论文标题
粘弹性电阻理论和游泳的应用良好
Well-posedness of a viscoelastic resistive force theory and applications to swimming
论文作者
论文摘要
我们提出并分析了一个简单的模型，以融合周围流体的线性粘弹性效应，以进化。该模型仅是沿曲线的方程式封闭形式系统，由于粘弹性，该曲线包括“存储器”项。对于平面细丝，鉴于首选曲率的强迫，我们证明了纤维进化的良好性以及在时间周期强迫的情况下存在独特的时间周期性解决方案。此外，我们从首选曲率方面获得了细丝的游泳速度的表达式。游泳速度以复杂的方式取决于与流体松弛时间和其他聚合物粘度相对应的粘弹性参数。我们详细研究了这种表达，并伴随着数值模拟，并表明这种简单的模型可以捕获粘弹性对游泳的复杂作用。特别是，在某些情况下，粘弹性游泳运动员比其牛顿的速度快，而在其他情况下则速度较慢。令人惊讶的是，我们甚至找到了一个例子，即粘弹性效应可能会导致牛顿环境中的游泳方向逆转，尽管这发生在牛顿和粘弹性游泳者的流离失所实际上可以忽略不计时。
We propose and analyze a simple model for the evolution of an immersed, inextensible filament which incorporates linear viscoelastic effects of the surrounding fluid. The model is a closed-form system of equations along the curve only which includes a `memory' term due to viscoelasticity. For a planar filament, given a forcing in the form of a preferred curvature, we prove well-posedness of the fiber evolution as well as the existence of a unique time-periodic solution in the case of time-periodic forcing. Moreover, we obtain an expression for the swimming speed of the filament in terms of the preferred curvature. The swimming speed depends in a complicated way on the viscoelastic parameters corresponding to the fluid relaxation time and additional polymeric viscosity. We study this expression in detail, accompanied by numerical simulations, and show that this simple model can capture complex effects of viscoelasticity on swimming. In particular, the viscoelastic swimmer is shown to be faster than its Newtonian counterpart in some situations and slower in others. Strikingly, we even find an example where viscoelastic effects may lead to a reversal in swimming direction from the Newtonian setting, although this occurs when the displacement for both the Newtonian and viscoelastic swimmers is practically negligible.
