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首页> 美国卫生研究院文献>PLoS Clinical Trials >From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow
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From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow

机译：从磁珠到棒：通过测量斯托克斯流中微米大小的磁珠链的平移阻力系数进行理论比较

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摘要

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.
机译：在斯托克斯流中，对象上的摩擦阻力与平移速度和平移阻力系数呈线性关系。此阻力系数与对象的大小，形状和方向有关。对于杆状物体，已经基于杆几何形状的三个粗略近似（珠子模型，椭球模型和圆柱模型）提出了阻力系数的解析解。这些理论都同意，杆状物体的平移阻力系数是杆长度和纵横比的函数，但是在方程式中的校正因子项上彼此不同。通过在磁性镊子装置中跟踪经过校准粘度固定流体的颗粒位移，我们通过实验测量了微米大小的微珠及其链长为2至27的微珠链形成的阻力系数。我们用分析解决方案验证了我们的方法对两个接触珠的二聚体进行分析，并将我们测得的棒状物体的阻力系数值与理论计算值进行比较。我们的比较揭示了几种使用更合适的近似值的解析解决方案，并且得出的公式与我们的测量结果更加吻合。

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