How does it work shear stress in fluids?

But shear stress can be applied to almost any material, even to fluids, which is the main topic of this article. Thanks to Isaac Newton's works and studies, we have the Viscosity Law. In here, each symbol represents the following:

• µ: viscosity
• du/dy: shear velocity

Shear stress in fluids can be defined as the amount of force applied to a fluid parallel to a very small surface element. For a much more accurate calculation, the elements must be infinitesimal; this means the values are smaller. It is important to remember that the largest source of shear stress in a fluid is the viscosity created by the friction between the layers.

How does shear stress work in fluids?

Shear stress in fluids differs depending on the typology that you are working with. It is produced by the interaction between the fluid layers at different speeds. Roughly speaking, it will be the result of the tangential forces summed up in each layer of the fluid, known as deformation or shear force.

To better understand the effect between fluids, we will review what viscosity is.

Viscosity

A basic concept to understand shear stress in fluids is viscosity. Since we will cover it consciously when discussing fluid mechanics and how different forces react depending on viscosity.

We understand viscosity as internal friction, or resistance to fluid flow. All real fluids possess this characteristic, caused by friction between the molecules. We know that, in liquids, viscosity is produced by resistance to short-range forces, while in gases it is due to collisions between molecules.

In the next graphic, we can see some daily use according to the interaction of the molecules by bonding forces:

Fluids with more viscosity, such as honey, are quite dense and slow compared to others such as water. Therefore, it's possible to notice how a spoon full of honey deforms when applying pressure on it, but it is impossible to notice the deformation of the air with our naked eye.

This is highly related to the stress caused by the shear force, since it occurs when the fluid layers meet or are in contact with a solid wall, changing their trajectory.

Viscosity is usually represented with the help of layers that make up a fluid’s viscosity; layers closer to the walls of a solid have slower velocities than those that are farther away. Viscosity’s effects will depend on the wall type or solid layers that establish contact with the flow.

The diversity of effects that shear force can have has been due to viscosity categories: Non-Newtonian and Newtonian fluids.

Newtonian fluids

With Newtonian fluid, the relationship between force and linear displacement velocity is directly proportional to the deformation rate. Water is a good example of this kind of fluid.

But, in addition, it is important to mention Newton's Law of viscosity, which we discuss before. According to this, Newtonian fluids, unlike non-Newtonian ones, remain constant despite the shear stress.

Newtonian fluids comply with absolute viscosity and their consistency is constant, even with the changes that shear stress can cause.

There are no completely Newtonian fluids, variations always consider other factors besides the law. However, the change is so inconspicuous that we classify them that way.

Non-Newtonian fluids

Non-Newtonian fluids are those who do not comply with Newton’s law of viscosity and in which the shear stress effect can change viscosity. Also is understood that, when applying cutting force, its effect is not proportional to the deformation suffered by the material. One of the examples that help show how this reaction works is toothpaste.

Toothpaste is an example of Bingham type, a non-Newtonian fluid, reacting as a rigid body under minor stresses and, conversely, under greater stresses, flows on contact. Thanks to this quality, we can manipulate the fluid, extract it from the tube and place it in a brush without throwing it.

In the next images, we can see non-Newtonian fluids represented according to viscosity variation and fluid behavior contacting shear stress:

Pseudoplastics: presents a decrease in viscosity with increasing strain ratio, changes shape when a force greater than zero is applied, and many non-Newtonian fluids are this type. Some examples are dental alginate, polymerically solutions or suspensions, such as medicament.

Dilatant: there is an increase in viscosity caused by the deformation ratio. The shape change occurs when there is an applied force less than zero. It is also known as shear thickening, and its behavior can be seen in suspensions or materials that are not pure. Examples are yeast dough, starch, or sand suspensions.

Bingham fluid: they are also known as ideal fluids and behave like a solid with the minimum strain and like a fluid at high pressure. Some examples of this kind of fluid are clay suspensions, toothpaste, or mayonnaise.

It is important to know what type of fluid we have when choosing an agitation or a container system and the behavior. In these cases, we can rely on a table of records according to the cut rate and graphs, among other materials.

To carry out this task, you can count on the Autmix Flow specialist, who will guide you in finding the ideal equipment for your project.

Some equipment and impellers that are known by creating a shear stress effect are:

Rotor-stator RE(S) series: this equipment belongs to large-capacity industrial agitators whose design combines a high degree of shearing and great power to provide good results in homogenization, emulsion, and treatment of fluids of various viscosities.

Cowles disc: this is a mobile that takes advantage of the cutting force with the help of a toothed disc that rotates at high speed and has better control of fluids with variable viscosity.

Gamma profile: it is an impeller that, due to its design, provides high shearing and the ability to work with less power than others. It can be used in pseudoplastic fluids, known for their variability and high viscosity.

Relation of the shear force with the fluids according to their movement behavior

Besides reviewing shear force in Newtonian and non-Newtonian fluids, we must consider the movement and their behavior. This classification or regimen is divided into laminar and turbulent flows.

Laminar Fluids

When a laminar flows inside a tube, the particles travel in parallel layers at different speeds. Shear stress causes fluid layers to move slower near the walls of a tube than the ones in the center, due to friction.

When a viscous fluid moves inside a tube, the speed varies even within the same cross-section when a viscous fluid moves inside a tube.

This is represented with help from the next equation:

Where the values are the next:

• V: liquid volume
• t: time
• v: fluid speed rate
• r: ratio
• Δp: pressure fall
• μ: dynamic viscosity
• L: characteristic length

Another law that we must keep in mind when we are checking the fluids dynamics is Stokes’s law. This will help us understand a fluid’s behavior around a sphere. This device will receive the resistance force from the fluid itself. The equation is this:

For a better explanation, you can imagine the flow of several people at different speeds when passing through a narrow street. If they are walking in the same direction, it won’t matter about the speed, the order continues, and it won’t be chaotic.

Turbulent fluids

Turbulent fluids are known as it because they occur chaotically, and it's possible to know their trajectory up to a certain scale. The shear stress in these fluids is generated in all directions, which is important in energy and material transfer processes.

Thanks to the Reynolds coefficient that relates density, speed, typical dimension, and viscosity, it is possible to know if a fluid is turbulent or laminar. According to experiments that are carried out to know the movement, when the Reynolds number is 2 000 or less, the fluid is laminar. On the other hand, when the coefficient is 2 000 or more, the fluid is turbulent.

Going back to the example with the narrow, busy street, the turbulent flow would be equivalent to several people walking chaotically and colliding with each other.

Why have we reviewed all of this?

You are now widely aware of shear stress in liquids like Newtonian and non-Newtonian fluids. In addition, you know the movement behavior in laminar or turbulent, and all of this is valuable knowledge in choosing the best way to work with them. For example, if you are selecting pumps, valves, or agitators, you must know all of this.

A wide variety of materials and components or equipment can be the best solution to each project. At Autmix, industrial-process specialists have extensive experience in the field, and you can schedule a professional consultation to obtain more information about the components and equipment you need.