Although high-pressure homogenization (HPH) is widely used in the dairy industry, predicting the size distribution of homogenized milk fat globules remains a significant challenge. In this study, the outlet size distribution of milk fat globules was measured using static light scattering over a broad range of operating pressures, from 3 to 100 MPa. Across this range, the outlet distribution was accurately described as a simple function of the inlet distribution, where each globule gives rise to three classes of fragments defined by five parameters. These parameters show strong interdependency and can be expressed as algebraic functions of the operating pressure, indicating a deterministic breakup mechanism in the HPH. The results support the fragmentation model proposed by Masbernat et al. (2022) and provide a foundation for practical prediction of size distributions in emulsions with high internal viscosity.

We report experimental investigations of an unconfined liquid-solid fluidized bed at low to moderate Reynolds number. The fluidization velocity Uf is measured when an upward flow is imposed, and the sedimentation velocity Used is measured when the flow is stopped. Only when the level of inlet flow fluctuation is sufficiently low will these two velocities coincide, as expected for an unbound system. A systematic comparison between Uf and Used should therefore be made when attempting to determine fluidization laws. Comparisons with previous studies show that Uf measurements gather on a single function of the ratio Phi/Phi pack between the particle volume fraction Phi and its packing value Phi pack, except for a factor K that encompasses all effects other than concentration: Stokes number, Reynolds number, confinement, and inlet condition. Time-resolved measurements of the fluidized bed surface show two contributions: uncorrelated high-frequency fluctuations and low-frequency oscillations that remain correlated over minutes. The coherent oscillations correspond to the arrival of upward concentration waves at the bed surface. Their wavelength, which characterizes the length scale of large-scale heterogeneities, was known to diverge as the packing state is approached. Here, we found that it also increases with decreasing concentration, suggesting that the loss of global bed stability observed in previous work at high expansions may be related to the development of heterogeneous structures of a size comparable to that of the column.

Bubbles and bubbly flows are omnipresent in nature and technology, showing a multitude of phenomena, which can be either beneficial or a hindrance. In any case, for their control and their applications, it is crucial to understand their fundamentals and therefore from the very beginning of the International Journal of Multiphase Flow they have been central. In this synoptic review we give some examples for the fascinating fluid dynamics of bubbles and bubbly flows, starting from their nucleation and cavitation phenomena, then going to single bubble phenomena, and finally to bubbly flows, in which the collective effects of bubbles are key, and to mass transfer in such bubbly flows. The review ends with an outlook on future direction and open issues in the research on bubbles and bubbly flows.

Axisymmetric direct numerical simulations are carried out to study the hydrodynamics of a laminar, stationary, incompressible, Newtonian, single-phase flow in an Annular Plane Couette (APC) channel. This configuration is that of a Straight Plane Couette (SPC) flow but curved around itself to form an annulus. These simulations are validated by Particle Image Velocimetry measurements at different Reynolds numbers. The flow is analyzed using three dimensionless parameters: the channel aspect ratio Ac, which controls the effects of sidewall confinement, the channel curvature ratio Cr, which affects the centrifugal forces due to curvature, and the Reynolds number Re. The rotation of the top annular plate generates a main flow in the azimuthal direction, while generating a secondary recirculation flow in the plane of the channel cross section due to the presence of a centrifugal force difference across the radius. As a result, the vertical profile of the longitudinal velocity deviates from the classical linear profile of the SPC flow, adopting an unexpected S shape similar to that observed in a turbulent SPC flow. Depending on the values of Ac and Cr, the flow exhibits a wide range of behaviors, from a quasi-2D flow with a homogeneous shear rate at moderate Re with appropriate geometrical parameters (Ac 5, Cr 0.1) to a complex 3D flow otherwise. Whereas it is laminar, the APC flow shares a strong analogy with a turbulent Taylor-Couette (TC) flow. At large Reynolds numbers, the velocity gradients concentrate near the wall and the flow reaches an asymptotic regime where the torque scales as Re alpha and the flow structure becomes independent of Re. Such properties make the APC flow an interesting configuration for fundamental investigations as a complement of the TC flow when shear and gravity are required to be in the same plane. In particular, it can be used to investigate the rheology of a dispersed two-phase mixture similarly to previous work by Yi et al. in the TC device.

Spectral analysis of dispersed two-phase flows is highly desirable to reveal the interplay of the various flow scales, much larger or much smaller than the size of the dispersed bodies. This is a challenging task as the matching conditions at the body interfaces generate singularities in the fields describing the two-phase mixture. The nature of these singularities and their consequences on the spectra are theoretically analyzed for bubble or droplet flows. Results of direct numerical simulations are reported and spatial spectra of the mixture velocity, the flow forces and their power are examined. The regular part of the spectral densities of energy production, dissipation and transfers between scales are separated from their singular part. The resulting spectral energy balance, free of the footprint of the singularities, is found in agreement with coarse-grained simulations where the interfaces are filtered out before solving the Navier–Stokes equations. These results pave the way for the spectral analysis of more complex turbulent dispersed flows.

We performed numerical simulations of a homogeneous swarm of bubbles rising at large Reynolds number, Re = 760, with volume fractions ranging from 1 % to 10 %. We consider a simplified model in which the interfaces are not resolved, but which allows us to simulate flows with a large number of bubbles and to emphasize the interactions between bubble wakes. The liquid phase is described by solving, on an Eulerian grid, the Navier-Stokes equations, including sources of momentum which model the effect of the bubbles. The dynamics of each bubble is determined within the Lagrangian framework by solving an equation of motion involving the hydrodynamic forces exerted by the fluid accounting for the correction of the fictitious self-interaction of a bubble with its own wake. The comparison with experiments shows that this coarse-grained simulations approach can reliably describe the dynamics of the resolved flow scales. We use conditional averaging to characterize the mean bubble wakes and obtain in particular the typical shear imposed by the rising bubbles. On the basis of the spectral decomposition of the energy budget, we observe that the flow is dominated by production at large scales and by dissipation at small scales and we rule out the presence of an intermediate range in which the production and dissipation are locally in balance. We propose that the k(-3) subrange of the energy spectra results from the mean shear rate imposed by the bubbles, which controls the rate of return to isotropy.

In this study, we propose a particle sedimentation/aggradation law for homogeneous concentrated suspensions. This law, valid in the Stokes flow regime, can be used to describe the sedimentation process observed in short-lived rapid flows, developed at high Reynolds numbers, that can be described as low-viscosity quasi-parallel flows traveling at constant velocity and that progressively sediment during the dominant phase of transport to leave a triangular or trapezoidal deposit of constant slope. The particle aggradation velocity can thus be predicted from the product of the mean flow velocity and the deposit slope and turns out to be roughly similar to that measured from static suspensions of the same concentration, provided that the flow Reynolds number, based on the mean flow velocity, the fluid properties, and the particle size, remains inferior to a few hundred, such as the mixture agitation cannot disturb the sedimentation process. These important results provide the possibility of describing the depositional dynamics during the final stage of extreme events, as well as to infer the mixture rheology, from physical parameters that can be easily measured in the field.

The size distribution of fat globules in homogenized concentrated dairy cream has been measured in High-Pressure Homogenizers (HPH), working at 80 ? and various operating pressures. For each pressure, the outlet size distribution is found to be self-similar to the inlet distribution, and can be accurately predicted dividing each class diameter of the inlet distribution by a single proportionality factor, which can be interpreted using a simplified deformation model of the fat globules as elongated filaments. The evolution of the factor with the operating pressure is consistent with a scaling analysis of the average shear rate in the HPH as well as with the value predicted from numerical simulations of the flow in the HPH, supporting the physical interpretation of the fragmentation model.

The physics of blood flow in small vessel networks is dominated by the interactions between Red Blood Cells (RBCs), plasma and blood vessel walls. The resulting couplings between the microvessel network architecture and the heterogeneous distribution of RBCs at network-scale are still poorly understood. The main goal of this paper is to elucidate how a local effect, such as RBC partitioning at individual bifurcations, interacts with the global structure of the flow field to induce specific preferential locations of RBCs in model microfluidic networks. First, using experimental results, we demonstrate that persistent perturbations to the established hematocrit profile after diverging bifurcations may bias RBC partitioning at the next bifurcations. By performing a sensitivity analysis based upon network models of RBC flow, we show that these perturbations may propagate from bifurcation to bifurcation, leading to an outsized impact of a few crucial upstream bifurcations on the distribution of RBCs at network-scale. Based on measured hematocrit profiles, we further construct a modified RBC partitioning model that accounts for the incomplete relaxation of RBCs at these bifurcations. This model allows us to explain how the flow field results in a single pattern of RBC preferential location in some networks, while it leads to the emergence of two different patterns of RBC preferential location in others. Our findings have important implications in understanding and modeling blood flow in physiological and pathological conditions.

By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor–Couette turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviours, i.e. the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction for O/W or for W/O. However, for W/O it is about $50\,\%$ larger than that of O/W. At the macro-scales, the effective viscosity of O/W is higher when compared to that of W/O. These asymmetric behaviours are expected to be caused by the presence of surface-active contaminants from the walls of the system. By introducing an oil-soluble surfactant at high concentration, remarkably, we recover the symmetry (droplet size and effective viscosity) between O/W and W/O emulsions. Based on this, we suggest a possible mechanism responsible for the initial asymmetry and reach conclusions on emulsions where interfaces are fully covered by the surfactant. Next, we discuss what sets the droplet size in turbulent emulsions. We uncover a $-6/5$ scaling dependence of the droplet size on the Reynolds number of the flow. Combining the scaling dependence and the droplet Weber number, we conclude that the droplet fragmentation, which determines the droplet size, occurs within the boundary layer and is controlled by the dynamic pressure caused by the gradient of the mean flow, as proposed by Levich ( Physicochemical Hydrodynamics , Prentice-Hall, 1962), instead of the dynamic pressure due to turbulent fluctuations, as proposed by Kolmogorov ( Dokl. Akad. Nauk. SSSR , vol. 66, 1949, pp. 825–828). The present findings provide an understanding of both the microscopic droplet formation and the macroscopic rheological behaviours in dynamic emulsification, and connects them.

The investigation of the fall of a sphere at finite Reynolds number in a concentrated suspension of small fluidized particles leads to unexpected results. By analyzing the drag force, it is shown that the average surface stress on the sphere is independent of the size of the sphere. It is proportional to an effective viscosity determined from the sedimentation velocity of the particles multiplied by the velocity of the sphere and divided by the size of the particles. These results question the role of concentration inhomogeneities that occur on a large scale in the overall flow around a moving obstacle and on a small scale near its surface.

We present a numerical method for simulating the flow induced by bubbles rising at large Reynolds number. This method is useful to simulate configurations of large dimensions involving a great number of bubbles. The action that each bubble exerts on the liquid is modelled as a volume source of momentum distributed over a few mesh-grid elements. The flow in the vicinity of the bubbles is thus not finely resolved. The bubbles are treated as Lagrangian particles that move under the influence of the hydrodynamic force exerted by the liquid. The determination of this force on a given bubble requires knowledge of the liquid flow that is undisturbed by this bubble. A model is developed to accurately estimate this disturbance for large-Reynolds-number objects and get rid of any spurious self-induced effect. Thanks to that, a homogeneous swarm of rising bubbles is simulated. Comparisons with experiments show a good agreement with the flow scales larger than the bubbles, which turn out to be controlled by the interactions between bubble wakes and rather independent of unresolved smaller scales. This method can be used to study the coupling between bubble-induced agitation and large-scale motions, such as those produced in industrial bubble columns.

The modeling of the fluidization or sedimentation velocity of a suspension of solid particles is revisited by examining experiments conducted in either a liquid or a gas. A general expression is found in the case of negligible fluid inertia, i.e. at low Reynolds or Archimedes number. It is built as the product of the velocity of an isolated particle by three non-dimensional corrections that each takes into account a specific physical mechanism. The first correction reflects the variation of the buoyancy with the particle concentration. The second correction describes how the drag force increases with the concentration in case of negligible particle inertia. The third one accounts for the further increase of the drag when the particle inertia is increased. Remarkably, each correction only relies on a single of the three independent non-dimensional groups that control the problem: (1) the particle volume fraction Φs; (2) the ratio Φs/Φpack where Φpack is the bed packing concentration; (3) the Stokes number St0, which characterizes the inertia of the particles and controls their agitation. Moreover, the onset of the instability that separates the homogeneous regime from the heterogeneous one is found to be controlled similarly by the Stokes number. Empirical expressions of the corrections are given, which provide a reliable tool to predict fluidization and sedimentation velocities for all values of the three non-dimensional numbers. The present results emphasize the crucial role of particle inertia, which is often disregarded in previous modeling approaches, such as that of Richardson and Zaki.

This work reports an experimental investigation of a liquid-solid fluidized bed involving inertial particles at a large Reynolds number. Owing to optical techniques and index matching, the statistics of the velocity fluctuations of both the particles and the liquid are measured for a wide range of the particle volume fraction αp. The dynamics of the fluctuations suggests that the flow possesses the following three properties: (1) The liquid volume involves a wake region in which vertical fluctuations are negative and an interstitial region where they are positive. (2) The statistics of the horizontal fluctuations are similar to vertical ones, except that they are symmetric. (3) Local instant particle fluctuations are proportional to liquid ones. Assuming these properties are true allows us to derive a model for the probability density functions (PDFs) of the two components of the velocity fluctuations of the two phases. This model involves a single reference PDF that is independent of αp and one weighting parameter for each phase. The weighting parameter of the liquid phase is an affine function of αp, which characterizes the volume of the wakes relative to that of the interstices. That of the particle phase depends on the preferential concentration of the particles, which tend to avoid the wakes at low αp. This model accurately describes the experimental PDFs up to the third-order moment and reproduces all their peculiar features: the skewness of the vertical fluctuations which reverses at a given volume fraction, the presence of exponential tails corresponding to rare intense events, and the symmetry between low and large volume fractions.

When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the two facing interfaces at the nanoscale is created. We report experimental investigations of the expansion of this initial bridge by means of high-speed imaging. By considering droplets of water, polydimethylsiloxane, or paraffin of a few hundred micrometers, we investigate regimes where inertia takes a major role. Depending on the Ohnesorge number (Oh), the dynamics of the bridge differs a lot. For Oh ≈1, the initial flow is rapidly attenuated and the connecting bridge between the two droplets adopts a smooth parabolic shape. The maximum interface curvature and the minimum liquid pressure remain at the bridge center. The expansion is thus caused by the capillary pressure that drives the fluid toward the center. At small Oh, in the inertial regime, the length of the initial bridge grows at constant speed and the bridge expansion can be described by the propagation of nondispersive capillary wave packets. The central part of the bridge takes a cylindrical shape connected to the droplets by a narrow region of very large curvature. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows that result in the presence of the slope discontinuities, we show that the apparent angle made by the interface controls the flow rate that enters the bridge and thus determines its radial expansion.

We develop a physical model of the dam-break flow of fine noncohesive particles initially fluidized by a gas. By revisiting previous experiments, we show that the dynamics of such flows involves two uncoupled phenomena. On the one hand, the settling of the particles is the same as that of a nonflowing suspension, so that the mass flux of particles that deposit can be related solely to the properties of the suspension. On the other hand, the flow of the gas-particle mixture is similar to that of an equivalent fluid of constant density and negligible viscosity. The momentum lost by the flowing mixture is equal to the product of the deposited mass flux and the longitudinal velocity. These properties allow us to model the time duration of the flow as the time taken by the particles to settle and the slope of the final deposit as the ratio between the growth rate of the deposit height and the velocity of the front of the dam-break flow. Finally, these findings lead to the formulation of consistent shallow-water equations involving specific terms of mass and momentum transfer at the bottom wall, which can be used to compute the dense lower layer of ash flows generated by a volcanic eruption. They also provide tools for the interpretation of field measurements by geologists.

We study the effects of hydrodynamic forces in frequency-modulation AFM experiments (FM-AFM) in liquid. We first establish the theoretical equations needed to derive the interaction stiffness k int and the damping β int due to the hydrodynamic forces from the frequency shift and the excitation amplitude. We develop specific FM-AFM experiments to measure the variation of k int and β int over a large range of distance in water up to 200 µm. Comparison between theory and experiments point out that the evolution of k int at short and long distance arises from unsteady hydrodynamic forces on the cantilever. On the other hand, β int is small at long distance and diverges at short probe-surface distance, as predicted by the classical Reynolds sphere model.

We present a method to measure the very small interfacial concentration of a contaminant that is irreversibly adsorbed on the interface of a bubble or droplet. It is an application of the linear theory of shape oscillation which relates the Gibbs elasticity to the damping, extended by numerical simulations to deal with moving droplets. It explains previous unexpected observations on the effect of contamination at various oscillation wavelengths. The experimental procedure is easy to implement and can thereby deeply enhance the analysis of most systems involving uncontrolled contamination.

A theoretical model of liquid and particle random fluctuations is proposed for gravity-driven flows of inertial homogeneous suspensions. It is based on a paradigm assuming that fluctuations of both liquid velocity and particle slip velocity are driven by fluctuations of the phase indicator function. It is shown that this model accurately predicts the energy of the fluctuations of both the fluid and particle phases measured in a homogeneous solid-liquid fluidized bed over a wide range of particle volume fractions, from 10% to 45%.

This work investigates the coalescence of water droplets settled on a water-oil interface in the presence of microparticles and surfactant. The successive stages of the coalescence process, including interstitial film formation, drainage, rupture, and retraction, are analyzed in detail. This leads us to distinguish between contrasted situations depending on the nature of the surfactant and its affinity with the microparticles. Hydrophilic particles have been previously shown to promote coalescence by means of a bridging mechanism. In that case, coalescence is a deterministic process that lasts the time required for the drainage to make the film thickness equal to the size of the particles. However, the present study shows how surfactants can totally change the effect of the particles upon coalescence. When surfactant both stabilizes the water-oil interface and adsorbs onto the particles, the bridging mechanism is inhibited and the coalescence becomes a random process. Since molecular forces between facing film interfaces are not attractive, thermal fluctuations are required to initiate the formation of a hole in the adsorbed surfactant layer. Provided the surfactant concentration in the bulk is large enough to ensure that the interfaces are close to saturation, the coalescence is delayed by a stochastic time interval and the drop coalescence becomes a Poisson process. These results shed a new light on the mechanisms of droplet coalescence in complex industrial applications where surfactant and particles are present, either purposely added or present as uncontrolled contaminants.