在离心加速度作用下测球在流体中的运动

I. Nyrkova, A. Semenov, A. Khokhlov, K. Linliu, B. Chu
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引用次数: 9

摘要

一种流体的粘度可以通过观察一个探针球(或球)在充满这种流体的离心管中的运动来测量。从理论上解决了探针球在离心管中运动的水动力行为。我们用唯一可调的参数——球与管之间的旋转摩擦系数,得到了终端球速度、流体粘度和离心机加速度之间的普遍关系(对于给定材料和尺寸的球在给定管中)。离心管在水平面上的旋转产生惯性力,这个惯性力被作用在球上的摩擦力抵消。结果,球沿着管道以某种特征速度运动,这是测量流体粘度的一种方法。这个速度是在润滑近似中计算出来的。重力加速度使球非常接近离心管的底部。在这种情况下,重力通过本文引入和计算的悬浮力来平衡。这种力的来源是在运动的球后面和下面形成的气泡。用专门设计的两种球的离心机和广泛的粘度标准,对水平离心管底部附近的球的终端速度的理论发展进行了试验。理论和实验之间的良好一致性表明,我们开发了一种在低剪切速率下测量高粘度流体的新方法,这可能对聚合物熔体的研究特别有用。
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Motion of a Probe Ball in the Fluid under Centrifugal Acceleration
The viscosity of a fluid can be measured by observing the motion of a probe sphere (or ball) in a centrifuge tube filled with this fluid. The hydrodynamic behavior of the probe ball moving in the centrifuge tube has been solved theoretically. We have got the universal relationship (for balls of a given material and size in a given tube) between the terminal ball velocity, the fluid viscosity and the centrifuge acceleration using the only adjustable parameter - the rotational friction coefficient between the ball and the tube. The rotation of the centrifuge tube in the horizontal plane induces an inertia force which is counterbalanced by the friction force acting on the ball. As a result, the ball moves along the tube with some characteristic speed, which is a measure of the viscosity of the fluid. This speed was calculated in the lubrication approximation. The gravitational acceleration causes the ball to move very close to the bottom of the centrifuge tube. In this situation, the gravity is balanced by a levitation force introduced and calculated in the present paper. The origin of this force is the formation of the bubble behind and below the moving ball. The theoretical development on the terminal velocity for the ball moving very near the bottom of the horizontal centrifuge tube is tested by using a specially designed centrifuge for two types of balls and a wide set of viscosity standards. Excellent agreement between theory and experiment suggests that we have developed a new approach to measure high viscosities of fluids at low shear rates which might be especially useful for the investigation of polymer melts.
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