets. Experimental assays in the literature on gas-liquid flow focusing have shown that different jet regimes can be obtained depending on the operating conditions. However, the underlying physical phenomena remain unclear, especially mechanical interactions between the fluids and the oscillation phenomenon of the liquid. In this paper, based on published studies, a numerical diphasic model has been developed to take into consideration the mechanical interaction between phases, using the Cahn-Hilliard method to monitor the interface. Depending on the liquid/gas inputs and the geometrical parameters, various regimes can be obtained, from a steady state regime to an unsteady one with liquid oscillation. In the dispersed phase, the model enables us to compute the evolution of fluid flow, both in space (size of the recirculation zone) and in time (period of oscillation). The transition between unsteady and stationary regimes is assessed in relation to liquid and gas dimensionless numbers, showing the existence of critical thresholds. This model successfully highlights, qualitatively and quantitatively, the influence of the geometry of the nozzle, in particular, its inner diameter. [ABSTRACT FROM AUTHOR]

Inspired by the design of the ribbed structure of shark skin, passive drag reduction methods using stream-wise riblet surfaces have previously been developed and tested over a wide range of flow conditions. Such textures aligned in the flow direction have been shown to be able to reduce skin friction drag by 4%-8%. Here, we explore the effects of periodic sinusoidal riblet surfaces aligned in the flow direction (also known as a "wrinkled" texture) on the evolution of a laminar boundary layer flow. Using numerical analysis with the open source Computational Fluid Dynamics solver OpenFOAM, boundary layer flow over sinusoidal wrinkled plates with a range of wavelength to plate length ratios (λ/Lλ/L), aspect ratios (2A/λ2A/λ), and inlet velocities are examined. It is shown that in the laminar boundary layer regime, the riblets are able to retard the viscous flow inside the grooves creating a cushion of stagnant fluid that the high-speed fluid above can partially slide over, thus reducing the shear stress inside the grooves and the total integrated viscous drag force on the plate. Additionally, we explore how the boundary layer thickness, local average shear stress distribution, and total drag force on the wrinkled plate vary with the aspect ratio of the riblets as well as the length of the plate. We show that riblets with an aspect ratio of close to unity lead to the highest reduction in the total drag, and that because of the interplay between the local stress distribution on the plate and stream-wise evolution of the boundary layer the plate has to exceed a critical length to give a net decrease in the total drag force. [ABSTRACT FROM AUTHOR]

This paper presents a systematic computational study of the flow in a shrouded rotor cavity (with depth of the order of 100 μm) with multiple discrete inflows revealing the physics of how an initially non-axisymmetric flow evolves, both in the Lagrangian and Eulerian frameworks, towards axisymmetry. The approach to axisymmetry happens faster for the tangential velocity as compared to the radial component. The non-uniform inlet condition for the radial and tangential velocities, consisting of high velocity at the inlet openings and zero velocity on the shroud wall in between two consecutive inlets, gives rise to an oscillatory variation in the velocity of a fluid particle, with progressively decreasing amplitude, if one tracks its motion along a surface streamline. The rate of decay of the amplitude increases, i.e., equivalently the approach to the axisymmetric condition happens at a greater radial location, as the number of inlets, Ninlet, is increased. When the rotational speed of the discs, Ω, is increased, the distribution of radial velocity (Ur) is significantly altered, which may result even in a change of the fundamental shape of its z-profile, changing from parabolic to flat to W-shaped. The fluid has to negotiate with two different non-uniformities within a short radial distance (Δrc): one in the θ-direction because of the presence of discrete inlets and the other in the z-direction due to the no-slip condition on the disc surface. An increase in Δrc from zero to a finite value assists in the attainment of the axisymmetric condition for both tangential and radial velocities, i.e., the axisymmetry is obtained at a larger radial location. The subtle and complex fluid dynamics of the approach to axisymmetry is comprehensively analysed by following the progressive development of the z-profiles of Ur along a surface streamline located on the middle-plane of the inter-disc-spacing for an eight-inlet flow-configuration. Two sets of velocity profiles are recorded-the first set at points whose azimuthal positions are directly aligned with the inlets and the second set at points which fall in the middle of two consecutive inlets. Both sets are of W-shape near the disc periphery, then they become flat in the middle, finally becoming parabolic. The velocity profiles of the two sets approach each other and finally become superposed when axisymmetry is attained. [ABSTRACT FROM AUTHOR]

Lagrangian statistics obtained from direct numerical simulations of turbulent planar jets and mixing layers are reported for the separation distance between the tracer particles at the outer edge of the turbulent/non-turbulent interface layer, and the entrained fluid particles. In the viscous superlayer (VSL) the mean square particle distance exhibits a ballistic evolution, while the Richardson-like scaling for relative dispersion prevails inside the turbulent sublayer (TSL). The results further support the existence of two different regimes within the interface layer, where small-scale outward enstrophy diffusion governs the entrained particles in the VSL, while inviscid small-scale motions govern the TSL. [ABSTRACT FROM AUTHOR]

Treating differential molecular diffusion correctly and accurately remains as a great challenge to the modeling of turbulent non-premixed combustion. The aim of this paper is to develop consistent modeling strategies for differential molecular diffusion in flamelet models. Two types of differential molecular diffusion models are introduced, linear differential diffusion models and nonlinear differential diffusion models. A multi-component turbulent mixing layer problem is analyzed in detail to gain insights into differential molecular diffusion and its characteristics, particularly the dependence of differential molecular diffusion on the Reynolds number and the Lewis number. These characteristics are then used to validate the differential molecular diffusion models. Finally, the new models are applied to the modeling of a series of laboratory-scale turbulent non-premixed jet flames with different Reynolds number (Sandia Flames B, C, and D) to further assess the models' performance. [ABSTRACT FROM AUTHOR]

We extend the penalty immersed boundary (pIB) method to the interaction between a rigid body and a surrounding fluid. The pIB method is based on the idea of splitting an immersed boundary, which here is a rigid body, notionally into two Lagrangian components: one is a massive component carrying all mass of the rigid body and the other is massless. These two components are connected by a system of stiff springs with 0 rest length. The massless component interacts with the surrounding fluid: it moves at the local fluid velocity and exerts force locally on the fluid. The massive component has no direct interaction with the surrounding fluid and behaves as though in a vacuum, following the dynamics of a rigid body, in which the acting forces and torques are generated from the system of stiff springs that connects the two Lagrangian components. We verify the pIB method by computing the drag coefficients of a cylinder and ball descending though a fluid under the influence of gravity and also by studying the interaction of two such descending cylinders and likewise the interaction of two such descending balls. The computational results are quite comparable to those in the literature. As a further example of an application, we include a freely falling maple seed with autorotation. [ABSTRACT FROM AUTHOR]

The concentration of a solute adsorbed at a phase boundary is affected by the motion of the surface on which it lies. Our aim is to account for this whether or not the surface is material. To do this we begin with a theorem presented by Milne, true for any moving surface, and derive a formula for d/dt ∫S dA c, where c is defined only on the surface S. [ABSTRACT FROM AUTHOR]

In this study, flow phenomena associated with inflectional and boundary-layer instabilities, as well as a mixed instability mode in quasi-two-dimensional magnetohydrodynamic flows in a rectangular duct are accessed with the help of a parametrical model, where the basic velocity profile with near-wall jets and associated points of inflection are produced by imposing an external flow-opposing force. By varying this force, various instability modes and transition scenarios are reproduced. First, linear stability analysis is performed and then nonlinear effects are studied using direct numerical simulation for Hartmann numbers 100 and 200 and Reynolds numbers from 1800 to 5000. A special attention is paid to the location of the inflection point with respect to the duct wall. A more complex flow dynamics, including various vortex-wall and vortex-vortex interactions, and even negative turbulence production are observed and analyzed as the inflection point approaches the wall. The analysis of obtained results and their comparison with relevant data for magnetohydrodynamic duct flows gain an insight into what is typically called 'jet instability,' including linear and nonlinear mechanisms. [ABSTRACT FROM AUTHOR]

This study investigates the occurrence of valveless pumping in a fluid-filled system consisting of two open tanks connected by an elastic tube. We show that directional flow can be achieved by introducing a periodic pinching applied at an asymmetrical location along the tube, and that the flow direction depends on the pumping frequency. We propose a relation between wave propagation velocity, tube length, and resonance frequencies associated with shifts in the pumping direction using numerical simulations. The eigenfrequencies of the system are estimated from the linearized system, and we show that these eigenfrequencies constitute the resonance frequencies and the horizontal slope frequencies of the system; “horizontal slope frequency” being a new concept. A simple model is suggested, explaining the effect of the gravity driven part of the oscillation observed in response to the tank and tube diameter changes. Results are partly compared with experimental findings. [ABSTRACT FROM AUTHOR]

The aim of this paper is the investigation of a layered sloshing fluid system using both a new Hamiltonian mathematical model and new laboratory experiments. The mathematical model is defined for a cylindrical tank with an arbitrary shape and subjected to an arbitrary rigid motion. The model consists of a pure evolution system of partial differential first order equations in the canonical four unknowns: water elevation at the upper free surface and at the separation surface and the gap in momentum potential density computed at each fluid surface. The system of equations is obtained by avoiding the construction of the Hamiltonian and its variational derivatives. An important advantage of this formulation, with respect to the Lagrangian formulation, is that the nonevolution constraint, which imposes for each fluid the same velocity component along the normal direction of the separation surface, is fulfilled by the model itself. The model implementation needs to define the so-called Neumann–Dirichlet operators, which are computed by an efficient algorithm, for any instantaneous configuration of the two fluid domains. A numerical integration of the model is performed by a suitable Galerkin projection of the evolution equations. New laboratory experiments, simulating the sloshing of a layered fluid system, inside a tank with a squared cross section, were performed. The experiments, with a two-dimensional sloshing, were carried out by varying the forcing frequency, the oscillation amplitude and the ratio of the two fluids’ depths. In some experiments, a traveling wave, with a shape similar to a moving hydraulic jump, was observed at the separation surface. Measurements of the space-time evolution of both the free and the separation surfaces were performed and compared with the model’s predictions. A good agreement between the model predictions and laboratory measurements is found, even for strong nonlinear cases such as the traveling wave. [ABSTRACT FROM AUTHOR]

The flight of a small bird under the influence of the ground effect is numerically investigated with a complete three-dimensional model including the bird's body and wings. The flight mode is not the conventional steady gliding flight but an unsteady flight consisting of flapping, twisting, and folding motions. As the bird approaches the ground, the average lift force gradually increases while the average drag force decreases. At a particular distance, the average lift force increases by approximately 47%, whereas the average drag force decreases by nearly 20%, relative to the absence of the ground effect. Because of the ground, the improved aerodynamic performance in flapping flight is much more significant than in steady flight, in which the modification of the lift-drag ratio is typically less than 10%. On the basis of the flow field, regardless of the presence or absence of the ground, there exists no evidence for an obstruction of a wing-tip vortex, which is a remarkable phenomenon and accounts for the improved performance in steady flight. The extent of the region of high pressure beneath the wing in the near-ground case seems to surpass that in the far-ground case, accounting for the greater lift and thrust forces in the near-ground case. This air cushion beneath the wing, known as the cram effect, is the dominant factor of the ground effect on a flapping bird. [ABSTRACT FROM AUTHOR]

During extrusion of viscoelastic fluids various flow instabilities may arise resulting in a distorted free surface. In order to investigate the factors generating these instabilities we performed a linear stability analysis at zero Reynolds number around the steady solution of the cylindrical or planar stick-slip flow for a viscoelastic fluid following the affine exponential Phan-Thien Tanner (PTT) model. Stick-slip flow is an important special case of the extrudate swell problem, since the latter reduces to it in the limit of infinite surface tension but avoids the complications of a free-boundary flow. The linear stability analysis is performed for various values of the rheological parameters of the PTT model in order to determine the effects of all material properties. It is found that the flow becomes unstable as the Weissenberg number increases above a critical value, due to a Hopf bifurcation suggesting that the flow will become periodic in time. Both the critical value of the Weissenberg number and the frequency of the instability depend strongly on the rheological parameters of the viscoelastic model. The corresponding eigenvectors indicate that the perturbed flow field has a spatially periodic structure, initiated at the rim of the die, extending for up to 5-7 die gaps downstream, but confined close to the surface of the extrudate, in qualitative agreement with existing experiments. This suggests that instability is generated by the combination of the singularity in the velocity and stress fields at the die lip and the strong extension that the extruded polymer undergoes near its surface. The elasticity alone can be responsible for the appearance of instabilities in the extrusion process of viscoelastic fluids and the often used assumptions of wall slip or compressibility, although they might be present, are not required. Finally, the mechanisms that produce these instabilities are examined through energy analysis of the disturbance flow. [ABSTRACT FROM AUTHOR]