Yang Kaiyuan, Lu Chen, Zhao Xiaodan, Kawamura Ryo
Mechanobiology Institute, National University of Singapore, 117411, Singapore, Singapore.
Center for Bio-Imaging Sciences, Department of Biological Sciences, National University of Singapore, 117543, Singapore, Singapore.
PLoS One. 2017 Nov 16;12(11):e0188015. doi: 10.1371/journal.pone.0188015. eCollection 2017.
Frictional drag force on an object in Stokes flow follows a linear relationship with the velocity of translation and a translational drag coefficient. This drag coefficient is related to the size, shape, and orientation of the object. For rod-like objects, analytical solutions of the drag coefficients have been proposed based on three rough approximations of the rod geometry, namely the bead model, ellipsoid model, and cylinder model. These theories all agree that translational drag coefficients of rod-like objects are functions of the rod length and aspect ratio, but differ among one another on the correction factor terms in the equations. By tracking the displacement of the particles through stationary fluids of calibrated viscosity in magnetic tweezers setup, we experimentally measured the drag coefficients of micron-sized beads and their bead-chain formations with chain length of 2 to 27. We verified our methodology with analytical solutions of dimers of two touching beads, and compared our measured drag coefficient values of rod-like objects with theoretical calculations. Our comparison reveals several analytical solutions that used more appropriate approximation and derived formulae that agree with our measurement better.
斯托克斯流中作用于物体的摩擦阻力与平移速度及平移阻力系数呈线性关系。该阻力系数与物体的尺寸、形状和取向有关。对于棒状物体，基于棒几何形状的三种粗略近似，即珠模型、椭球体模型和圆柱体模型，已提出了阻力系数的解析解。这些理论都认为棒状物体的平移阻力系数是棒长度和纵横比的函数，但在方程中的校正因子项上彼此不同。通过在磁镊装置中跟踪颗粒在具有校准粘度的静止流体中的位移，我们实验测量了微米级珠子及其链长为2至27的珠链结构的阻力系数。我们用两个接触珠子二聚体的解析解验证了我们的方法，并将我们测量的棒状物体阻力系数值与理论计算进行了比较。我们的比较揭示了几种使用更合适近似的解析解以及与我们的测量结果更相符的推导公式。
