A few upstream bifurcations drive the spatial distribution of red blood cells in model microfluidic networks.

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.

Long-range hydrodynamic forces in liquid FM-AFM.

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 ß 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 ß 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, ß int is small at long distance and diverges at short probe-surface distance, as predicted by the classical Reynolds sphere model.

Determination of Interfacial Concentration of a Contaminated Droplet from Shape Oscillation Damping.

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.

Interfacial Dynamics and Rheology of a Crude-Oil Droplet Oscillating in Water at a High Frequency.

We report investigations of a pendant diluted crude-oil droplet in water that is forced to oscillate at a frequency ω. The droplet interface contains a significant amount of surface-active agents and displays a marked viscoelastic rheology with elastic moduli larger than viscous ones. At a low frequency, fluid viscosity and inertia are negligible, which allows a direct determination of the dilatational interface rheology. At a large frequency, eigenmodes of inertial shape oscillations are excited. By decomposing the interface shape into spherical harmonics, the resonance curves of the inertial modes of the interface are determined, as well as the frequency and damping rate of each mode. These two parameters are of major importance for the prediction of the deformation and breakup of a droplet in any unsteady flow without any prior knowledge of either the chemical composition or the detailed rheological properties of the interface. Then, interfacial rheology is related to interface dynamics by solving the coupled dynamic equations for the two fluids and the interface. It turns out that the rheology of the interface is well described by an equivalent two-dimensional viscoelastic material, the elasticities and viscosities of which depend upon the frequency. A first significant result is that shear and dilatational elasticities are closely connected, as are shear and dilatational viscosities. This implies that intrinsic rheology plays a major role and that compositional rheology is either negligible or strongly coupled to the intrinsic one. A second major result is that, for moderately aged droplets (≤5000 s), the elasticity and viscosity at a high frequency (10-80 Hz) can be extrapolated from low-frequency measurements (≤1 Hz) by a simple power law of the frequency, ωz. The exponent z is related to the loss angle θloss by a relation found in many previous low-frequency investigations of crude-oil interfaces: z = θloss/2π. The present work thus extends classic observations obtained at a low frequency to a higher frequency range corresponding to the natural frequency of the droplets, where the droplet shape results from the balance between dynamic pressure and surface stresses and the interface involves simultaneous shear and dilatation. These results bring about serious constraints regarding the modeling of physicochemical underlying mechanisms and provide some insights for the understanding of the structure of crude-oil interfaces.

Going beyond 20 µm-sized channels for studying red blood cell phase separation in microfluidic bifurcations.

Despite the development of microfluidics, experimental challenges are considerable for achieving a quantitative study of phase separation, i.e., the non-proportional distribution of Red Blood Cells (RBCs) and suspending fluid, in microfluidic bifurcations with channels smaller than 20 µm. Yet, a basic understanding of phase separation in such small vessels is needed for understanding the coupling between microvascular network architecture and dynamics at larger scale. Here, we present the experimental methodologies and measurement techniques developed for that purpose for RBC concentrations (tube hematocrits) ranging between 2% and 20%. The maximal RBC velocity profile is directly measured by a temporal cross-correlation technique which enables to capture the RBC slip velocity at walls with high resolution, highlighting two different regimes (flat and more blunted ones) as a function of RBC confinement. The tube hematocrit is independently measured by a photometric technique. The RBC and suspending fluid flow rates are then deduced assuming the velocity profile of a Newtonian fluid with no slip at walls for the latter. The accuracy of this combination of techniques is demonstrated by comparison with reference measurements and verification of RBC and suspending fluid mass conservation at individual bifurcations. The present methodologies are much more accurate, with less than 15% relative errors, than the ones used in previous in vivo experiments. Their potential for studying steady state phase separation is demonstrated, highlighting an unexpected decrease of phase separation with increasing hematocrit in symmetrical, but not asymmetrical, bifurcations and providing new reference data in regimes where in vitro results were previously lacking.

Velocimetry of red blood cells in microvessels by the dual-slit method: effect of velocity gradients.

The dual-slit is a photometric technique used for the measurement of red blood cell (RBC) velocity in microvessels. Two photometric windows (slits) are positioned along the vessel. Because the light is modulated by the RBCs flowing through the microvessel, a time dependent signal is captured for each window. A time delay between the two signals is obtained by temporal cross correlation, and is used to deduce a velocity, knowing the distance between the two slits. Despite its wide use in the field of microvascular research, the velocity actually measured by this technique has not yet been unambiguously related to a relevant velocity scale of the flow (e.g. mean or maximal velocity) or to the blood flow rate. This is due to a lack of fundamental understanding of the measurement and also because such a relationship is crucially dependent on the non-uniform velocity distribution of RBCs in the direction parallel to the light beam, which is generally unknown. The aim of the present work is to clarify the physical significance of the velocity measured by the dual-slit technique. For that purpose, dual-slit measurements were performed on computer-generated image sequences of RBCs flowing in microvessels, which allowed all the parameters related to this technique to be precisely controlled. A parametric study determined the range of optimal parameters for the implementation of the dual-slit technique. In this range, it was shown that, whatever the parameters governing the flow, the measured velocity was the maximal RBC velocity found in the direction parallel to the light beam. This finding was then verified by working with image sequences of flowing RBCs acquired in PDMS micro-systems in vitro. Besides confirming the results and physical understanding gained from the study with computer generated images, this in vitro study showed that the profile of RBC maximal velocity across the channel was blunter than a parabolic profile, and exhibited a non-zero sliding velocity at the channel walls. Overall, the present work demonstrates the robustness and high accuracy of the optimized dual-slit technique in various flow conditions, especially at high hematocrit, and discusses its potential for applications in vivo.

Dynamical model for the buoyancy-driven zigzag motion of oblate bodies.

We describe a dynamical model that predicts the zigzag motion of disks and oblate spheroids moving freely in a viscous liquid over a continuous range of aspect ratios and Reynolds numbers. This model combines the generalized Kirchhoff equations to describe the linear and angular momentum balances for the fluid-body system with a dynamical model for the wake-induced force and torque that incorporates the main characteristics of the wake dynamics deduced from previous experimental observations. The resulting model is shown to be able to reproduce quantitatively the oscillatory paths measured experimentally.

Wake attenuation in large Reynolds number dispersed two-phase flows.

The dynamics of high Reynolds number-dispersed two-phase flow strongly depends on the wakes generated behind the moving bodies that constitute the dispersed phase. The length of these wakes is considerably reduced compared with those developing behind isolated bodies. In this paper, this wake attenuation is studied from several complementary experimental investigations with the aim of determining how it depends on the body Reynolds number and the volume fraction alpha. It is first shown that the wakes inside a homogeneous swarm of rising bubbles decay exponentially with a characteristic length that scales as the ratio of the bubble diameter d to the drag coefficient Cd, and surprisingly does not depend on alpha for 10(-2)

Compression of a capsule: mechanical laws of membranes with negligible bending stiffness.

The compression of a capsule between two plates is considered. The problem is solved numerically for a capsule made of an incompressible liquid drop surrounded by a thin elastic membrane which has a negligible bending stiffness. Numerical results are provided for three different mechanical laws of the membrane. By considering elastic moduli independent of the deformation, we show that the isotropic dilation plays the major role. In particular, an asymptotic behavior independent of the shear modulus is found for large deformations. For more complex models, the deformation limits beyond which the variation of elastic moduli starts to play a role are examined. The results indicate that the distinction between the different models requires a careful inspection of both small and large deformations. The theoretical predictions are compared with experimental results. For millimetric capsules with membranes made of covalently linked human serum albumin and alginate, the best agreement is obtained by considering that the elastic moduli are independent of the deformation and range from 0.1 to 4 N/m.