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The defining equations for viscosity are not fundamental laws of nature, so their usefulness, as well as methods for measuring or calculating the viscosity, must be established using separate means. A potential issue is that viscosity depends, in principle, on the full microscopic state of the fluid, which encompasses the positions and momenta ...
A simple and widespread empirical correlation for liquid viscosity is a two-parameter exponential: = / This equation was first proposed in 1913, and is commonly known as the Andrade equation (named after British physicist Edward Andrade). It accurately describes many liquids over a range of temperatures.
The equation can be applied either to the shear stress or to the uniform tension in a material. In the former case, the viscosity corresponds to that for a Newtonian fluid. In the latter case, it has a slightly different meaning relating stress and rate of strain. The model is usually applied to the case of small deformations.
This functional relationship is described by a mathematical viscosity model called a constitutive equation which is usually far more complex than the defining equation of shear viscosity. One such complicating feature is the relation between the viscosity model for a pure fluid and the model for a fluid mixture which is called mixing rules.
The viscosity of the sample is then calculated using the following equation: = ˙ where is the sample viscosity, and is the force applied to the sample to pull it apart. Much like the Meissner-type rheometer, the SER rheometer uses a set of two rollers to strain a sample at a given rate. [ 31 ]
The higher the viscosity, the larger the damping imposed on the resonator. The resonator's damping may be measured by one of several methods: Measuring the power input necessary to keep the oscillator vibrating at a constant amplitude. The higher the viscosity, the more power is needed to maintain the amplitude of oscillation.
where η is the dynamic viscosity of the fluid, N is the entrainment speed of the fluid and P is the normal load per length of the tribological contact. Hersey's original formula uses the rotational speed (revolutions per unit time) for N and the load per projected area (i.e. the product of a journal bearing's length and diameter) for P.
Any equation that makes explicit one of these transport coefficient in the conservation variables is called an equation of state. [9] Apart from its dependence of pressure and temperature, the second viscosity coefficient also depends on the process, that is to say, the second viscosity coefficient is not just a material property.