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arXiv 1905.12985cond-mat.softphysics.flu-dyn
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剪切流中柔性纤维吸引周期解的方法

Flexible fibers in shear flow approach attracting periodic solutions

A. M. Slowicka, H. A. Stone, M. L. Ekiel-Jezewska

摘要:

在没有惯性的情况下,对剪切流中单个非布朗柔性纤维的三维动力学进行了数值计算。广泛的比率A的弯曲水动力和数百个初始配置被认为是。我们表明,在剪切流中的柔性纤维表现出更复杂的演变模式比在拉伸流的情况下,当A超过连续的阈值时,观察到的特征形状的高阶模式的过渡。在剪切流中,我们确定存在一个吸引稳定的配置和不同的吸引周期性运动,分别接近长期滚动,翻滚和蜿蜒的动力学模式。我们证明了第一和第二模式的最后阶段是有效的杰弗里轨道,与常数参数C替换为指数函数,要么衰减或增加的时间,分别对应于系统漂移的轨迹。在C趋于零时,纤维与涡度方向对齐,在C趋于无穷大时,纤维在剪切平面内周期性地翻滚。对于中等的A值,存在三维曲折周期运动,其对应于中等的C值。瞬态,接近周期性振荡也检测到在第一阶段的模式。

英文摘要:

The three-dimensional dynamics of a single non-Brownian flexible fiber in shear flow is evaluated numerically, in the absence of inertia. A wide range of ratios A of bending to hydrodynamic forces and hundreds of initial configurations are considered. We demonstrate that flexible fibers in shear flow exhibit much more complicated evolution patterns than in the case of extensional flow, where transitions to higher-order modes of characteristic shapes are observed when A exceeds consecutive threshold values. In shear flow, we identify the existence of an attracting steady configuration and different attracting periodic motions that are approached by long-lasting rolling, tumbling and meandering dynamical modes, respectively. We demonstrate that the final stages of the first and second modes are effective Jeffery orbits, with the constant parameter C replaced by an exponential function that either decays or increases in time, respectively, corresponding to a systematic drift of the trajectories. In the limit of C going to zero, the fiber aligns with the vorticity direction and in the limit of C going to infinity, the fiber periodically tumbles within the shear plane. For moderate values of A, a three-dimensional meandering periodic motion exists, which corresponds to intermediate values of C. Transient, close to periodic oscillations are also detected in the first stages of the modes.

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