Quantifying Shear Thickening Behavior Using the Power Law Model on a Rotational Rheometer

Introduction

While most suspensions and polymer structured materials are Shear ThinningThe most common type of non-Newtonian behavior is shear thinning or pseudoplastic flow, where the fluid vis­cosity decreases with increasing shear.shear thinning, some materials can also show Shear ThickeningWhile most suspensions and polymer structured mate­rials are shear thinning, some materials can also show shear thickening behavior where viscosity increases with increasing shear rate or shear stress.shear thickening behavior where viscosity increases with increasing shear rate or shear StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress. This phenomenon is also often referred to as dilatancy, and although this refers to a specific mechanism for Shear ThickeningWhile most suspensions and polymer structured mate­rials are shear thinning, some materials can also show shear thickening behavior where viscosity increases with increasing shear rate or shear stress.shear thickening, the terms are often used interchangeably. In most cases, Shear ThickeningWhile most suspensions and polymer structured mate­rials are shear thinning, some materials can also show shear thickening behavior where viscosity increases with increasing shear rate or shear stress.shear thickening occurs over a decade of shear rates and there can be a region of Shear ThinningThe most common type of non-Newtonian behavior is shear thinning or pseudoplastic flow, where the fluid vis­cosity decreases with increasing shear.shear thinning at lower and higher shear rates. 

Usually, dispersions or particulate suspensions with high concentration of solid particles, pastes, associative polymers such as HASE, HEUR polymers, etc., exhibit Shear ThickeningWhile most suspensions and polymer structured mate­rials are shear thinning, some materials can also show shear thickening behavior where viscosity increases with increasing shear rate or shear stress.shear thickening. Materials exhibiting Shear ThickeningWhile most suspensions and polymer structured mate­rials are shear thinning, some materials can also show shear thickening behavior where viscosity increases with increasing shear rate or shear stress.shear thickening are much less common in industrial applications than materials exhibiting Shear ThinningThe most common type of non-Newtonian behavior is shear thinning or pseudoplastic flow, where the fluid vis­cosity decreases with increasing shear.shear thinning, however, where encountered shear thickening, materials can lead to severe processing problems. Materials which undergo microstructural or orientation changes on application of shear, that lead to increased resistance to flow, will tend to show shear thickening. 

For suspensions, this generally occurs in materials that show Shear ThinningThe most common type of non-Newtonian behavior is shear thinning or pseudoplastic flow, where the fluid vis­cosity decreases with increasing shear.shear thinning at lower shear rates and shear stresses. At a critical shear StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress or shear rate, the organized flow regime responsible for Shear ThinningThe most common type of non-Newtonian behavior is shear thinning or pseudoplastic flow, where the fluid vis­cosity decreases with increasing shear.shear thinning, is disrupted and so called ‘hydro-cluster’ formation or ‘jamming’ can occur. This gives a transient solidlike response and an increase in the observed viscosity. Shear thickening can also occur in polymers, in particular amphiphilic polymers, which at high shear rates may open-up and stretch, exposing parts of the chain capable of forming transient intermolecular associations.

Mathematically, the shear thickening behavior can be modeled using the powerlaw model:

Where

k is the consistenc
n is the power law index
σ is the shear rate,
·γ is the shear rate.

With n greater than 1 for shear thickening fluids.

It should be noted that an upturn in viscosity at high shear rates can occur through other phenomenon such as fluid turbulence. This effect, however, tends to occur with lower viscosity fluids and can be predicted from Reynolds number calculations

Experimental

1) Viscosity-shear rate dependence of a corn starch-water mixture

Results and Discussion

Figure 1 shows the viscosity-shear rate profile for the Corn Starch dispersion. At low shear rates, the sample exhibits shear thinning behavior; however, at a critical shear rate of approximately 8 s-1, a sharp upturn in viscosity, characteristic of shear thickening behavior, is observed. Fitting a Power Law ModelThe power law model is a common rheological model to quantify (typically) the shear thinning nature of a sample, with the value closer to zero indicating a more shear thinning material.power law model to the data between 0.15 s-1 and 6.5 s-1, the reported value for the power law index (n) is 0.57, thus confirming shear thinning behavior (n<1). Fitting the same model to the data between 10 s-1 and 20 s-1, the value of n is 3.01, which indicates significant shear thickening (n>1).s.

Conclusion

The corn starch-water mixture tested exhibited strong shear-thickening behaviour above 8 s-1 as confirmed by the power law index (n) which gave a value of 3 for data between 10 and 20 s-1.

Please note...

that a cone-plate geometry or a cylindrical geometry can also be used. A sand blasted geometry should be considered if the material is likely to show wall slip effects. Larger geometries are useful for measurements at low torques, which are more likely to be encountered at lower shear rates and stresses. The use of a solvent trap is also recommended for these tests since evaporation of solvent (e.g., water) around the edges of the measuring system

Literature

  1. [1]
    An Introduction to Rheology – Barnes, Hutton & Walters
  2. [2]
    Colloidal Suspension Rheology – Mewis & Wagner