Influence de l’agrégation érythrocytaire sur la migration axiale de microparticules simulant des plaquettes sanguines

Lors du phénomène d’hémostase primaire ou de thrombose vasculaire, les plaquettes sanguines doivent adhérer aux parois afin de remplir leur fonction réparatrice ou pathologique. Pour ce faire, certains facteurs rhéologiques et hémodynamiques tels que l’hématocrite, le taux de cisaillement local et les contraintes de cisaillement pariétal, entrent en jeu afin d’exclure les plaquettes sanguines de l’écoulement principal et de les transporter vers le site endommagé ou enflammé. Cette exclusion pourrait aussi être influencée par l’agrégation de globules rouges qui est un phénomène naturel présent dans tout le système cardiovasculaire selon les conditions d’écoulement. La dérive de ces agrégats de globules rouges vers le centre des vaisseaux provoque la formation de réseaux d’agrégats dont la taille et la complexité varient en fonction de l’hématocrite et des conditions de cisaillement présentes. Il en résulte un écoulement bi-phasique avec un écoulement central composé d’agrégats de globules rouges avoisinés par une région moins dense en particules où l’on peut trouver des globules rouges singuliers, des petits rouleaux de globules rouges et une importante concentration en plaquettes et globules blancs. De ce fait, il est raisonnable de penser que plus la taille des agrégats qui occupent le centre du vaisseau augmente, plus il y aura de plaquettes expulsées vers les parois vasculaires. L'objectif du projet est de quantifier, in vitro, la migration des plaquettes sanguines en fonction du niveau d’agrégation érythrocytaire présent, en faisant varier l’hématocrite, le taux de cisaillement et en promouvant l’agrégation par l’ajout d’agents tels que le dextran à poids moléculaire élevé. Cependant, le comportement non Newtonien du sang dans un écoulement tubulaire peut être vu comme un facteur confondant à cause de son impact sur l’organisation spatiale des agrégats de globules rouges. De ce fait, les études ont été réalisées dans un appareil permettant de moduler, de façon homogène, la taille et la structure de ces agrégats et de quantifier ainsi leur effet sur la migration axiale des plaquettes. Du sang de porc anti coagulé a été ajusté à différents taux d’hématocrite et insérer dans un appareil à écoulement de Couette, à température ambiante. Les plaquettes sanguines, difficilement isolables in vitro sans en activer certains ligands membranaires, ont été remplacées par des fantômes en polystyrène ayant un revêtement de biotine. La quantification de la migration de ces fantômes de plaquettes a été réalisée grâce à l’utilisation de membranes biologiques fixées sur les parois internes de l’entrefer du rhéomètre de Couette. Ces membranes ont un revêtement de streptavidine assurant une très forte affinité d’adhésion avec les microparticules biotynilées. À 40% d’hématocrite, à un cisaillement de 2 s-1, 566 ± 53 microparticules ont été comptées pour un protocole préétabli avec du sang non agrégeant, comparativement à 1077 ± 229 pour du sang normal et 1568 ± 131 pour du sang hyper agrégeant. Les résultats obtenus suggèrent une nette participation de l’agrégation érythrocytaire sur le transport des fantômes de plaquettes puisque l’adhésion de ces derniers à la paroi du rhéomètre de Couette augmente de façon quasi exponentielle selon le niveau d’agrégation présent.

Heat transfer in plane Couette flow of a rarefied gas using Bhatnagar-Gross-Krook model

Using the linearized BGK model and the method of moments of half-range distribution functions the temperature jumps at two plates are determined, and it is found that the results are in fair agreement with those of Gross and Ziering, and Ziering.

Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified "half-range" quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Linear stability, transient growth and the role of viscosity stratification in compressible Couette flow

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M, the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, α) of each mean flow belongs to different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II.” For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, Gmax, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For α=0, the linear stability operator can be partitioned into L∼L̅ +Re2 Lp, and the Re-dependent operator Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t∕Re)∼Re2. In contrast, the dominance of Lp is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

Rheometry of granular materials in cylindrical Couette cells: Anomalous stress caused by gravity and shear

The cylindrical Couette device is commonly employed to study the rheology of fluids, but seldom used for dense granular materials. Plasticity theories used for granular flows predict a stress field that is independent of the shear rate, but otherwise similar to that in fluids. In this paper we report detailed measurements of the stress as a function of depth, and show that the stress profile differs fundamentally from that of fluids, from the predictions of plasticity theories, and from intuitive expectation. In the static state, a part of the weight of the material is transferred to the walls by a downward vertical shear stress, bringing about the well-known Janssen saturation of the stress in vertical columns. When the material is sheared, the vertical shear stress changes sign, and the magnitudes of all components of the stress rise rapidly with depth. These qualitative features are preserved over a range of the Couette gap and shear rate, for smooth and rough walls and two model granular materials. To explain the anomalous rheological response, we consider some hypotheses that seem plausibleapriori, but showthat none survive after careful analysis of the experimental observations. We argue that the anomalous stress is due to an anisotropic fabric caused by the combined actions of gravity, shear, and frictional walls, for which we present indirect evidence from our experiments. A general theoretical framework for anisotropic plasticity is then presented. The detailed mechanics of how an anisotropic fabric is brought about by the above-mentioned factors is not clear, and promises to be a challenging problem for future investigations. (C) 2013 AIP Publishing LLC.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

拟压缩性方法在非定常球形Couette-Taylor流模拟中的应用

本文以拟压缩性法和物理时间/伪时间双重时间推进,数值求解非定常不可压缩流N=S方程。拟压缩性项是对伪时间的导数项,在每一物理时间层,进行对伪时间的推进使拟压缩性项趋于零,从而使连续方程得到满足。用Lower-Upper Symmetric Gaus-—Seidel(LU-SGS)恪式求解离散所得的方程。针对前人LU-SGS格式未计及隐式物理粘性,在计算中低Re数流动时容易发散或造成收敛率低的问题,利用简化的隐式粘性项改善了格式的稳定性,并用三阶迎风紧致差分逼近无粘通量,提高了伪时间推进的收敛率。模拟了间隙比σ=0.18的两同心旋转球之间轴对称Couette-Taylor流的0-、1-和2-涡三种流态和它们之间的转变过程。

过渡领域圆柱间Couette流动

<正> 圆柱间Couette流动问题是最简单的流动情况之一,当圆柱转速较大(M≈1)而间隙与半径之比[δ=(R_2-R_1)/R_1]不为小量时,却可用以检验求解过渡领域中非线性问题的各种方法。不久前,文献[1,2]在M≈1,δ=0.5条件下用电子束做了同心圆柱间氩气密度分布的测量,提供了一组比较流场结构的实验数据。在较早的稀薄气体Couette

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220