WHAT ARE THE NEWTONIAN LIQUIDS?

Liquid and gas are 2 different states of matter yet they have a lot in common. Both are fluid and both have free flow. In physics, the term fluid refers to any material that continuously changes its shape and form under the influence of any force or stress. The shear modulus of fluid is zero, which means such substances cannot resist any force. And Free Flow is a characteristic attribute of fluids that describes the continuous and irreversible change in position of one portion of a material relative to another when it is subjected to shear stress. But before diving into the concept of fluid, we must have a basic understanding of very important 3 terms. These are: Viscosity, Shear Stress and Shear Strain.

VISCOSITY: is the measure of a fluid’s resistance to flow, namely to deformation at a particular rate.

At a molecular level, viscosity is the result of interaction between the different molecules in a fluid. This can be also understood as friction between the molecules in the fluid. Just like in the case of friction between moving solids, with other words we can say that viscosity will determine the energy required to make a fluid flow. There are 2 main types of viscosity: dynamic and kinematic.

Dynamic viscosity (η= “eta”) (also known as absolute viscosity) gives you information on the force needed to make the fluid flow at a certain rate. The most commonly used unit for dynamic viscosity is the CGS unit centipoise (cP), which is equivalent to 0.01 Poise (P). The viscosity of distilled water at 20°C is used to define 1 cP.

The SI unit for dynamic viscosity is the Pascal-second (Pa-s), which corresponds to the force (N) per unit area (m²) divided by the rate of shear (s^-1) a.k.a. Newton second per square meter (N·s/m²). However, since the viscosity of most fluids is below 1 Pa-s the millipascal-second (mPa-s) is often used instead. 1 mPa-s = 1 cP. 

Kinematic viscosity (ν = “nu”) refers to how fast does the fluid flow when a  certain force is applied. The kinematic viscosity is often measured in the CGS unit centistokes (cSt), which is equivalent to 0.01 stokes (St or cm²·s⁻¹ = 0.0001 m²·s⁻¹). 1St = 1P/ρ (ρ = ”rho” = density of the fluid in g/cm³). The kinematic viscosity of water at 20 °C is about 1 cSt.

The SI unit for kinematic viscosity is square meters per second (m²/s). However, due to the viscosity values of most common fluids, square centimeters per second (cm²/s) is used more often. 1 cm²/s = 100 cSt.

These are the most basic units used for viscosity measurement, but there is a large variety of units that are specific to some particular measurement system or application. For instance, In the automotive industry the viscosity index is used to describe the change of viscosity with temperature.

SHEAR STRESS (τ = “tau) : is the component of stress that is parallel to the surface and can be defined as force (N) per unit area (A), with the force being applied externally due to various reasons. It is commonly measured in Pascal (Pa) (1Pa= 1N/m²). In comparison the normal stress (σ = “sigma”) (compression or tension) is perpendicular to the surface but is also measured in Pascal.

SHEAR STRAIN: can be defined as the amount of deformation experienced by the body in the direction in which the force is applied, divided by the original or initial dimensions of the body. Strain can be a result of stress itself. A shearing strain is never accompanied by a change in volume. That means in shear strain the body gets distorted resulting only in an alternation in its shape but not in size. Change in shape or size need not necessarily imply strain. For example, if a body is heated to expand, its volume changes. It acquired new size due to expansion. However, the strain remains zero. Unless and until internal elastic forces operate to bring the body to the original state, no strain exists. Shear strain is unitless and dimensionless.

Sir Isaac Newton used a differential equation for the first time, to find out the relation between these 3 terms for fluids. Among his many well-known accomplishments, Newton discovered the basic principles of viscosity in 1687. According to Newton’s observations, a fluid’s viscosity is a function of shear stress and temperature, therefore he established a mathematical relationship between the 3 terms which is today called in his honor the Newton’s Law of Viscosity.

NEWTON’S LAW OF VISCOSITY

The Newtonian law of viscosity states that the shear stress must be directly proportional to the velocity gradient, also called the rate of shear strain. Mathematically the Newton’s equation is explained in fig 2 below:

According to Newton no stirring or such actions will change the viscosity of a fluid. However, this does not always happen. You may have noticed that if curd is beaten for a long time, its consistency becomes thinner. However, in case of water, there is no change in the viscosity even if it is stirred for long. Therefore it can be said that Newton understood only half of the picture of the whole scenario. That’s why now we divide fluids in 2 main categories: Newtonian fluids (which obey Newton’s law of viscosity) and Non-Newtonian fluids (which don’t behave according to Newton’s law).

NEWTONIAN FLUIDS.

A fluid is a Newtonian fluid: if its viscosity remains constant for a given temperature and pressure, no matter the amount of shear applied (such as mixing or a sudden application of force), hence the viscosity is simply defined as the ratio of shear stress to shear strain rate.

Newtonian fluids are single-phase fluids made up of tiny molecules in general (but not always). In the case of Newtonian Fluids “Viscosity of the Newtonian fluid is solely a function of the fluid’s condition, particularly its temperature“. The viscosity tensor is reduced to 2 real coefficients reflecting the fluid’s resistance to continuous shear deformation and continuous compression or expansion, respectively, when the fluid is also isotropic (mechanical properties are the same in all directions). It is possible for the viscosity of a Newtonian fluid to change through factors other than externally applied force, such as through temperature and pressure. In case of liquids, those which are Newtonian are also incompressible, namely they exhibit a negligible change under pressure. The defining factor of any Newtonian fluid is that it will flow the same when a great deal of force is applied as when it is left alone. This means that it can be mixed vigorously without changing its viscosity.

While no real liquid or gas exactly meets the description, many common liquids and gases, like water and air, can be considered to be Newtonian for practical calculations under normal circumstances. The viscosity of a Newtonian fluid, at a given temperature and pressure, can be determined with a single measurement at any shear rate. Newtonian fluids are mathematical models of fluids that are the simplest and viscous.

One well known example is water, since it flows the same way regardless of whether it is left alone or agitated vigorously. This can be contrasted with non-Newtonian fluids, which can become thicker or thinner when stress is applied. However, it is possible for the viscosity of a Newtonian fluid to change if it is exposed to different temperatures or pressures instead of external applications of force. Many fluids become thicker as they are cooled, for example, though they still react to shear forces without a change in viscosity. Water retains its viscosity even after the application of external force.

The great majority of most common fluids (liquids and gases) such as water, organic solvents, oils, air, steam, nitrogen, oxygen, hydrogen or rare gases are Newtonian in wide temperature and pressure ranges.

WHY DO YOU NEED TO KNOW THE DIFFERENCE BETWEEN NEWTONIAN AND NON-NEWTONIAN LIQUIDS?

It’s important to fully understand the properties of the fluids you’re transferring, mixing, or pumping because viscosity plays a major role in sizing and selecting equipment, such as the pump and sizing for sanitary, industrial, water and wastewater, pulp & paper, and tissue applications and many more. Understanding how a fluid reacts to shear will help you properly size and select all the equipment it touches.

For instance one common application for Newtonian liquids is for Lubricants. Newtonian fluids (such as oil and its derivates) are ideal for lubrication applications. Even though they alter viscosity as a function of temperature, these fluids do not change viscosity as a function of shear. A good example is motor oil. In a nutshell, it remains fluid at lower temperatures but doesn’t get too thin at higher engine operating temperatures. The important thing is that it does not change viscosity when it is shared between the engine elements. This is critical if it is to perform its function of separating parts and decreasing friction and wear. If the viscosity tumbled as a function of shear, it would be easily dislodged, and the metal components would destroy each other.