弹性胶囊在剪切流中的摆动和翻滚
Swinging and tumbling of elastic capsules in shear flow
摘要：
用谱方法研究了弹性微胶囊在无限剪切流场中的变形。胶囊的形状和流体动力学流场展开成光滑的基函数。基函数的导数的解析表达式允许在膜中的指定网格点处的弹性和流体动力学应力和弯曲力的评估。与采用三角剖分方案的方法相比，该方法的优点在于所得到的胶囊形状是自动平滑的，并且需要很少的模式来准确地描述变形。计算进行胶囊与球形和椭球形无应力参考形状。初始球形胶囊的小变形的结果与分析预测相一致。对于最初的椭圆形胶囊，最近的近似理论预测稳定振荡的坦克踩踏倾角，并在低剪切速率下翻滚的过渡。这两种现象也在实验中观察到。使用我们的数值方法，我们可以重现振荡和过渡到翻滚。探索了不同剪切速率和粘度比的全相图。虽然数值计算得到的相图与理论定性一致，但在我们的模拟时间内无法观察到间歇性行为。我们的研究结果表明，初始翻滚运动只是短暂的，在这个区域的相图。
英文摘要：
The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules both with spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximative theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we could reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.
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