Pierre Mills

Apparent viscosity and particle pressure of a concentrated suspension of non-Brownian hard spheres near the jamming transition

We consider the steady shear flow of a homogeneous and dense assembly of hard spheres suspended in a Newtonian viscous fluid. In a first part, a mean-field approach based on geometric arguments is used to determine the viscous dissipation in a dense isotropic suspension of smooth hard spheres and the hydrodynamic contribution to the suspension viscosity. In a second part, we consider the coexistence of transient solid clusters coupled to regions with free flowing particles near the jamming transition. The fraction of particles in transient clusters is derived through the Landau-Ginzburg concepts for first-order phase transition with an order parameter corresponding to the proportion of “solid” contacts. A state equation for the fraction of particle-accessible volume is introduced to derive the average normal stresses and a constitutive law that relates the total shear stress to the shear rate. The analytical expression of the average normal stresses well accounts for numerical or experimental evaluation of the particle pressure and non-equilibrium osmotic pressure in a dense sheared suspension. Both the friction level between particles and the suspension dilatancy are shown to determine the singularity of the apparent shear viscosity and the flow stability near the jamming transition. The model further predicts a Newtonian behavior for a concentrated suspension of neutrally buoyant particles and no shear thinning behavior in relation with the shear liquefaction of transient solid clusters.

Aggregation of human red blood cells after moderate heat treatment.

The aggregation behaviour of normal and heat treated (48.4 degrees C, 48.8 degrees C, 49.5 degrees C) red blood cells (RBCs) suspended in dextran-saline solutions (Dx 70, Dx 173) was investigated by a laser light reflectometric method over a wide range of bridging energies. The characteristic times of rouleau formation were found to be increased after RBC heat treatment. The disaggregation shear stress is not significantly different between normal RBCs and heat treated RBCs. The loss of cell deformability is nevertheless shown to improve slightly the dissociation efficiency of the flowing liquid in a shear flow resulting in a small reduction of the disaggregation shear rate after heat treatment. Heat treatment is also shown to alter the structure of RBC network at equilibrium. These results indicate that heat induced alterations of erythrocytes only affects the mechanical properties of the cell membrane without significant changes in the macromolecular bridging energy.

Velocity Profile Measurements by Laser-Doppler Velocimetry (LDV) in Plane Capillaries. Comparison with Theoretical Profiles from a Two-Fluid Model

Since the yeh and CUMMINS’ work 1 the velocity measurement of suspension flow with Laser Doppler Velocimeter has been widely developped. There are no important problems when the suspension concentration is low and when the tube dimensions are greater than those of the volume where the light beams interfere.

Rheology of Granular Materials and Sound Emission near the Jamming Transition

It is supposed that the shear stress of non cohesive granular material in the vicinity of the jamming transition is connected to the formation of transient rigid clusters of particles. Their characteristics are investigated as a function of the imposed pressure, the solid volume fraction and the shear rate. Those clusters are responsible for an increase of the shear stress for a vanishing shear rate, which leads to an instability close to the jamming transition. We debate the consequences for stick‐slip motion and flows down an inclined plane, in agreement with the observations. The oscillation of the granular material between two flow states generates fast velocity fluctuations. We infer that under certain conditions regarding the particles and the average flow height, an intermittent regime near the jamming transition, at a well defined frequency, can be a source of sound emission.

Aggregation and deformation of red blood cells as probed by a laser light scattering technique in a concentrated suspension: comparison between normal and pathological red blood cells

Changes in aggregability and/or deformability of red blood cells (RBC) can cause severe complications in blood circulation. We use a laser light scattering technique, which can distinguish between normal and pathological RBCs by studying the angular distributions of backscattered and transmitted light of concentrated suspensions of RBCs submitted to a simple shear flow. In order to study the deformation, we induced partial rigidity in the RBC membrane, and showed that the gradients of deformation and the relaxation times of normal and partially rigidified RBC membranes can be quantified using a non-Newtonian rheological model. We observe that blood aggregation of patients with `microcirculatory diseases, such as diabetes, differs from that of healthy individuals.

A Two-Fluid Model for Highly Concentrated Suspension Flow Through Narrow Tubes and Slits: Velocity Profiles, Apparent Fluidity and Wall Layer Thickness

Viscometric flows of highly concentrated suspensions in narrow slits and pipes exhibit a two phase structure if the particle size cannot be considered as infinitesimally small in comparison with the transverse dimension of the vessel. In pipes this leads to a Well-known1,2 annular structure with a particle rich axial core surrounded by a particle depleted wall layer. The former results in a blunted velocity profile and in a reduced mean concentration in the tube, compared to the feed reservoir concentration1. The latter works as a lubricant layer which lowers the apparent viscosity, hence, which decreases extensively the viscous energy loss, even if this layer is very thin, as it was usually observed with highly concentrated suspensions.

Aggregation and deformation of red blood cells as probed by a laser light scattering technique in a concentrated suspension: methodology

A light scattering technique is presented which investigates the backscattered and transmitted flux of He-Ne laser light illuminating a concentrated suspension of red blood cells (RBC) submitted to a simple shear flow. Our experiments show that the angular distributions of scattered light are closely related to the state of the suspension (at rest, or submitted to a simple shear flow) and the rheological parameters of the suspension such as viscosity and volume concentration. Transmitted and reflected light measurements demonstrated reproducible and predictable changes in scattering cross sections of oriented and deformed RBCs by shear flow. Additionally, it is shown that the scattering cross-section of aggregated RBCs is different from disaggregated RBCs. A theoretical model, substantiated by Monte- Carlo simulations, is proposed which relates the changes in shape of the angular distribution of scattered light to the rate of aggregation and the gradients of deformation of RBCs.

The Influence of the Internal Viscosity of Washed Red Blood Cells on Their Rheological Behaviour

The rheological characterization of washed RBC suspensions has been performed both using a low shear viscosimeter and a optical light back scattering system. Changing the volume of the cells and in such a way the hemoglobin concentration in the cells and/or the structure of the cell membrane by treatments with the antibiotic Amphotericin B and different pH, osmotic pressure or ionic strengths of the medium it was found that the rheological behaviour (relative viscosity in dependence on the shear rate,.02 s−1 – 128 s−1; intrinsic viscosities and the relaxation time corresponding to the orientation and desorientation) seems to be mainly connected with the change of the internal hemoglobin concentration.

An Optical Method for Studying Red Blood Cells Orientation and Aggregation in a Couette Flow of Blood Suspension

Red blood cell aggregation is certainly the most important factor in the non newtonian behaviour of normal human blood. Aggregated red blood cells build up rouleaux; this aggregation is reversible: at rest, the rouleaux form a three dimensional network structure; when a finite stress is applied to the suspension the structure breaks. Increasing the stress, the rouleaux are gradually disrupted and are finally reduced up to individual cells. With decrease in stress individual cells build up again rouleaux. In a steady state a dynamical equilibrium exists between the size of rouleaux and the stress applied. When the applied stress is high enough to break the rouleaux, cells can be oriented and deformed in the flow. There was studied an experimental method which allows us to rely the luminous flux backscattered by rouleaux and individual cells to their mean size and to their orientation.