Wei Da, Dehnavi Parviz Ghoddoosi, Aubin-Tam Marie-Eve, Tam Daniel
Department of Bionanoscience, Delft University of Technology, 2628CJ Delft, Netherlands.
Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CD Delft, Netherlands.
Phys Rev Lett. 2019 Mar 29;122(12):124502. doi: 10.1103/PhysRevLett.122.124502.
Stokes equations are commonly used to model the hydrodynamic flow around cilia on the micron scale. The validity of the zero Reynolds number approximation is investigated experimentally with a flow velocimetry approach based on optical tweezers, which allows the measurement of periodic flows with high spatial and temporal resolution. We find that beating cilia generate a flow, which fundamentally differs from the stokeslet field predicted by Stokes equations. In particular, the flow velocity spatially decays at a faster rate and is gradually phase delayed at increasing distances from the cilia. This indicates that the quasisteady approximation and use of Stokes equations for unsteady ciliary flow are not always justified and the finite timescale for vorticity diffusion cannot be neglected. Our results have significant implications in studies of synchronization and collective dynamics of microswimmers.
斯托克斯方程通常用于对微米尺度上纤毛周围的流体动力流进行建模。基于光镊的流速测量方法通过实验研究了零雷诺数近似的有效性，该方法能够以高空间和时间分辨率测量周期性流动。我们发现，摆动的纤毛会产生一种流动，这与斯托克斯方程预测的斯托克斯子场有根本区别。特别是，流速在空间上的衰减速度更快，并且在离纤毛距离增加时逐渐出现相位延迟。这表明，对于非定常纤毛流，准稳态近似和斯托克斯方程的使用并不总是合理的，涡度扩散的有限时间尺度不能被忽略。我们的结果对微游动器的同步和集体动力学研究具有重要意义。
