Zero Shear Viscosity: What It Is and Its Applications

Viscosity is a fluid’s resistance to flowing; honey has a high viscosity, while water has a low one. For simple fluids like water, this property is constant regardless of force. However, the viscosity of many materials changes depending on the rate at which they are moved, known as the shear rate.

For instance, rubbing lotion onto skin is a high shear rate, whereas squeezing it from a tube is a low one. This dependency means a single viscosity value is often insufficient to describe these complex fluids.

The Zero Shear Plateau

Zero shear viscosity is the viscosity of a non-Newtonian fluid measured under very slow flow, representing its resistance when nearly at rest. For these materials, like paint or ketchup, a graph plotting viscosity against shear rate reveals a distinct pattern. At very low shear rates, the viscosity is high and constant, forming a flat region on the graph known as the zero shear plateau.

This plateau represents the material’s maximum viscosity before force causes it to become less viscous, a behavior known as shear-thinning. The zero shear viscosity, abbreviated as η0 (eta-zero), is the value taken from this plateau.

Molecular Basis and Significance

The high viscosity at the zero shear plateau results from a material’s internal structure at rest. In complex fluids like polymer solutions, long molecular chains are randomly coiled and physically entangled, much like a bowl of spaghetti. This intertwined state creates significant resistance to initial movement. The zero shear viscosity value is a direct quantification of this internal resistance.

A higher zero shear viscosity value suggests a more robust internal network. This can be attributed to longer polymer chains, which lead to more complex entanglements and increase the resting viscosity. Stronger intermolecular forces also contribute by making it more difficult to pull molecules past one another. The relationship is so pronounced that zero shear viscosity is proportional to the weight-average molecular weight raised to a power of approximately 3.4.

Measurement and Modeling

Measuring zero shear viscosity is challenging because a true shear rate of zero is impossible to achieve experimentally. This limitation is overcome using specialized instruments called rheometers, which apply precise and controlled shear rates. The procedure involves measuring a fluid’s viscosity at a series of progressively lower shear rates. These data points form the zero shear plateau on a viscosity-versus-shear-rate curve.

To find the final value, researchers extrapolate the data from this flat plateau back to the y-axis, where the shear rate is zero. This extrapolation is guided by mathematical models, such as the Carreau or Cross models, that are fitted to the data. The zero shear viscosity (η0) is a key parameter within these models, allowing for its precise calculation.

Practical Applications

Zero shear viscosity is relevant in many industrial processes where fluid behavior at rest is a factor. In the paints and coatings industry, a high value ensures that paint on a vertical surface will not drip or sag under the force of gravity. The paint remains stable when no shear from brushing or rolling is applied.

In the food industry, zero shear viscosity determines texture and shelf stability. For products like yogurt or sauces, it provides a thick consistency in the container. It also prevents solid particles, such as fruit pieces in yogurt or herbs in a dressing, from settling to the bottom over time.

Pharmaceutical and cosmetic products also rely on controlled zero shear viscosity. In medicinal suspensions, it prevents the active ingredients from settling out, ensuring proper dosage with each use. For creams and lotions, high zero shear viscosity provides a rich texture and prevents the separation of water and oil phases.