Simulation of neutrophil motion and deformation: influence of rheology and flow configuration

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Path instability of deformable bubbles rising in Newtonian liquids: A linear study

The first stages of the path instability phenomenon known to affect the buoyancy-driven motion of gas bubbles rising in weakly or moderately viscous liquids are examined thanks to a recently developed numerical tool designed to assess the global linear stability of incompressible flows involving freely-evolving interfaces. Predictions for the critical bubble size and frequency of the most unstable mode are found to agree well with reference data obtained in ultrapure water and in several silicone oils. By varying the bubble size, stability diagrams are built for several specific fluids, revealing three distinct regimes characterized by different bifurcation sequences. The spatial structure of the corresponding unstable modes is analysed, together with the variations of the bubble shape, position and orientation. For this purpose, displacements of the bubble surface are split into rigid-body components and volume-preserving deformations, allowing us to determine how the relative magnitude of the latter varies with the fluid properties and bubble size. Predictions obtained with freely-deformable bubbles are compared with those found when the bubble shape determined in the base state is constrained to remain frozen during the stability analysis. This comparison reveals that deformations leave the phenomenology of the first bifurcations unchanged in low-viscosity fluids, especially water, only lowering the critical bubble size and increasing the frequency of path oscillations. In contrast, they introduce a dramatic change in the nature of the primary bifurcation in oils slightly more viscous than water, whereas, somewhat surprisingly, they leave the near-threshold phenomenology unchanged in more viscous oils.Comment: 35 pages, 16 figure

Bifurcations in the wake of a thick circular disk

Using DNS, we investigate the dynamics in the wake of a circular disk of aspect ratio χ = d/w = 3(where d is the diameter and w the thickness) embedded in a uniform flow of magnitude U0 perpendicular to its symmetry axis. As the Reynolds number Re = U0d/ν is increased, the flow is shown to experience an original series of bifurcations leading to chaos. The range Re ∈ [150, 218] is analysed in detail. In this range, five different non-axisymmetric regimes are successively encountered, including states similar to those previously identified in the flow past a sphere or an infinitely thin disk, as well as a new regime characterised by the presence of two distinct frequencies. A theoretical model based on the theory of mode interaction with symmetries, previously introduced to explain the bifurcations in the flow past a sphere or an infinitely thin disk (Fabre et al. in Phys Fluids 20:051702, 2008), is shown to explain correctly all these results. Higher values of the Reynolds number, up to 270, are also considered. Results indicate that the flow encounters at least four additional bifurcations before reaching a chaotic state

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube.

Buoyancy-driven turbulent mixing of fluids of slightly different densities [At = Δρ/(2〈ρ〉) = 1.15×10−2] in a long circular tube tilted at an angle θ = 15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube

On the dispersion of solid particles in a liquid agitated by a bubble swarm

This article deals with the dispersion of solid particles in a liquid agitated by a homogeneous swarm of bubbles. The scale of interest lies between the plant scale (of the order of the tank) and the microscale (less than the bubble diameter). The strategy consists in simulating both the twophase flow of deforming bubbles and the motion of solid particles. The evolution of the spatial distribution of particles together with the encounter and entrainment phenomena is studied as a function of the void fraction and the relative size and mass of particles. The influence of the shape of the bubble and of the model of forces that govern the motion of particles is also considered