Falling sphere viscosimeter

A falling sphere viscosimeter (Fig. 3.10) consists of a tube with the radius R, which is filled with the sample solution. In this tube, a sphere with the radius r is falling through the sample fluid. After a short period of acceleration, the velocity reaches a constant value, which results from the equilibrium between frictional resistance and gravity. The time t is measured that the sphere needs to cover the distance I between two marks Mj and M2. 

A special form of the falling sphere viscosimeter is the Hoppler viscosimeter (Fig. 3.11), which works with a sphere with a diameter very close to the diameter of the sloped tube. 

The influence of the Reynolds number Re is negligible, because in contrast to a free falling sphere, the flow profile is dominated by the wall effects. The diameter of the sphere should not be too small. If the gap between the tube and the sphere gets smaller than 0.1 mm, the effects of roughness of the tube and sphere gain too much influence on the results. An evaluation of the shear rate is not possible, so that an application of this type of viscosimeter for fluids with a strong non-Newtonian flow behavior is not advisable. An attempt to empirically determine the shear rate in a micro falling sphere viscosimeter is described in [23]. 

The principle of the viscobalance as a pulling sphere viscosimeter is related to the falling sphere viscosimeter. However, in this case the sphere is attached to the viscobalance and pulled through the sample fluid in a calibrated tube. The traction is usually measured by different weights that are applied on the other side of the arm of the balance. A determination of the viscosity q via the time t needed for the movement of the sphere along a defined distance has to be done via the following equation ... 

Start and end marks at capillary and falling sphere viscosimeters, molar mass of different solvent components Number, rotational frequency Number of bonds in a polymer chain Avogadro number Sodium azide Sodium hydroxide Pressure... 

The determination of the viscosity with this device is done according to DIN 53015. The relative flow around the sphere is similar to the flow through a gap. In the Hoppler viscosimeter, the slope of the falling tube is 10° and its diameter is 16 mm. In this case, a sphere with a diameter of approx. 15 mm is used to achieve a sliding state. Evaluation of the state of flow is very difficult and in some cases impossible. For this reason, a calibration of the device with a calibration fluid is very important. With these calibration measurements, a constant K can be obtained ... 

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