The different viscosities

(according to fluid mechanics, polymer physics, rheology)

Viscosity is both a common-sense notion and a scientific concept, common to the fields of fluid mechanics, polymer physics and rheology.

Unfortunately, these different fields do not have quite the same use of this concept, so that there are no less than ten qualifiers of viscosity - apparent, dynamic, kinematic, absolute, relative, intrinsic, reduced, complex, elongational, …

We also encounter “proprietary” qualifiers, such as Brookfield viscosity, Krebs viscosity, etc., which tend to make this notion particularly complex for the non-specialist. We share in this article some elements of clarification.

Apparent viscosity

Apparent viscosity refers to the viscosity instant, i.e. the viscosity value at time t as measured in a device intended for this purpose.

This notion takes into account the fact that for most products, the viscosity measured depends on the shear stresses applied to it. It also takes into account transient phenomena likely to cause changes in the measured viscosity. It is only in the case of so-called Newtonian fluids (corresponding globally to liquids containing no complex molecule) that the viscosity is a constant (depending despite everything on the temperature).

Apparent viscosity is therefore a concept of a more educational than scientific nature, intended to draw attention to the possible ambiguity in the interpretation of the measured value.

Dynamic viscosity

Dynamic viscosity is the scientific concept defining the viscosity as a ratio between two measured quantities: the shear stress imposed on the product and the shear rate gradient within the product.

Taking into account the possible transitory phenomena during theapplication stresses, the dynamic viscosity corresponds to this ratio in steady state, for a given shear rate and temperature.

Absolute viscosity

Absolute viscosity corresponds to dynamic viscosity.e.

Contrary to the current use in science of the qualifier "absolute" to signify a constant value (only the case for a Newtonian fluid, modulo the variation in temperature), absolute translates here the objective dimension of the value as soon as it is determined from a scientific quantification of shear stress and velocity gradient.

Kinematic viscosity

The kinematic viscosity corresponds to the ratio between dynamic viscosity and density of the product. This quantity appears in the fluid mechanics equations (Navier-Stokes).

In the strict sense, the kinematic viscosity does not have the usual dimension of a viscosity - one could speak of "volumic viscosity".

Relative viscosity and specific viscosity

Relative viscosity is a concept developed in the context of polymer physics and corresponds to the ratio of the viscosity of a polymer solution to the viscosity of the solvent.

The relative viscosity is a dimensionless number which therefore translates the viscosity (of the polymer solution) relative to that of the solvent. It can be noted that this notion loses its meaning when the polymer solution becomes non-Newtonian. It is therefore most often reserved for weakly concentrated solutions. Note also that despite the qualifier "relative", it is in no way opposed to "absolute" viscosity.

The specific viscosity, on the other hand, expresses the variation in relative viscosity. The specific viscosity is also a dimensionless number.

Inherent Viscosity, Reduced Viscosity and Intrinsic Viscosity

The field of polymers has introduced three other types of viscosity: inherent viscosity, reduced viscosity and intrinsic viscosity, in order to take into account the effect of polymer concentration.

La inherent viscosity is the ratio of the logarithm of the relative viscosity to the concentration. The reduced viscosity is the ratio of specific viscosity to concentration. Finally, the intrinsic viscosity is the limit of reduced viscosity (or inherent viscosity) when the polymer concentration tends towards 0. It aims to reflect the limit contribution of a polymer chain.

Here again, these notions do not have the dimension of viscosity in the strict sense but rather of a “molar viscosity”.

It is important to note that these notions lose their meaning for concentration regimes in which the polymers begin to interact (semi-dilute and concentrated regimes). In these regimes, the variation with the concentration is no longer linear but in power law.

Complex viscosity

The complex viscosity is a concept resulting from the models of the rheology in small oscillations. She represents the ratio of stress response to oscillating shear stress. We will not go into more detail in this article.

Elongational or extensional viscosity

Where the different viscosities are determined by the application of shear stress, the elongational or extensional viscosity corresponds to the response by the application of a tension/elongation stress.

The elongational viscosity is the ratio between the applied stress and the strain gradient.

"Proprietary" viscosities

One could add to the list the viscosities associated with the use of a particular measuring device, such as the Brookfield or Krebs viscometer, and their associated measurement protocols.

The measured values ​​are relative to calibrated values, making it possible to compare values ​​with a view to quality control. Nevertheless, these values ​​cannot claim to be interpreted as viscosity values ​​as such.

Conclusion

If the concept of viscosity seems at first sight intuitive, the existence of so many notions of viscosity reflects the concrete complexity of the associated phenomena, for which different scientific fields have been led to establish sub-concepts for their study needs.

Given the lack of homogeneity of these concepts between them, it is useful to have a sufficient understanding of their nuances to be able to exploit them in the appropriate contexts.