Collective Flows Drive Cavitation in Spinner Monolayers

Hydrodynamic interactions can give rise to a collective motion of rotating particles. This, in turn, can lead to coherent fluid flows. Using large scale hydrodynamic simulations, we study the coupling between these two in spinner monolayers at weakly inertial regime. We observe an instability, where the initially uniform particle layer separates into particle void and particle rich areas. The particle void region corresponds to a fluid vortex, and it is driven by a surrounding spinner edge current. We show that the instability originates from a hydrodynamic lift force between the particle and fluid flows. The cavitation can be tuned by the strength of the collective flows. It is suppressed when the spinners are confined by a no-slip surface, and multiple cavity and oscillating cavity states are observed when the particle concentration is reduced

Blood crystal: emergent order of red blood cells under wall-confined shear flow

Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report experiments and numerical simulations revealing that red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The order is of pure hydrodynamic and inertialess origin, and emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls which drives deformable cells towards the channel mid-plane and (ii) intercellular hydrodynamic interactions which can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order. The difference in structuring ability of healthy (deformable) and diseased (stiff) RBCs creates a flow signature potentially exploitable for diagnosis of blood pathologies

Inversion of hematocrit partition at microfluidic bifurcations

Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit ($\phi_0$) partition depends strongly on RBC deformability, as long as $\phi_0 <20$% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough $\phi_0$, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.Comment: 16 page

Predicting optimal hematocrit in silico

Optimal hematocrit $H_o$ maximizes oxygen transport. In healthy humans, the average hematocrit $H$ is in the range of 40-45$\%$, but it can significantly change in blood pathologies such as severe anemia (low $H$) and polycythemia (high $H$). Whether the hematocrit level in humans corresponds to the optimal one is a long standing physiological question. Here, using numerical simulations with the Lattice Boltzmann method and two mechanical models of the red blood cell (RBC) we predict the optimal hematocrit, and explore how altering the mechanical properties of RBCs affects $H_o$. We develop a simplified analytical theory that accounts for results obtained from numerical simulations and provides insight into the physical mechanisms determining $H_o$. Our numerical and analytical models can easily be modified to incorporate a wide range of mechanical properties of RBCs as well as other soft particles thereby providing means for the rational design of blood substitutes. Our work lays the foundations for systematic theoretical study of the optimal hematocrit and its link with pathological RBCs associated with various diseases (e.g. sickle cell anemia, diabetes mellitus, malaria, elliptocytosis)

Unsteady drag force on an immersed sphere oscillating near a wall

The unsteady hydrodynamic drag exerted on an oscillating sphere near a planar wall is addressed experimentally, theoretically and numerically. The experiments are performed by using colloidal-probe atomic force microscopy in thermal noise mode. The resonance frequencies and quality factors are extracted from the measurement of the power spectrum density of the probe oscillation for a broad range of gap distances and Womersley numbers. The shift in the resonance frequency of the colloidal probe as the probe goes close to a solid wall infers the wall-induced variations of the effective mass of the probe. Interestingly, a crossover from a positive to a negative shift is observed as the Womersley number increases. In order to rationalize the results, the confined unsteady Stokes equation is solved numerically using a finite-element method, as well as asymptotic calculations. The in-phase and out-of-phase terms of the hydrodynamic drag acting on the sphere are obtained and agree well with the experimental results. All together, the experimental, theoretical and numerical results show that the hydrodynamic force felt by an immersed sphere oscillating near a wall is highly dependent on the Womersley number

Circulation du sang dans des architectures microfluidiques : comportements collectifs de particules déformables en écoulement confiné

Dynamics and rheology of a 2D confined suspension of vesicles (a model for RBCs) is studied numerically by using an immersed boundary lattice Boltzmann method (IB-LBM). We pay a special attention to the link between the spatiotemporal organization of the suspension and rheology. We first analyze situations in which vesicles perform tank-treading. The pair of vesicles settles into an equilibrium state with constant relative distance, which is regulated by the confinement. The equilibrium distance increases with the gap between walls following a linear relationship. However, no stable equilibrium distance between two tumbling vesicles is observed. The presence or the lack thereof of an equilibrium distance between two vesicles dictates the spatiotemporal organization of the suspension (order or disorder). Ordering of the suspension is accompanied with quite ample oscillation of normalized viscosity as a function of concentration, while the effective viscosity exhibits plateau. The oscillations amplitude of normalized viscosity is suppressed when disordered pattern prevails.Beside the interactions in the shear plane discussed in 2D framework, the interactions in the vertical direction to the shear plane are also analyzed by 3D simulations of capsules (a model for RBCs) and experiments. We show that in a confined blood suspension RBCs spontaneously organize in a crystalline-like structure under the sole effect of hydrodynamic interaction. It is further shown that when RBCs are substituted by rigid particles order disappears in favor of disorder. Various crystalline orders take place depending on concentration and confinement. The intercellular distance of the crystalline structure is a linear function of confinement. Order appears as a subtle interplay between the lift force that pushes RBCs away from walls towards the center and hydrodynamics interaction in the vertical of shear flow plane. This study introduces a new paradigm in the field of dilute non-colloidal suspensions where the prevalence of disorder was up-to date the rule.The partition of RBCs at the level of bifurcations is addressed in our computer simulations and in vitro experiments, which reveal that the hematocrit partition depends strongly on the viscosity contrast between the viscosities of the RBC hemoglobin and the suspending fluid, as long as hematocrit is less than 20% (which is the normal range in microcirculation). In the extreme hemodilution, our results exhibit a new phenomenon: the low flow rate branch may receive higher hematocrit than the high flow rate branch in opposition to the known Zweifach-Fung effect. This phenomenon is observed under moderate confinement and is the result of a peculiar structuring of the cell suspension. Our findings suggest that the various RBCs properties must be taken into consideration and carefully analyzed in order to have a firm understanding of RBC distribution in microcirculation and thus oxygen delivery in the microcirculation in general.Finally, we carry out numerical simulations of a large number of RBCs flowing in a network that is structured in a honeycomb pattern. Our results reveal that as long as the hematocrit is less than 20% the RBCs with higher membrane rigidity show a larger lateral displacement in the network. Furthermore, we discover a deviation of RBC flux in network from that in straight tube where the more rigid RBCs get the smaller flux. Oppositely, the larger RBC flux is observed for the more rigid RBCs in the network. Finally, we report on the manifestation of a faster longitudinal diffusion of crowded RBCs with smaller deformability in the network. Our results provide interesting information on the RBC delivery in the network, which should be significant not only in the understanding of the blood perfusion and the RBC transit in the microcirculation but also in practical applications such as cell sorting and chemical analysis.La dynamique et la rhéologie d'une suspension 2D confinée de vésicules (un modèle de RBCs (globules rouges) ) sont étudiées numériquement en utilisant une méthode de Boltzmann sur réseau frontière immergée. Nous analysons d'abord les situations dans lesquelles les vésicules effectuent le mouvement de chenille de char. Des paires de vésicules se placent dans un état d'équilibre avec une distance relative constante et régulée par le confinement. La distance d'équilibre augmente avec l'intervalle entre les parois suivant une relation linéaire. Cependant, aucune distance d'équilibre stable entre deux vésicules en mouvement de tumbling n’est observée. La présence ou l'absence d'une distance d'équilibre entre deux vésicules dicte l'organisation spatio-temporelle de la suspension. L’organisation de la suspension s’accompagne d’assez amples oscillations de la viscosité normalisée variant en fonction de la concentration, tandis que la viscosité effective ne varie pas.Les interactions dans la direction verticale par rapport au plan de cisaillement sont analysées par des simulations en 3D de capsules et des expériences. Nous montrons que dans une suspension confinée de sang, les RBCs s’organisent spontanément en une structure cristalline sous le seul effet de l'interaction hydrodynamique. Il est en outre démontré que lorsque les RBCs sont remplacés par des particules rigides, l'ordre disparait pour laisser place au désordre. Différents ordres cristallins peuvent apparaître selon la concentration et le confinement. La distance intercellulaire de la structure cristalline est une fonction linéaire du confinement. L’ordre apparaît comme une interaction subtile entre la force de portance qui pousse les RBCs des murs vers le centre et l'interaction hydrodynamique dans la verticale du plan d'écoulement de cisaillement. Cette étude introduit un nouveau paradigme dans le domaine des suspensions non-colloïdales diluées où la prévalence des désordres était mise à jour la règle.La répartition des RBCs au niveau d’une bifurcation est abordée dans nos simulations sur ordinateur ainsi que dans des expériences in vitro. Ces études révèlent que la répartition de RBCs dépend fortement du contraste de viscosité entre la viscosité de l'hémoglobine du RBC et le fluide suspendant, tant que l'hématocrite est inférieure à 20%. Pour des dilutions importantes, nos résultats montrent un nouveau phénomène : la branche de faible débit peut recevoir une concentration plus élevé que la branche de haut débit, en opposition à l'effet Zweifach-Fung. Ce phénomène est observé sous confinement modéré et est le résultat d'une structuration particulière de la suspension cellulaire. Nos résultats suggèrent que les différentes propriétés des RBCs doivent être prises en compte et soigneusement analysées afin d'avoir une bonne compréhension de la distribution de RBCs dans la microcirculation et donc de la livraison de l'oxygène dans la microcirculation en général.Enfin, nous réalisons des simulations numériques d'une grande quantité de RBCs, circulant dans un réseau qui est structuré selon un motif en nid d'abeilles. Nos résultats montrent que tant que l'hématocrite est inférieure à 20%, les RBCs dont la membrane est plus rigide présentent un déplacement latéral plus important dans le réseau. En plus, nous découvrons une différence par rapport à la circulation de RBCs dans un tube droit où le débit pour des globules rigides est plus petit. Au contraire, un débit plus important est observé pour les RBCs plus rigides dans le réseau. Enfin, nous présentons la manifestation d'une diffusion longitudinale plus rapide d’une suspension dense de RBCs de faible déformabilité dans le réseau. Nos résultats fournissent des informations intéressantes sur la livraison de RBCs dans le réseau, ce qui pourrait être important non seulement sur la compréhension de la perfusion du sang et le transit de RBC dans la microcirculation, mais aussi sur des applications pratiques

Blood flow in microfluidic architectures : collective behaviors of deformable particles in confined flow

La dynamique et la rhéologie d'une suspension 2D confinée de vésicules (un modèle de RBCs (globules rouges) ) sont étudiées numériquement en utilisant une méthode de Boltzmann sur réseau frontière immergée. Nous analysons d'abord les situations dans lesquelles les vésicules effectuent le mouvement de chenille de char. Des paires de vésicules se placent dans un état d'équilibre avec une distance relative constante et régulée par le confinement. La distance d'équilibre augmente avec l'intervalle entre les parois suivant une relation linéaire. Cependant, aucune distance d'équilibre stable entre deux vésicules en mouvement de tumbling n’est observée. La présence ou l'absence d'une distance d'équilibre entre deux vésicules dicte l'organisation spatio-temporelle de la suspension. L’organisation de la suspension s’accompagne d’assez amples oscillations de la viscosité normalisée variant en fonction de la concentration, tandis que la viscosité effective ne varie pas.Les interactions dans la direction verticale par rapport au plan de cisaillement sont analysées par des simulations en 3D de capsules et des expériences. Nous montrons que dans une suspension confinée de sang, les RBCs s’organisent spontanément en une structure cristalline sous le seul effet de l'interaction hydrodynamique. Il est en outre démontré que lorsque les RBCs sont remplacés par des particules rigides, l'ordre disparait pour laisser place au désordre. Différents ordres cristallins peuvent apparaître selon la concentration et le confinement. La distance intercellulaire de la structure cristalline est une fonction linéaire du confinement. L’ordre apparaît comme une interaction subtile entre la force de portance qui pousse les RBCs des murs vers le centre et l'interaction hydrodynamique dans la verticale du plan d'écoulement de cisaillement. Cette étude introduit un nouveau paradigme dans le domaine des suspensions non-colloïdales diluées où la prévalence des désordres était mise à jour la règle.La répartition des RBCs au niveau d’une bifurcation est abordée dans nos simulations sur ordinateur ainsi que dans des expériences in vitro. Ces études révèlent que la répartition de RBCs dépend fortement du contraste de viscosité entre la viscosité de l'hémoglobine du RBC et le fluide suspendant, tant que l'hématocrite est inférieure à 20%. Pour des dilutions importantes, nos résultats montrent un nouveau phénomène : la branche de faible débit peut recevoir une concentration plus élevé que la branche de haut débit, en opposition à l'effet Zweifach-Fung. Ce phénomène est observé sous confinement modéré et est le résultat d'une structuration particulière de la suspension cellulaire. Nos résultats suggèrent que les différentes propriétés des RBCs doivent être prises en compte et soigneusement analysées afin d'avoir une bonne compréhension de la distribution de RBCs dans la microcirculation et donc de la livraison de l'oxygène dans la microcirculation en général.Enfin, nous réalisons des simulations numériques d'une grande quantité de RBCs, circulant dans un réseau qui est structuré selon un motif en nid d'abeilles. Nos résultats montrent que tant que l'hématocrite est inférieure à 20%, les RBCs dont la membrane est plus rigide présentent un déplacement latéral plus important dans le réseau. En plus, nous découvrons une différence par rapport à la circulation de RBCs dans un tube droit où le débit pour des globules rigides est plus petit. Au contraire, un débit plus important est observé pour les RBCs plus rigides dans le réseau. Enfin, nous présentons la manifestation d'une diffusion longitudinale plus rapide d’une suspension dense de RBCs de faible déformabilité dans le réseau. Nos résultats fournissent des informations intéressantes sur la livraison de RBCs dans le réseau, ce qui pourrait être important non seulement sur la compréhension de la perfusion du sang et le transit de RBC dans la microcirculation, mais aussi sur des applications pratiques.Dynamics and rheology of a 2D confined suspension of vesicles (a model for RBCs) is studied numerically by using an immersed boundary lattice Boltzmann method (IB-LBM). We pay a special attention to the link between the spatiotemporal organization of the suspension and rheology. We first analyze situations in which vesicles perform tank-treading. The pair of vesicles settles into an equilibrium state with constant relative distance, which is regulated by the confinement. The equilibrium distance increases with the gap between walls following a linear relationship. However, no stable equilibrium distance between two tumbling vesicles is observed. The presence or the lack thereof of an equilibrium distance between two vesicles dictates the spatiotemporal organization of the suspension (order or disorder). Ordering of the suspension is accompanied with quite ample oscillation of normalized viscosity as a function of concentration, while the effective viscosity exhibits plateau. The oscillations amplitude of normalized viscosity is suppressed when disordered pattern prevails.Beside the interactions in the shear plane discussed in 2D framework, the interactions in the vertical direction to the shear plane are also analyzed by 3D simulations of capsules (a model for RBCs) and experiments. We show that in a confined blood suspension RBCs spontaneously organize in a crystalline-like structure under the sole effect of hydrodynamic interaction. It is further shown that when RBCs are substituted by rigid particles order disappears in favor of disorder. Various crystalline orders take place depending on concentration and confinement. The intercellular distance of the crystalline structure is a linear function of confinement. Order appears as a subtle interplay between the lift force that pushes RBCs away from walls towards the center and hydrodynamics interaction in the vertical of shear flow plane. This study introduces a new paradigm in the field of dilute non-colloidal suspensions where the prevalence of disorder was up-to date the rule.The partition of RBCs at the level of bifurcations is addressed in our computer simulations and in vitro experiments, which reveal that the hematocrit partition depends strongly on the viscosity contrast between the viscosities of the RBC hemoglobin and the suspending fluid, as long as hematocrit is less than 20% (which is the normal range in microcirculation). In the extreme hemodilution, our results exhibit a new phenomenon: the low flow rate branch may receive higher hematocrit than the high flow rate branch in opposition to the known Zweifach-Fung effect. This phenomenon is observed under moderate confinement and is the result of a peculiar structuring of the cell suspension. Our findings suggest that the various RBCs properties must be taken into consideration and carefully analyzed in order to have a firm understanding of RBC distribution in microcirculation and thus oxygen delivery in the microcirculation in general.Finally, we carry out numerical simulations of a large number of RBCs flowing in a network that is structured in a honeycomb pattern. Our results reveal that as long as the hematocrit is less than 20% the RBCs with higher membrane rigidity show a larger lateral displacement in the network. Furthermore, we discover a deviation of RBC flux in network from that in straight tube where the more rigid RBCs get the smaller flux. Oppositely, the larger RBC flux is observed for the more rigid RBCs in the network. Finally, we report on the manifestation of a faster longitudinal diffusion of crowded RBCs with smaller deformability in the network. Our results provide interesting information on the RBC delivery in the network, which should be significant not only in the understanding of the blood perfusion and the RBC transit in the microcirculation but also in practical applications such as cell sorting and chemical analysis

Two-Phase Crystallization in a Carpet of Inertial Spinners

We study the dynamics of torque driven spherical spinners settled on a surface, and demonstrate that hydrodynamic interactions at finite Reynolds numbers can lead to a concentration dependent and non-uniform crystallisation. At semi-dilute concentrations, we observe a rapid formation of a uniform hexagonal structure in the spinner monolayer. We attribute this to repulsive hydrodynamic interactions created by the secondary flow of the spinning particles. Increasing the surface coverage leads to a state with two co-existing spinner densities. The uniform hexagonal structure deviates into a high density crystalline structure surrounded by a continuous lower density hexatically ordered state. We show that this phase separation occurs due to a non-monotonic hydrodynamic repulsion, arising from a concentration dependent spinning frequency