What Is Rheology?
Rheology is the study of the flow of materials and involves the flow properties of materials and whether they be liquidlike, solidlike, and intermediate compounds. The main behaviour that is of interest in rheology is the relationship between how material flows and force and the key characteristic which describes this which is viscosity. Another benefit of rheology is the ability to provide mathematical models for the behaviour of materials.
Theory of Rheology
Viscosity is the measure of a fluid’s resistance to flow and describes the internal friction of a moving fluid. The viscosity (m) (or dynamic viscosity which is more correct (equation 1). One of the best ways to visualize viscosity is by using a scenario such as fluid flowing between two plates (orange colour) with the bottom plate being stationary (figure 1).
Figure 1: Fluid flowing between two plates
$\frac{F}{A}=\mu \frac{d{\nu}_{o}}{d\mathcal{d}}$
Equation 1: Viscosity equation
$\mu \u2013Vis\mathrm{cos}ity\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{F}{A}\u2013TheshearstressortheforceFrequiredtomovetheplatedividedby\phantom{\rule{0ex}{0ex}}surfaceareaincontactwiththefluidA.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{d{\nu}_{o}}{d\mathcal{d}}\u2013Velocitygradientorshearrate,where{\nu}_{o}isthevelocityoftheplate\phantom{\rule{0ex}{0ex}}and\mathcal{d}isthethicknessofthefluidlayer.\phantom{\rule{0ex}{0ex}}$
The units of viscosity are Pa.s which is the same as (N.s)/m^{2 }or kg/(m.s)
What Is Shear Stress?
Shear stress is the force per unit area acting parallel to an infinitesimal surface element. The primary reason for shear stress is due to friction between fluid particles caused by different parts of a fluid relative to each other move at different velocities. When the shear stress is applied to a fluid at rest, the fluid will no longer remain at rest and will move because of the shear stress.
Consider a stream of flowing liquid in a pipe, the fluid velocity is zero at the pipe walls and will be the greatest towards the centre of the pipe, this shows that the adjacent layers of the fluid are moving at different velocities (figure 2). Within the fluid, there will be a continuous interchange of molecules between the flayers of fluid which will affect the velocities of the fluid layers, with molecules moving from a faster layer to a slower layer resulting in an acceleration in the adjacent fluid layers velocity and vice versa. This phenomenon is known as viscous drag and leads to viscous forces in adjacent layers within the fluid causing velocity changes. These forces are also known as viscous shear stresses and shear stresses in fluids are induced by fluid flow and the differing velocities within the flowing fluid. The effect of viscous shear stress is to reduce the velocity profile and between the fluid layers. Another way of thinking of shear stress is that it is a source of resistance to change in a fluid motion.
Figure 2: Fluid velocity profile in a pipe (Wikipedia, 2020.
Viscosity Values
For liquids, viscosity is affected by temperature and not pressure, as the strength of the intermolecular forces changes with temperature and the greater the temperature the weaker the intermolecular force and shear becomes easier (table 1). Gases have low viscosities and are a function of both temperature and pressure.
Fluid 
Viscosity (mPa s) 
Water at 0°C 
1.79 
Water at 20°C 
1.002 
Water at 100°C 
0.28 
Glycerol at 0°C 
12070 
Glycerol at 20°C 
1410 
Glycerol at 30°C 
612 
Gases 
0.01 
Sulphuric acid 
30 
Rubber compounds 
10,000,000 – 10,000,000,000 
Table 1: Examples of fluid viscosities.
By seeing the values of the table, you can see how much resistance some fluids have towards flow such as rubber compounds, and how some fluids slow very easily, such as water.
Description Of Newtonian Fluids
Newtonian fluids obey Newton’s law of viscosity, where the shear rate and shear rate (the rate of change of the velocity of the fluid when one layer of fluid passes over an adjacent layer) is linear and the constant of proportionality is the viscosity. This means that the viscosity of the fluid remains constant regardless of changes to the rate of flow and any external stress from mixing or sudden application of force. Examples of Newtonian fluids are water, alcohol, air, glycerol, thin motor oils and some types of singlephase fluids made up of small molecules.
Description Of NonNewtonian Fluids
NonNewtonian fluids don’t obey Newton’s law of viscosity, and the viscosity which is referred to as apparent viscosity isn’t constant and it varies with the rate the fluid is sheared and the time the fluid is subjective to shear, this makes NonNewtonian fluids a lot more complicated than Newtonian fluids.
Examples of shear rate dependant NonNewtonian fluids are; pseudoplastic (shear thinning) where the viscosity decrease as the shear rate increases, dilatant (shearthickening) the viscosity increases as the shear rate increases, Bingham plastic where there is no flow until critical shear stress is reached and then the rheogram becomes linear and Casson plastics that have no flow until shear stress is reached and then the rheogram is nonlinear.
Examples of time dependant NonNewtonian fluids are; Thixotropic (time dependant thinning) where the structure breaks down and viscosity decrease with increasing shear stress and Rheopectic (time dependant thickening) as the structure builds up the viscosity increases with the increase of shear stress.
A Rheogram Example
To visualize the flow characteristic of Newtonian and NonNewtonian fluids a rheogram is used (figure 3). Programs are a plot of shear stress or sometimes viscosity against shear rate and are a collective of points collected from experimental data with a curve drawn through them. Sometimes calculations can be fitted to the curve to show the behaviours of fluids, but the calculations aren’t accurate outside of the conditions they are determined at.
Remember: Viscosity is shear stress divided by the shear rate or the gradient of the line.
Figure 3: Rheogram showing Newtonian and NonNewtonian fluids (Simscale, 2020) and rheogram using viscosity on the yaxis (Hub, 2020)
Examples of Newtonian and NonNewtonian Fluids
Fluid Type 
Examples 
Newtonian 
water, all gases, and lowmolecularweight liquids 
NonNewtonian 

pseudoplastic 
Adhesives, rubber solutions, and polymer solutions 
Bingham plastics 
Margarine, cooking fats, and toothpaste 
Casson plastics 
Blood, tomato sauce (ketchup), and orange juice 
Dilatant 
A mixture of corn starch and water (a cooking agent used to thicken) and silica and polyethylene glycol (used in body armour) 
Thixotropic

Some types of clay, cytoplasm, and solder pastes (used in electronics manufacturing printing)

Rheopectic

Gypsum, printer inks, and some types of lubricants.

References
Hub, S. L. (2020). NonNewtonian fluids. Retrieved from Science Learning Hub: https://www.sciencelearn.org.nz/resources/1502nonnewtonianfluids
Simscale. (2020). NonNewtonian Models. Retrieved from Simscale: https://www.simscale.com/docs/simulationsetup/materials/nonnewtonianmodels/
Wikipedia. (2020). Entrance length. Retrieved from Wikipedia: https://en.wikipedia.org/wiki/Entrance_length