Shear thinning and shear thickening of a confined suspension of vesicles.

Widely regarded as an interesting model system for studying flow properties of blood, vesicles are closed membranes of phospholipids that mimic the cytoplasmic membranes of red blood cells. In this study we analyze the rheology of a suspension of vesicles in a confined geometry: the suspension, bound by two planar rigid walls on each side, is subject to a shear flow. Flow properties are then analyzed as a function of shear rate γ[over ̇], the concentration of the suspension ϕ, and the viscosity contrast λ=η_{in}/η_{out}, where η_{in} and η_{out} are the fluid viscosities of the inner and outer fluids, respectively. We find that the apparent (or effective viscosity) of the suspension exhibits both shear thinning (decreasing viscosity with shear rate) or shear thickening (increasing viscosity with shear rate) in the same concentration range. The shear thinning or thickening behaviors appear as subtle phenomena, dependant on viscosity contrast λ. We provide physical arguments on the origins of these behaviors.

Boltzmann equations and ab initio calculations: comparative study of cubic and wurtzite CdSe.

The electronic and optical properties of CdSe in two phases, cubic and wurtzite, have been studied by first principal calculations using the density functional theory. The optical parameters such as transmittance, optical absorption, refractive index and extinction coefficient have been investigated. We have calculated also the band structure, and total/partial density of state using the full potential-linearized augmented plane wave method with the local density approximation, generalized gradient approximation and the modified Becke-Johnson functional (mBJ), implemented in the Wien2k package. With the mBJ approximation the gap found for cubic and wurtzite structure is direct and is equal to 1.85 and 1.7 eV respectively, what corresponds to the experiment results. The optical absorption is significant in the ultraviolet field while it becomes low beyond 600 nm in the visible light for CdSe in different structures. From λ = 400 nm the transmittance is stable and reaches 80 %. With Boltztrap package, we have investigated also that with increasing temperature, the electrical conductivity increases. During the calculation, the cubic structure has presented an isotropy. While for wurtzite CdSe, the propagation of waves into system is different in xx and zz directions. These results can be exploited in several applications of CdSe in optoelectronic devices.

On the problem of slipper shapes of red blood cells in the microvasculature.

Red blood cells (RBC) are known to exhibit non symmetric (slipper) shapes in the microvasculature. Vesicles have been recently used as a model for RBC and numerical simulations proved the existence of slipper shapes under Poiseuille flow (both in unconfined and confined geometry). However, in our recent numerical simulations the transition from symmetric (parachute) shape to the slipper one was found to take place upon decreasing the flow strength, while experiments on RBCs showed the contrary. In this work we show that if the viscosity contrast (ratio between the internal over external fluid viscosities) is different from unity, as is the case with RBCs, the transition from parachute to slipper shape occurs upon increasing the flow strength, in agreement with experiments. We provide the phase diagram of shapes in the microcirculation. The slipper is found to have a higher speed than the parachute (for the same parameters), that we believe to be the basic reason for its prevailing in the microvasculature. We provide a simple geometrical picture that explains the slipper flow efficiency over the parachute one. Finally, we show that there exists in parameter space regions of co-existence of slipper/parachute shapes and suggest simple experimental protocols to test these findings. The coexistence of shapes seems to be supported by experiments, though a systematic experimental study is lacking. A potential application of this work is to guide designing flow-based experiments in order to link the shape of RBCs to pathologies affecting cell deformability, such as sickle cell diseases, malaria, and those affecting blood hematocrit, as in polycythemia vera disease.

Complexity of vesicle microcirculation.

This study focuses numerically on dynamics in two dimensions of vesicles in microcirculation. The method used is based on boundary integral formulation. This study is inspired by the behavior of red blood cells (RBCs) in the microvasculature. Red RBCs carry oxygen from the lungs and deliver it through the microvasculature. The shape adopted by RBCs can affect blood flow and influence oxygen delivery. Our simulation using vesicles (a simple model for RBC) reveals unexpected complexity as compared to the case where a purely unbounded Poiseuille flow is considered [Kaoui, Biros, and Misbah, Phys. Rev. Lett. 103, 188101 (2009)]. In sufficiently large channels (in the range of 100 µm; the vesicle size and its reduced volume are taken in the range of those of a human RBC), such as arterioles, a slipperlike (asymmetric) shape prevails. A parachutelike (symmetric) shape is adopted in smaller channels (in the range of 20 µm, as in venules), but this shape loses stability and again changes to a pronounced slipperlike morphology in channels having a size typical of capillaries (5-10 µm). Stiff membranes, mimicking malaria infection, for example, adopt a centered or off-centered snakelike locomotion instead (the denomination snaking is used for this regime). A general scenario of how and why vesicles adopt their morphologies and dynamics among several distinct possibilities is provided. This finding potentially points to nontrivial RBCs dynamics in the microvasculature.

Rheology of particulate suspensions in a Poiseuille flow.

Particulate dense suspensions behave as complex fluids. They do not lend themselves easily to analytical solution. We propose an analytical model to mimic this problem. Namely, we consider arrays of long parallel plates which represent a simplification of arrays of chains of spherical particles. This simplified model can be solved analytically. The effect of effective rotation of the spherical particles is taken into account by attributing different velocities on each side of the plate that mimics the fact that particles are subject to shear. This work is an extension of a previous study where particle rotation was disregarded. The flow rate, the dissipation and the apparent viscosity are studied as a function of the underlying structure. For a single plate placed out of the flow center, the viscosity is lower when rotation is taken into account. For two plates, the minimal viscosity corresponds to the situation where the particles are as close as possible to the center and arranged symmetrically with respect to the center. We compute the rheological properties for arbitrary plate positions, and exploit them for a periodic arrangement. For N plates, and in a confined geometry, the viscosity is about twice as small as compared to the situation where rotation is ignored. We have conducted a numerical study of a suspension of spherical particles, and linear chains of spherical particles. The numerical study is in good qualitative and semiquantitative agreement with the analytical theory considering long plates. This agreement highlights the fact that our analytical model captures the essential features of a real suspension. The numerical study is based on a fluid dynamic particle method where the particles are represented by a scalar field having high viscosity inside.

On coupling between the orientation and the shape of a vesicle under a shear flow.

A simple 2D model of deformable vesicles tumbling in a shear under flow is introduced in order to account for the main qualitative features observed experimentally as shear rates are increased. The simplicity of the model allows for a full analytical tractability while retaining the essential physical ingredients. The model reveals that the main axes of the vesicle undergo oscillations which are coupled to the vesicle orientation in the flow. The model reproduces and sheds light on the main novel features reported in recent experiments [M. Mader et al., Eur. Phys. J. E. 19, 389 (2006)], namely that both coefficients A and B that enter the Keller-Skalak equation, d psi/dt = A+B cos(2 psi) (psi is the vesicle orientation angle in the shear flow), undergo a collapse upon increasing shear rate.

Anisotropy effect on two-dimensional cellular-automaton traffic flow with periodic and open boundaries.

Using computer simulations we investigate, in a version of the Biham-Middleton-Levine model with random sequential update on a square lattice, the anisotropy effect of the probabilities of the change of the motion directions of cars, from up to right (p(ur)) and from right to up (p(ru)), on the dynamical jamming transition and velocities under periodic boundaries on one hand and the phase diagram under open boundaries on the other hand. However, in the former case, the sharp jamming transition appears only for p(ur)=0=p(ru)=0 (i.e., when the cars alter their motion directions). In the open boundary conditions, it is found that the first-order line transition between jamming and moving phases is curved. Hence, by increasing the anisotropy, the moving phase region expands as well as the contraction of the jamming and maximal current phases takes place. Moreover, in the anisotropic case, the transition between the jamming phase (or moving phase) and the maximal current phase is of second order while in the isotropic case, and when each car changes its direction of motion at every time step (p(ru)=p(ur)=1), the transition is of first order. Furthermore, in the maximal current phase, the density profile decays with an exponent gamma approximately 1/4.

Edge wetting of an Ising three-dimensional system.

The effect of edge on wetting and layering transitions of a three-dimensional spin-1/2 Ising model is investigated, in the presence of longitudinal and surface magnetic fields, using mean field theory and Monte Carlo simulations. For T=0, the ground state phase diagram shows that there exist only three allowed transitions, namely, surface and bulk transition, surface transition, and bulk transition. However, there exist a surface intralayering temperature T(s)(L), above which the surface and the intralayering surface transitions occur. While the bulk layering and intralayering transitions appear above another finite temperature T(b)(L)(>or=T(s)(L)). These surface and bulk intralayering transitions are not seen in the perfect surfaces case. Numerical values of T(s)(L) and T(b)(L), computed by Monte Carlo method are found to be smaller than those obtained using mean field theory. However, the results predicted by the two methods become similar, and are exactly those given by the ground state phase diagram, for very low temperatures. On the other hand, the behavior of the local magnetizations as a function of the external magnetic field, shows that the transitions are of the first order type. T(s)(L) and T(b)(L) decrease when increasing the system size and/or the surface magnetic field. In particular, T(b)(L) reaches the wetting temperature T(w) for sufficiently large system sizes.