# The Influence of Critical Shear Stress on Shear-Thinning and Shear-Thickening Fluids

### Key Takeaways

• An external force that acts on a fluid to induce shear flow is called shear stress.

• Yield stress is the applied stress above which the fluid attains a structured flow.

• In shear-thickening fluids, the disruption of shear-thinning behavior occurs at critical shear stress and brings a solid-like transition in the fluid behavior with an increase in viscosity

In shear-thinning fluids, the shear stress value at which a large drop in the viscosity occurs is called critical shear stress

Fluid deformation is related to force and time. Rheology is the study of the flow and how deformation can be interrelated with force and time. Rheological studies deal with deformation in solids, the flow of liquids, and the behavior of viscoelastic materials, which show the properties of both solids and liquids.

When working on fluid deformation, you might come across different Newtonian and non-Newtonian fluid behaviors. Two such behaviors are shear thinning and shear thickening. Critical shear stress signifies the commencement of behavioral changes in shear-thinning fluid. In shear thickening, a solid-like transition is observed at critical shear stress.

In this article, we will look at the influence of critical shear stress on shear-thinning and thickening fluids.

## Shear Flow, Shear Stress, Shear Strain, and Shear Rate

Among shear flow and extensional flow, the former is the most common flow behavior. In shear flow, layers of the fluid slide over each other at a speed greater than that of the layer beneath it. The maximum velocity is at the top layer and the bottom layer is stationary.

An external force that acts on the fluid to induce shear flow is called shear stress. The shear stress denoted by is the force per unit area.

The displacement gradient across the fluid layers is called shear strain. When the shear strain continues to increase on the application of shear stress, the velocity gradient is created.

The velocity gradient, otherwise called shear rate or strain rate, is the rate of change of strain with time. The behavior of fluid varies with the value of shear rate or shear stress. One such behavior is shear thinning.

## Shear Thinning and Critical Shear Stress

Shear thinning is a behavior commonly seen in non-Newtonian fluids. It is also called Pseudoplastic flow. Shear thinning results from rearrangements in the microstructure level in fluids. The rearrangements occurring in the plane of applied shear stress change the behavior of fluids. In shear-thinning fluids, as the applied stress increases, the fluid velocity decreases. There is a particular shear stress value at which a large drop in the viscosity is observed, which is called critical shear stress.

Shear-thinning fluids show constant viscosity values at low shear rates. The constant viscosity value of shear-thinning fluids is called zero shear viscosity or the zero shear viscosity plateau. As the shear stress applied increases, a large drop in viscosity is observed at a particular point. This value of shear stress or shear rate is called critical shear stress or critical shear rate. It is at the critical shear rate point that the shear thinning behavior of the fluid starts.

## Yield Stress

Emulsion, polymer solutions, and melts are examples of shear-thinning fluids. In highly shear-thinning fluids, the viscosity attains an infinite value and the characteristics of the solid become visible. This behavior comes into existence below a critical shear stress value, called yield stress. The resulting behavior or flow response due to yield stress is called plastic flow. The plastic flow is characterized by continuously increasing viscosity as the shear rate approaches zero.

## The Importance of Yield Stress

Yield stress is the applied stress above which the fluid attains a structured flow. The yield stress is significant in applications involving pumping, coating, and spreading. In fluids with relatively low stress induced by gravitational force, the yield stress inhibits the flow. This is mostly seen as slump and sag resistance in products like fire-retardant coatings, paint, plaster, adhesives, etc. The yield stress introduces both desirable and undesirable qualities in a fluid flow.

Next, let’s see how critical shear stress influences shear thickening.

## Shear Thickening and Critical Shear Stress

In certain fluids, the viscosity increases with an increase in shear rate or shear stress. Such a fluid is called a shear-thickening fluid, and the phenomenon is known as dilatancy. Shear thickening is usually exhibited by particulate suspension or dispersions with a high concentration of solid particles.

Shear-thickening fluids are used in shock absorbers and protective equipment. Most shear-thickening fluids show shear-thinning behavior at low shear rates and stress. The disruption of shear-thinning behavior occurs at critical shear stress and brings a solid-like transition in the fluid behavior with an increase in viscosity.

The critical shear stress is a significant parameter influencing the flow response of fluids. The behavior of the fluids that showcase shear-thickening and shear-thinning properties are dependent on the critical shear stress.

## Analyze Shear Stress With CFD Tools From Cadence

Cadence’s CFD tools offer you an opportunity to understand the shear stresses acting on fluids and their effect on flow behavior. With Cadence tools, you can learn more about the characteristics of shear-thinning as well as shear-thickening fluids.