Ye Ting, Phan-Thien Nhan, Lim Chwee Teck, Li Yu
Department of Computational Mathematics, Jilin University, China.
Department of Mechanical Engineering, National University of Singapore, Singapore.
J Biomech. 2017 Dec 8;65:12-22. doi: 10.1016/j.jbiomech.2017.09.027. Epub 2017 Oct 7.
The flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications, such as red blood cells (RBCs) passing through the curved arteries in circulation, and cells sorting through a shear-induced migration in a curved channels. Most of past numerical studies focused on the cell deformation in small straight microvessels, or on the flow pattern in large curved vessels without considering the cell deformation. However, there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel. In this work, a particle-based method, smoothed dissipative particle dynamics (SDPD), is used to simulate the motion and deformation of a RBC in a curved microvessel of diameter comparable to the RBC diameter. The emphasis is on the effects of the curvature, the type and the size of the curved microvessel on the RBC deformation and the flow pattern. The simulation results show that a small curved shape of the microvessel has negligible effect on the RBC behavior and the flow pattern which are similar to those in a straight microvessel. When the microvessel is high in curvature, the secondary flow comes into being with a pair of Dean vortices, and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel. The RBC also loses the axisymmetric deformation, and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature. It is also found that a pair of Dean vortices arise only under the condition of De>1 (De is the Dean number, a ratio of centrifugal to viscous competition). The Dean vortices are more easily observed in the larger or more curved microvessels. Finally, it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel, i.e., the fluid close to the inner wall flows faster than that close to the outer wall. This is contrary to the common sense in large curved vessels. This velocity skewness was found to depend on the curvature of the microvessel, as well as the viscous and inertial forces.
在各种生物医学和生物工程应用中，经常会遇到细胞在弯曲血管中的流动情况，例如循环中红细胞（RBC）通过弯曲的动脉，以及细胞在弯曲通道中通过剪切诱导迁移进行分选。过去的大多数数值研究都集中在小直径直管微血管中的细胞变形，或者大直径弯曲血管中的流动模式，而没有考虑细胞变形。然而，很少有人尝试研究弯曲微血管中的细胞变形及相关流动模式。在这项工作中，采用基于粒子的方法——平滑耗散粒子动力学（SDPD），来模拟直径与红细胞直径相当的弯曲微血管中红细胞的运动和变形。重点是弯曲度、弯曲微血管的类型和尺寸对红细胞变形及流动模式的影响。模拟结果表明，微血管的小弯曲形状对红细胞行为和流动模式的影响可忽略不计，这与直管微血管中的情况相似。当微血管曲率较高时，会形成带有一对迪恩涡的二次流，主流的速度剖面会向微血管内壁倾斜。红细胞也会失去轴对称变形，在通过大曲率微血管的弯曲部分时，它会先被拉伸然后收缩。还发现只有在迪恩数De>1（De是迪恩数，即离心力与粘性力竞争的比值）的条件下才会出现一对迪恩涡。在更大或更弯曲的微血管中更容易观察到迪恩涡。最后，观察到主流的速度剖面朝着弯曲微血管的内壁倾斜，即靠近内壁的流体比靠近外壁的流体流动得更快。这与大弯曲血管中的常识相反。发现这种速度倾斜取决于微血管的曲率以及粘性力和惯性力。
