What is viscosity?

A fluid’s viscosity is a measure of its resistance to flow. It describes the internal friction of a moving fluid. Viscous fluids resist motion because their molecular makeup creates a lot of internal friction. Fluids with low viscosity flow easily because their molecular makeup creates little friction when they are in motion.

On a molecular level, viscosity is caused by the interactions between different molecules in a fluid. This can also be considered to be friction between the molecules. Just like in the case of friction between moving solids, viscosity will determine the energy required to make a fluid flow.

The best way to visualize this is through an example. Consider a cup made of styrofoam with a hole at the bottom. I notice that the cup drains very slowly when we pour honey into it. This is because honey’s viscosity is relatively high when compared to other liquids. When we fill the same cup with water, for example, the water will drain much more quickly. A fluid with a low viscosity is said to be “thin,” while a high viscosity fluid is said to be “thick.” It is easier to move through a low-viscosity fluid (like water) than a high-viscosity fluid (like honey).

Factors affecting viscosity

Viscosity is influenced by many factors. Examples include temperature, pressure, and the addition of other molecules. Pressure has a small effect on liquids and is often ignored. Adding molecules can have a significant effect. Sugar, for example, makes water more viscous.

Temperature, however, has the greatest impact on viscosity. Temperature increases in a liquid decreases viscosity because it gives molecules enough energy to overcome intermolecular attraction. The effect of temperature on viscosity is the opposite for gases. As gas temperature increases, viscosity increases. Gas viscosity is not significantly affected by intermolecular attraction, but by increasing temperature, which causes more molecules to collide.

Dynamic and Kinetic viscosity

There are two ways to report viscosity. Absolute or dynamic viscosity is a measure of a fluid’s resistance to flow while kinematic viscosity is the ratio of dynamic viscosity to a fluid’s density. While the relationship is straightforward, it’s important to remember two fluids with the same dynamic viscosity values may have different densities and thus difference kinematic viscosity values. And, of course, dynamic viscosity and kinematic viscosity have different units.

Viscosity Units

The SI unit for viscosity is newton-second per square meter (N·s/m2). However, you’ll often see viscosity expressed in terms of pascal-second (Pa·s), kilogram per meter per second (kg·m−1·s−1), poise (P or g·cm−1·s−1 = 0.1 Pa·s) or centipoise (cP). This makes the viscosity of water at 20 °C about 1 cP or 1 mPa·s.

In American and British engineering, another common unit is pound-seconds per square foot (lb·s/ft2). An alternative and equivalent unit is pound-force-seconds per square foot (lbf·s/ft2).

Dynamic Viscosity Units

Poise (symbol: P)

Poise (symbol: P) Named after the French physician Jean Louis Marie Poiseuille (1799– 1869), this is the CGS unit of viscosity, equivalent to dyne-second per square centimetre. It is the viscosity of a fluid in which a tangential force of 1 dyne per square centimetre maintains a difference in velocity of 1 centimetre per second between two parallel planes 1 centimetre apart. Even in relation to high-viscosity fluids, this unit is most usually encountered as the centipoise (cP), which is 0.01 poise. Many everyday fluids have viscosities between 0.5 and 1000 cP

Pascal-second (symbol: Pa·s)

This is the SI unit of viscosity, equivalent to newton-second per square metre (N·s m–2). It is sometimes referred to as the “poiseuille” (Pl). One poise is exactly 0.1 Pa·s. One poiseuille is 10 poise or 1000 cP, while 1 cP = 1 mPa·s (one millipascal-second).

Kinematic viscosity units

Stokes (symbol: St)

This is the cgs unit, equivalent to square centimetre per second. One stokes is equal to the viscosity in poise divided by the density of the fluid in g cm–3. It is most usually encountered as the centistokes (cSt) (= 0.01 stokes).

Saybolt Seconds Universal

This is the time for 60 ml of fluid to flow through the calibrated orifice of a Saybolt Universal viscometer at a Kinematic viscosity specified temperature, as prescribed by test method ASTM D 88. For higher viscosities, SSF (Saybolt Seconds Furol) is used.

Formula for viscosity

Basic model of flow between two plates [1]

The ratio of the external force (F) to the affected area (A) is defined as the shear stress (σ):

σ = F/A

The shear strain (γ) is defined as the relative change in the length of the material due to the external force:

γ = l/l₀

The ratio between the shear stress (σ) and the shear strain (γ) is defined as the modulus (G):

G = σ/ γ

If the top plate in Figure 1 is moving at a certain velocity (v), the velocity gradient dv/dx is defined as the shear rate (γ̇). Sir Isaac Newton, who formulated the laws of motion and universal gravitation, discovered that in ideal fluids (known as Newtonian fluids), the shear stress (σ) is directly related to the shear rate (γ̇):

σ = ηγ̇ or η = σ/γ̇

Newtonian and Non-Newtonian Fluids

Newtonian fluids, as they are called, have a constant viscosity. As you increase the force, the resistance increases, but it’s a proportional increase. No matter how much force is applied to a Newtonian fluid, it keeps acting like a fluid. A Newtonian fluid is a fluid that obeys Newton’s law of friction, where viscosity is independent of the strain rate.

Viscosity remains constant regardless of changes in shear rate or agitation. As pump speed increases, flow increases proportionately. Liquids displaying Newtonian behavior include water, mineral oils, syrup, hydrocarbons, and resins.

Non-Newtonian fluids

A non-Newtonian fluid is one which does not obey Newton’s law of friction. Most fluid systems, are not Newtonian (known as non-Newtonian fluids) and their viscosity is not constant, but changes as a function of increasing or decreasing the applied shear rate.

Many fluids show a decrease in viscosity as a function of increasing shear rate. These fluids are called pseudoplastic fluids. The “structure” of the fluid in these systems is broken down due to the external force, resulting in a shear thinning behavior. If the initial inter-particle (or molecular) association is strong, the system may behave like a solid at rest. The initial shear stress that is required to overcome the internal forces and disrupt the structure is defined as the yield value of the system. Materials that exhibit a yield value and then demonstrate shear thinning with increasing shear rate are defined as plastic fluids. Some fluids exhibit an increase in viscosity with increasing shear rate, a phenomenon known as shear thickening. These materials are defined as dilatant fluids.

Shear stress as a function of shear rate [1]

Viscosity as a function of shear rate [1]

Flow behaviour over time: Thixotropy

A complex fluid rearranges itself over time when an external force is removed. Thus, viscosity should not only be measured by increasing shear rate as the structure is broken up, but also by decreasing shear rate as the system re-establishes itself. This is called hysteresis.

In a fast recovery, the plot of viscosity versus decreasing shear rate would be superimposed on the plot of viscosity versus increasing shear rate. If the fluid takes time to restore its structure, the “down curve” would be below the “up curve”. Thixotropy is defined as exhibiting shear thinning with increased shear rate and slower recovery with decreasing shear rate. In non-thixotropic materials, the “up” and “down” curves overlap and in rheopectic materials, the “down” curve is above the “up” curve.

But while thixotropic fluids are occasionally mistaken for pseudoplastic fluids, and rheopectic fluids are occasionally mistaken for dilatant fluids, these two types of fluids differ in one crucial way: time dependence. The change in viscosity with respect to stress for dilatant and pseduoplastic fluids is independent of time. But for thixotropic fluids, the viscosity decreases with increased stress the longer the stress is applied. The same goes for rheopectic fluids, the viscosity increases with increased stress the longer said stress is applied.

We use a lot of products in daily life that exhibit thixotropic behavior. Thixotropy is the property that explains why personal care products like hair gels and toothpaste go from liquid to solid when squeezed, but return to their solid states afterwards in order to keep their shape. The rheological properties of structural decomposition and regeneration in relation to time determine the quality of a product.

Viscosity as a function of shear rate – thixotropic and non-thixotropic behavior (arrows show increasing or decreasing shear rate) [1]

Viscosity with respect to stress over time (Thixotropic Vs Rheopectic behaviour) [2]

Importance of viscosity in daily life

In many different fields, viscosity can actually be quite useful, even though it seems to be of minor importance in daily life. For instance:

• Lubrication in vehicles.When you put oil in your car or truck, you should consider its viscosity. It’s because viscosity affects friction, which affects heat. Furthermore, viscosity affects both the rate of oil consumption and the ease with which your vehicle starts in hot and cold conditions. The viscosity of some oils remains the same as they heat and cold, while others become thinner as they heat, causing problems as you operate your car during a hot summer day.
• In the preparation and serving of food, viscosity plays a significant role. Many cooking oils become much more viscous with cooling, while others may not change viscosity at all. As fat is viscous when heated, it becomes solid when chilled. The viscosity of sauces, soups, and stews is also important in different cuisines. When thinned out, a thick potato and leek soup becomes French vichyssoise. Honey, for instance, is quite viscous and can change the “mouth feel” of certain foods.
• The equipment in manufacturing needs to be properly lubricated to operate smoothly. Pipelines can be jammed and clogged by viscous lubricants. Thin lubricants provide insufficient protection for moving parts.
• When fluids are injected intravenously, viscosity can be crucial. A major concern involves blood viscosity: blood that is too viscous can form internal clots, while blood that is too thin will not clot, causing dangerous blood loss and even death.

Some typical viscosities