What is the viscosity of a fluid?
Definition: viscosity is a physical quantity that characterizes a fluid’s resistance to movement by flow. A viscous product like honey, for example, has a higher viscosity value than a more free-flowing sample like water.
What are the viscosity quantities and their units?
In the laboratory, several types of viscosity can be determined. The viscosity measured is generally the dynamic viscosity. It is denoted η and its SI base unit is the Pa.s. However, it is also often expressed in mPa.s for the most fluid liquids. Other units exist, such as the poise (0.1 Pa.s) or the poiseuille (1 Pa.s), but they are less widely used.
Kinematic viscosity is another frequently encountered viscosity. It is denoted ν and its SI base unit is m2.s. It can also be expressed in an older unit: the Stokes ( 1 St = 10-4 m2/s). The dynamic and kinematic viscosities of a product are related to its density ρ according to the following equation:
η = ν . ρ
Other related physical quantities are sometimes used, such as fluidity, which is simply the inverse of dynamic viscosity.
Relationship between shear gradient and viscosity: the special case of Newtonian fluids
The viscosity of most fluids depends on several parameters. The first, of course, is temperature: the viscosity of liquids tends to decrease as temperature rises. Conversely, the viscosity of gases increases with temperature.
The viscosity of a sample also varies with the shear stress applied to it, which has the effect of deforming it. The viscosity of rheo-fluidizing fluids decreases as the rate or gradient of shear increases. On the contrary, fluids with rheo-thickening behavior exhibit higher viscosity at high shear rates.
Newtonian fluids are fluids whose viscosity does not vary whatever the shear gradient applied. This sounds common, since water and many oils have this property. However, this does not apply to the majority of fluids: most liquid mixtures, even water-based ones that may contain particles, have a viscosity that depends on the shear stress applied, and are therefore not Newtonian.
Why determine the viscosity of a fluid?
Viscosity is a crucial parameter for many applications. In particular, it can be used to dimension pipes and tubes in which fluids are to flow, with or without pumping systems. It can also be used to assess the pressure a pump will have to supply via its motor to make a fluid flow easily at a constant speed or flow rate: these are the pressure losses. Viscosity can also be used to estimate the time in seconds it will take for a fluid to flow out of a container at constant force, under the only effect of gravity, for example. Finally, viscosity is a parameter often used to control the quality of finished products. It is used to validate their compliance with a given application.
How to measure viscosity and with what equipment?
In the laboratory, the instrument used to determine a fluid’s viscosity is called a viscometer. Many different types of viscometer have been developed over the years. Here are some examples of viscometers used in the laboratory and a brief explanation of how they work:
A free-flow viscometer is probably the simplest technique for assessing viscosity. La méthode consiste à mesurer le temps en secondes nécessaire pour qu’un récipient percé se vide sous l’effet constant de la gravité. The container used is often called a cup and resembles a calibrated funnel.
Falling ball viscometer (or rolling ball)
Falling ball viscometers measure the falling time of a ball in the fluid to determine its viscosity. The fluid to be analyzed is placed in a standardized capillary, into which a steel ball is also inserted. The capillary is then inserted into the viscometer and the device regulates its temperature. It then tilts the ball at different angles and calculates its travel time using a detection system which in most cases is magnetic. Finally, the dynamic viscosity of the fluid is calculated from the density values given or measured in parallel. This type of measurement is carried out at constant but low shear: thus, only the study of Newtonian fluids is relevant with this method. Implementing this type of measurement is delicate, and requires knowledge of the viscosity range concerned in order to choose the right capillary and bead.
Rotational viscometers are probably the simplest instruments. They use a motor to drive the rotation of a moving part immersed in the fluid to be analyzed, by a rod or spring. Nevertheless, this type of device should be avoided as much as possible, except for comparative services between similar samples. In fact, the results obtained often depend on the “conditions/apparatus” and their reproducibility is rather poor.
Other viscometers, such as Stabinger viscometers, are much more reliable rotational viscometers. In the latter, a tube containing the sample is put into rotation at high speed. This tube also contains a magnet bar which is immersed in the sample when the former is injected into the device. As the tube rotates, so does the fluid, which in turn rotates the rod. An electronic device calculates the speed of rotation, which varies according to the viscosity of the fluid. The more viscous the fluid, the higher the rod speed. This type of instrument measures viscosity over a wide range of viscosities and temperatures. The measurement is carried out at a constant, but unknown shear rate, which allows only Newtonian fluids to be characterized.
Capillary rheometers use an actuator to force the fluid to be analyzed through a die of calibrated diameter at a desired flow rate. By measuring the pressure at the die inlet and outlet when the flow is established, the viscosity of the fluid can be determined as a function of temperature and shear rate.
This is the most widely used type of viscometer for continuous measurements in industrial processes. The method consists of vibrating a mobile in the fluid to be analyzed. The amplitude reached by the mobile varies according to the viscosity of the fluid in which it is immersed.
Viscosity measurement of non-Newtonian fluids
Most viscometers operate at constant shear, which is not necessarily known. When the fluid is Newtonian, this doesn’t matter, as the fluid has the same viscosity regardless of the shear rate applied. However, if the fluid is not Newtonian, the measured viscosity will only correspond to this shear rate. This can have a huge impact. The viscosity of a fluid can vary by several orders of magnitude when shear changes, and in both directions. This type of fluid then requires a more in-depth study by rheological analysis. A flow curve, or rheogram, representing viscosity as a function of shear rate must then be determined.