Transport of spheres suspended in the fluid flowing between hexagonally arranged cylinders

The motion of a spherical particle suspended in an incompressible Newtonian fluid flowing longitudinally between hexagonally arranged circular cylinders has been numerically analysed by a finite-element method in the Stokes flow regime. The results are applied to study the diffusive and convective transport of spherical solutes across the vascular endothelial surface glycocalyx, based on the quasi-periodic ultrastructural model. The obtained values of diffusive permeability and reflection coefficient of the solutes show a reasonable agreement with experimental observations, and conform to the hypothesis that the endothelial surface glycocalyx forms the primary size selective structure to solutes in microvascular permeability

Experimental and numerical identification of the spiral wave in a wide-gap spherical Couette flow

Spherical Couette flow experiments were conducted according to the work of Egbers and Rath [Acta Mech. 111 pp.125--140 (1995)]. The flow was visualized using aluminum flakes drifted on a horizontal plane illuminated by a laser sheet. A comparison between the numerically calculated phase velocity and that calculated from the visualized flow images indicates the robust formation of a spiral wave with azimuthal wavenumber m=3. By solving the equation of motion for the infinitesimal surface elements advecting in the flow field obtained numerically, this study obtained a visual distribution of reflected light, which is in good agreement with the picture obtained experimentally

Axial and nonaxial migration of red blood cells in a microtube

Human red blood cells (RBCs) are subjected to high viscous shear stress, especially during microcirculation, resulting in stable deformed shapes such as parachute or slipper shape. Those unique deformed RBC shapes, accompanied with axial or nonaxial migration, cannot be fully described according to traditional knowledge about lateral movement of deformable spherical particles. Although several experimental and numerical studies have investigated RBC behavior in microchannels with similar diameters as RBCs, the detailed mechanical characteristics of RBC lateral movement—in particular, regarding the relationship between stable deformed shapes, equilibrium radial RBC position, and membrane load—has not yet been fully described. Thus, we numerically investigated the behavior of single RBCs with radii of 4 µm in a circular microchannel with diameters of 15 µm. Flow was assumed to be almost inertialess. The problem was characterized by the capillary number, which is the ratio between fluid viscous force and membrane elastic force. The power (or energy dissipation) associated with membrane deformations was introduced to quantify the state of membrane loads. Simulations were performed with different capillary numbers, viscosity ratios of the internal to external fluids of RBCs, and initial RBC centroid positions. Our numerical results demonstrated that axial or nonaxial migration of RBC depended on the stable deformed RBC shapes, and the equilibrium radial position of the RBC centroid correlated well with energy expenditure associated with membrane deformations.Takeishi N, Yamashita H, Omori T, Yokoyama N, Sugihara-Seki M. Axial and Nonaxial Migration of Red Blood Cells in a Microtube. Micromachines. 2021; 12(10):1162. https://doi.org/10.3390/mi1210116

Segregation by size difference in binary suspensions of fluid droplets in channel flow

In channel flow of multicomponent suspensions, segregation behavior of suspended components perpendicular to the flow direction is often observed, which is considered to be caused by the differential properties of the lateral migration depending on their shape, size, flexibility, and other characteristics. In the present study, we investigate the effect of size differences between suspended components on the segregation behavior, by a two-dimensional numerical simulation for binary dispersed suspensions of fluid droplets of two different sizes subjected to a plane Poiseuille channel flow. The small and large droplets are assumed to have equal surface tensions and equal viscosity ratios of internal to external fluids. The time evolutions of the lateral positions of large and small droplets relative to the channel centerline were computed by changing the area fraction of the small droplets in a mixture with a constant total area fraction. The large droplets are found to migrate closer to the channel centerline and the small droplets are found to migrate closer to the channel wall compared to the corresponding lateral positions in mono-dispersed suspensions at the same area fractions, although the mean lateral positions of the large and small droplets in mono-dispersed suspension are comparable. This segregation behavior as well as the margination of small droplets are enhanced when the size difference between large and small droplets is increased and the area fraction of large droplets is increased. These results may arise from higher tendencies for the large droplets to approach the channel centerline compared to the small droplets, which consequently expel small droplets from the central region toward the channel walls

Two Phase Model Analysis for the Stokes Flow past a Sphere Attached to the Circular Tube Wall

微小血管内では,血管壁近傍に赤血球がほとんど通らない領域が見られ,血漿層と呼ばれている.本研究では,細静脈壁に接着している白血球に血流が及ぼす剪断応力に対して,血漿層が与える影響をモデル解析によって調べた.血管を直円管,白血球を剛体球とし,血液の流れを血漿層と,赤血球が多数通過する中心層とからなる二層流と仮定して白血球周りの流れ場を数値的に解析した.その結果として,血漿層の効果によって白血球に作用する剪断応力は増加することが示された.\nThe blood flow past a leukocyte adhered to the microvessel wall is analyzed by a numerical simulation, taking the presence of a cell-free layer into account. The adherent leukocyte is modeled as a sphere attached to the wall of a circular cylindrical tube. The blood flow is modeled as a two-phase flow, consisting of a plasma flow in a cell-free layer adjacent to the vessel wall and the cell-rich flow in the central region of the vessel. It is assumed that each fluid in both regions is Newtonian with a uniform viscosity and that the viscosity of the cell-free layer is smaller than that of the central core. The interface between the two regions is assumed to be parallel to the streamlines. Numerical simulations by a finite element method have demonstrated that there are two different cases of the flow pattern around a sphere: one is a case where the whole sphere is embedded in the cell-free layer, and the other is a case where the sphere is covered by the central core. In both cases, the maximum magnitudes of the shear stress acting on the leukocyte are higher than those in the absence of the cell-free layer

Transition of planar Couette flow at infinite Reynolds numbers

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<105) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit. © 2013 American Physical Society