The red blood cell (RBC) membrane is often modeled by Skalak strain energy and Helfrich bending energy functions, for which high-order representation of the membrane surface is required. We develop a numerical model of RBCs using an isogeometric discretization with T-splines. A variational formulation is applied to compute the external load on the membrane with a direct discretization of second-order parametric derivatives. For fluid–structure interaction, the isogeometric analysis is coupled with the lattice Boltzmann method via the immersed boundary method. An oblate spheroid with a reduced volume of 0.95 and zero spontaneous curvature is used for the reference configuration of RBCs. The surface shear elastic modulus is estimated to be N/m, and the bending modulus is estimated to be J by numerical tests. We demonstrate that for physiological viscosity ratio, the typical motions of the RBC in shear flow are rolling and complex swinging, but simple swinging or tank-treading appears at very high shear rates. We also show that the computed apparent viscosity of the RBC channel flow is a reasonable agreement with an empirical equation. We finally show that the maximum membrane strain of RBCs for a large channel (twice of the RBC diameter) can be larger than that for a small channel (three-quarters of the RBC diameter). This is caused by a difference in the strain distribution between the slipper and parachute shapes of RBCs in the channel flows.

中文翻译：

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使用 T 样条等几何公式和格子玻尔兹曼方法的红细胞计算模型

红细胞 (RBC) 膜通常通过 Skalak 应变能和 Helfrich 弯曲能函数进行建模，为此需要膜表面的高阶表示。我们使用 T 样条等几何离散化开发了红细胞数值模型。应用变分公式通过二阶参数导数的直接离散化来计算膜上的外部载荷。对于流体-结构相互作用，等几何分析通过浸入边界法与格子玻尔兹曼方法相结合。红细胞的参考配置使用体积缩小为 0.95 且自发曲率为零的扁球体。通过数值试验估算表面剪切弹性模量为N/m，弯曲模量估算为J。我们证明，对于生理粘度比，红细胞在剪切流中的典型运动是滚动和复杂的摆动，但在非常高的剪切速率下会出现简单的摆动或坦克踩踏。我们还表明，计算出的红细胞通道流的表观粘度与经验方程合理一致。我们最终证明，大通道（红细胞直径的两倍）的红细胞最大膜应变可以大于小通道（红细胞直径的四分之三）的最大膜应变。这是由通道流中红细胞的拖鞋形状和降落伞形状之间的应变分布差异引起的。