# Rheological analysis

Rheology is the study of the flow of matter and the links that exist between the stress applied to a material and its structural modifications.

In rheology, viscosity is an important concept: this quantity characterizes the resistance of a fluid to its flow. The viscosity of a fluid generally depends on the temperature, but also on the mechanical stress applied to the fluid (shear).

## The special case of Newtonian fluids

Newtonian fluids are very special fluids: their viscosity does not depend on the mechanical stress applied to them. Water is the best known Newtonian fluid. However, the rheological behavior of this fluid changes very quickly when other compounds are added to it. Water-based mixtures are then often non-Newtonian fluids.

## Why not just measure viscosity with a viscometer?

A viscosity measurement can be carried out with many devices with very different technologies: falling ball, free flow, etc. These devices are simple to implement and generally allow viscosity to be measured as a function of temperature. However, these devices often measure viscosity at a fixed, and often low, shear rate. Thus, if it is non-Newtonian, the viscosity of a measured fluid may be different depending on the device, since it is produced under different mechanical conditions. If these viscosity measurements are carried out on proven Newtonian fluids, or on similar fluids for which a simple comparison must be made, this does not pose any particular problem.

## The case of non-Newtonian fluids

For this type of fluid, a measurement at a given shear rate should not be considered for an application at another shear rate. Indeed, the viscosity of a non-Newtonian fluid can vary by several orders of magnitude depending on the shear rate. For example, the viscosity of a fluid measured by a falling ball viscometer should not be used to size a pump through which this fluid will pass in an industrial process. Indeed, the fluid undergoes in a pump potentially very high shear stresses and therefore different from those in which the viscosity measurement was carried out. The fluid viscosity measurement must be made under the temperature and shear conditions of the planned pump: this is referred to as the flow curve. Ideally, a flow curve will be made at different temperatures, to determine the viscosity over a wide range of shear and temperature.

## What are the deliverables of a rheology study?

The deliverables of a rheology study are typically flow curves that show fluid viscosity as a function of shear rate at each temperature. These curves make it possible to check the Newtonian character of the fluid (constant viscosity according to the rate of shearing). If the fluid is not Newtonian, then it is possible to determine the parameters of a fluid flow model. These mathematical models thus make it possible to describe at all points the viscosity of the fluid as a function of shear. This is the ideal input data for simulation software used to size a process: pressure drops, pumps, types of heat exchanger, etc.