Before you select a pump for any service, you need to know and understand the characteristic properties of the fluid you wish to pump. Fluids fall into two classifications—Newtonion or non-Newtonion. Every time I review the characteristics of both fluids, I get caught up in the overwhelming array of nomenclature and technical terms. I call non-Newtonian fluids rascals because they do not follow the rules. I was thinking I might take a simpler approach for the purpose of this column.

A major portion of any discussion regarding the subject concerns viscosity, and I suggest you read my article on the subject (*Pumps & Systems*, November 2017). For a more in-depth, technical article, see my co-contributor’s article from *Pumps & Systems*, December 2011, by Dr. Lev Nelik.

## Viscosity Definition

Viscosity is a fluid’s resistance to flow or pour, but not all fluids resist or react in the same way or even in the same time reference. With rare exceptions, the viscosity for every fluid will change indirectly with the temperature; if the temperature of the fluid goes up, the viscosity will decrease and vice versa. One way to visualize viscosity is by watching a metal ball fall through a glass container of the liquid at different speeds for various viscosities. The faster the ball falls, the lower the viscosity of the fluid. To take the viscosity concept another step, it is also that property of a fluid that resists a shearing force. Simply put, it pours either fast or slow. Pouring slow means a thicker fluid, which also means a higher viscosity, or you can think of it as possessing a higher resistance to the applied force. Lastly, an alternate method to visualize viscosity is the internal fluid friction resulting when one layer of fluid is forced to move in relation to another layer. Note that the opposite or inverse of viscosity is fluidity.

## Terms

A set of terms we need to explain to understand viscosity are stress and strain and how they will affect the fluid properties. First, imagine you are pushing two or more flat plates or boards stacked on top of one another. In the example, you exert a fixed amount of force to the top plate and it consequently moves at a certain speed (velocity) over a specific distance in a measured amount of time. Note that in this imaginary stack of plates, the second, third and fourth plates in the stack will also move, but with lesser amounts of distance and speed. If the moving plate reaction is constant (linear), then the resulting action of the moving pieces represents approximately the same way a Newtonion fluid would react.

We call these fluids Newtonion because they act in a predictable (classic physics) sort of way. These classic fluid properties are named for scientist Sir Isaac Newton. For the simple and perhaps more natural fluids that existed during Newton’s lifetime (1642-1726), he figured out that the viscosity of most fluids changed only with temperature. In the modern era and the advent of polymers and other modern liquids, we now have fluids where this is no longer true. Consequently, this newer class of liquids/fluids is referred to as non-Newtonion.

If a material has a viscosity that is independent of the applied shear stress, then it is referred to as an ideal or Newtonion fluid. Water is considered a Newtonion fluid because it behaves in a classical way. If you stir a glass of water with a spoon, the viscosity does not change no matter how vigorously or how long you stir. The viscosity of a Newtonion fluid is only dependent on the temperature of the fluid (consequently, the requirements for pumping water through a pipe is an easily predictable evolution). Water, oil, alcohol, glycerin and gasoline are common examples of Newtonion fluids. Also note that if you were pumping a viscous liquid like oil at 100 centipoise (cP) with a pump operating at 1,750 revolutions per minute (rpm), the viscosity of a Newtonion fluid does not change even if you increase the speed to 3,550 rpm. If held at constant temperature and the shear rate doubles, the viscosity does not change.

A non-Newtonion fluid has a viscosity that varies with the shear stress and shear rate, so it becomes harder to predict the fluid behavior when it is pumped. Examples are latex paints, soaps, tars, glues, most slurries, colloids, polymers and peanut butter.

## Newton's Law of Viscosity

Newton’s law of viscosity is simply:

Stress = [Viscosity] X [Rate]

Slightly more complex, the formula is really:

Shear Stress = [Viscosity] X [Shear Rate]

## What is Shear Stress & Shear Rate?

Skip this section if you are looking for simplicity in this column.

Stress is how a force is distributed over or through a material. Shear (for a liquid) is defined as the relative motion between the adjoining layers of a moving fluid. Shear stress is a force per unit area in the simplest definition and applies when the stress is applied at right angles to the subject (for a solid). When you apply a shear stress to a fluid, it will deform at a constant rate, and that is called the shear rate. These types of stresses are calculated parallel to the subject fluid.

Shear rate is the fluid velocity divided by the distance moved. Another way to describe shear rate is as the speed of relative motion between layers of a liquid that is moving. Note that just the simple action of pumping certain fluids can irreversibly damage them, while others require the shear rate to increase to a certain level to change the viscosity and get them moving in the first place. Shear sensitive fluids are usually pumped with positive displacement pumps such as progressive cavity or internal gear pumps. Latex and glue are good common examples of shear sensitive fluids.

## Non-Newtonion Fluids

The viscosity of a non-Newtonion fluid changes with temperature, but more importantly how it is agitated (how a force is applied) or with the amount of pressure; these are classed as shear stresses. Non-Newtonion fluids fall into three categories:

- time dependent
- time independent
- viscoelastic

From these three, there are five main subclasses of non-Newtonion fluids:

- plastic (time independent)
- pseudo-plastic (time independent)
- dilatant (time independent)
- thixotropic (time dependent)
- rheopectic (time dependent)

## Dilatant & Thixotropic Fluids

When the viscosity of a fluid changes with the shear rate, the fluid can be either dilatant or thixotropic. Note there are categories where time dependency or independency comes into play and subcategories.

Dilatant and pseudo-plastic fluids are both types of non-Newtonian fluids where the relationship between viscosity and shear rate is not time dependent.

When the viscosity increases with an increase in agitation (shear rate) these fluids are known as dilatant. Dilatant properties are not normally found in pure materials and are usually suspensions, mixtures or compounds. Examples are clay, slurries and silly putty.

If the viscosity decreases as the agitation rate (shear rate) increases, this is typically known as a thixotropic fluid. Examples include soaps, tar and vegetable oil. In a thixotropic fluid, the viscosity decreases with stress over time. At a constant shear rate, the shear stress decreases monotonically. Note that a function that decreases monotonically does not exclusively have to decrease, it simply must not increase.

My favorite example for a thixotropic fluid is ketchup. Every hungry human has tried to get cold ketchup out of the bottle and on to hot french fries as fast as they can, but the ketchup will not cooperate. So you shake or smack the bottle and the product eventually comes out, and then sometimes perhaps too fast. When you shake the bottle, you are applying a shear stress to the fluid. That stress causes the fluid to become less viscous. This a simple example of a shear sensitive fluid—in this case, a thinning fluid. An industrial example of a thixotropic fluid from the oil and gas market is drilling mud.

The initial viscosity may be too high to get the fluid flow started, but the viscosity decreases as the shear rate increases, and then it flows very well as long as there is stress. Other fluids similar to ketchup are gels, latex paints and lotions.

As an example, when you squeeze suntan lotion from the tube, it may be difficult to get the flow started, but when you rub the lotion on your hands, the added sheer stress causes the lotion to be more of a liquid and quickly soak in. A similar example would be shaving cream or toothpaste.

Another instance is paint. You want the liquid to adhere to the brush when you slowly dip the brush into the can, but you also want the paint to flow when you are applying it to the surface to be painted.

Quicksand, while technically a valid fluid, is probably more of a movie and urban myth example. But if you ever get stuck in quicksand, it is best not to struggle vigorously as you will sink deeper and faster. You can possibly float to the top if you simply stop moving.

From a pumping perspective with thixotropic fluids, once you overcome the initial resistance, the fluid will flow similar to a standard Newtonian fluid. It is also important to realize the time dependent aspect. Note: You will require more horsepower to get this fluid started (initiated) to flow and you need to keep it flowing.

For dilatant fluids, although there are shear thinning fluids like above, there are also shear thickening fluids. These fluids behave in the opposite way, which means the more you agitate them (shear stress), the more they will thicken and resist flow (higher viscosity). The most common dilatant liquid for this example is mixing cornstarch with water.

If you agitate it quickly, it will act as a solid, but if you move an object through the fluid medium very slowly, it reacts more like a liquid.

There are dozens of videos on the web that will entertain and educate you on this subject of thickening fluids.

The properties of dilatant fluids are being studied for use in body armor and football helmets.

## Summary

For most non-Newtonion fluids, it will be wise to consider the type and speed of pump you choose to move the fluid. Understand that viscous fluid behavior changes with different flow rates. The more you try to force a dilatant fluid through a pipe, the more it will resist in what seems like a pushback on the system.

The size of the pipe will also be a factor since the smaller pipes will have increased velocity with associated higher shear rates. Additional consideration may be required and focused on the pump clearances.

For Newtonion fluids, the relationship between shear stress and shear rate is linear. For non-Newtonion fluids, the relationship is different since it is mostly nonlinear and can also be time dependent.

For Newtonion fluids, temperature is the only thing that changes the viscosity. For non-Newtonion fluids, temperature still changes the viscosity, but more importantly viscosity changes with applied shear stresses (agitation or pressure).

The viscosity of a dilatant fluid becomes more viscous when agitated (shear stressed).

This is very important when pumping clay slurries. Clay slurries are widely used in the paper and ceramics industries. Dilatants are known as shear thickening fluids.

The viscosity of thixotropic fluids will decrease with increased stress and be easier to pump after some time and effort to get them started, but if allowed to rest will return to the more resistant state. In these cases, make sure you size the driver for the initial load of getting the fluid flow initialized. That is, size the driver torque and brake horsepower (BHP) for the apparent viscosity in lieu of the normal working viscosity. Size the pump hydraulics for the working viscosity.

Lastly—and just because I grew up on a dairy farm—do not confuse density with viscosity. Cream is thicker than milk, but is less dense.

## Conclusion

Fluid behavior and rheology are much more complicated than this column would indicate. The purpose here is simply to make you aware of the basics and to be cognizant as to the potential deleterious effects on the pump and the system.

## References

Fluid Mechanics (6th Edition), Frank M. White

Cameron Hydraulic Data Book (19th Edition)