Understanding the flow of deformable particles such as liquid drops, synthetic capsules and vesicles, and biological cells confined in a small channel is essential to a wide range of potential chemical and biomedical engineering applications. Computer simulations of this kind of fluid-structure (membrane) interaction in low-Reynolds-number flows raise significant challenges faced by an intricate interplay between flow stresses, complex particles' interfacial mechanical properties, and fluidic confinement. Here, we present an isogeometric computational framework by combining the finite-element method (FEM) and boundary-element method (BEM) for an accurate prediction of the deformation and motion of a single soft particle transported in microfluidic channels. The proposed numerical framework is constructed consistently with the isogeometric analysis paradigm; Loop's subdivision elements are used not only for the representation of geometry but also for the membrane mechanics solver (FEM) and the interfacial fluid dynamics solver (BEM). We validate our approach by comparison of the simulation results with highly accurate benchmark solutions to two well-known examples available in the literature, namely a liquid drop with constant surface tension in a circular tube and a capsule with a very thin hyperelastic membrane in a square channel. We show that the numerical method exhibits second-order convergence in both time and space. To further demonstrate the accuracy and long-time numerically stable simulations of the algorithm, we perform hydrodynamic computations of a lipid vesicle with bending stiffness and a red blood cell with a composite membrane in capillaries. The present work offers some possibilities to study the deformation behavior of confining soft particles, especially the particles' shape transition and dynamics and their rheological signature in channel flows.

中文翻译：

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微流体通道中软颗粒流动的等几何边界元方法

了解可变形粒子的流动，例如液滴、合成胶囊和囊泡，以及限制在小通道中的生物细胞，对于广泛的潜在化学和生物医学工程应用至关重要。低雷诺数流动中这种流体-结构（膜）相互作用的计算机模拟提出了面临的重大挑战，即流动应力、复杂粒子的界面机械性能和流体限制之间的复杂相互作用。在这里，我们通过结合有限元法 (FEM) 和边界元法 (BEM) 来提出等几何计算框架，以准确预测在微流体通道中传输的单个软粒子的变形和运动。提议的数值框架与等几何分析范式一致；Loop 的细分元素不仅用于几何图形的表示，还用于膜力学求解器 (FEM) 和界面流体动力学求解器 (BEM)。我们通过将模拟结果与高精度基准解决方案与文献中两个众所周知的例子进行比较来验证我们的方法，即圆管中具有恒定表面张力的液滴和正方形中具有非常薄的超弹性膜的胶囊渠道。我们表明数值方法在时间和空间上都表现出二阶收敛性。为了进一步证明算法的准确性和长时间数值稳定的模拟，我们对具有弯曲刚度的脂质囊泡和在毛细血管中具有复合膜的红细胞进行流体动力学计算。目前的工作为研究软颗粒的变形行为提供了一些可能性，特别是颗粒的形状转变和动力学及其在通道流动中的流变特征。