Measuring specific viscous and other rheological properties require you to relate two quantities (shear stress and shear rate, as described in the following). The different types of instruments (called rheometers) will then produce and measure those two properties differently, each having its benefits and drawbacks. In this blog, we’ll cover essential questions and principles on the different types of rheometers and the results they can provide. Hopefully, by the end of this article, selecting the right rheometer for you will be simple!
How to Measure Viscosity and Other Rheological Properties
In our blog post “Why Shear Rate Matters in Process Control,” we discussed how viscosity quantifies the amount of force that is needed when deforming a liquid or substance: We all know that it requires greater force to mix cookie dough in a bowl than to stir in a cup of coffee.
To describe and evaluate the different types of rheometers, we need to be more mathematically stringent in describing the measuring of viscosity.
How is Viscosity Defined?
On a small scale, imagine viscosity as the friction arising between different “fluid layers” sliding against each other while you shear the fluid.
Think of the layers as a stack of cards – each layer having a slightly different velocity than the neighboring layers. The same happens when shearing a liquid, as illustrated below, where you conceive many “fluid layers” sliding between a fixed lower plate and a moving upper plate. The shear rate is then the difference in velocity between two fluid layers, divided by the layers’ distance. (*) The shear rate is also described below to the right, by the first mathematical relation.
Now we turn the attention towards the force needed to obtain the fluid’s shearing, illustrated by the force arrow in the above Figure.
The force is distributed evenly over the upper plate. It results from a constantly applied shear stress (denoted σ) given by the force divided by the upper plate area (the second relation).
Viscosity is simply the shear stress divided by the shear rate! – Nothing more, nothing less.
This example of force distribution is the last relation, above, and surprisingly enough, even high-end rheometers today compute viscosities by this simple relation.
The Working Principle of Different Rheometer Types
Nearly all rheometers rely on creating well-controlled fluid layers and precisely relate the applied shear stress to the resulting shear rate.
I will clarify this process in the following table, which describes the most common rheometers based on the generated fluid layers’ shape. I’ll also include short comments on their pros and cons of the various rheometers.
Rotational rheometer, confining the liquid between a cone and a plate
The liquid is sheared between an upper rotating cone and a lower fixed plate as seen from the side. The shear stress comes directly from the torque.
The cone and plate combination evenly shears the liquid, having completely horizontal fluid layers.
Pros: It requires an exceedingly small volume of the sample liquid and measures at a very well-defined shear-rate.
Cons: It is not optimal when measuring thin liquids or if the sample contains particles, as they can wedge between the narrow central gap. Evaporation can have a large effect.
Rotational rheometer, confining the liquid between a plate and a plate
The liquid is sheared between an upper rotating plate and a lower fixed plate, as seen from the side. The shear stress comes from the torque.
The liquid is sheared between the two plates in a controlled manner, but not evenly as with the cone-plate geometry.
Pros: Compared to the cone-plate, this geometry can handle samples containing particles.
Cons: The instrument software typically compensates for varying shear rate measurement effects. Evaporation can have an enormous impact.
Rotational rheometer, confining the liquid between a cup and a bob (having a cylindrical gap)
The cross-section view below shows how the liquid shears between the central rotating bob and the fixed cup. Like the former, the shear stress comes from the torque.
Here, the fluid layers become concentrical cylinders, such that the shear stress acts on a large surface area, compared to, e.g., the cone-plate geometry.
Pros: A cup-bob geometry is more sensitive when measuring on thin liquids compared to cone-plate or plate-plate. It is also less affected by possible evaporation effects.
Cons: The measurements require large sample volumes. Cleaning the geometry is more time-consuming than cone-plate or plate-plate.
A Rotating viscometer, using rotating rods inside a cup filled with the liquid sample
A numerical simulation of the central liquid flow and shear around the rods (shown below). The shear rate’s value varies greatly, as shown by the color-coding on the rod, where it peaks at the tips. The shear stress is poorly controlled and at most proportional to the torque.
Simulating the shape of a fluid “layer” (in yellow) shows that it wraps around the rods’ tip and is significantly deformed, having no well-defined shape.
Pros: Such viscometers are cheap and easy to operate.
Cons: Can only measure Newtonian liquids’ viscosity (having constant viscosity, see Why Shear Rate Matters in Process Control). Measures using un-controlled fluid layers and varying shear rates, as seen in the simulation figures to the right. The measurements have poor reproducibility since the cup is often aligned manually.
A capillary rheometer, pumping the sample through a narrow tube (capillary)
The pressure-drop over the capillary is measured as the sample is pumped through. From thermodynamics, the shear stress directly relates to the pressure drop.
Because the capillary flow is laminar (smooth and calm), the fluid layers of cylinders sliding along their common axis. This type of flow gives a well-defined shear rate on the inner wall of the capillary.
Pros: The flow can enable an easy exchange of samples. The instrument is a closed system such that sample-evaporation is not an issue.
Cons: The large deformation (flow) of the sample prevents it from measuring some complex rheological features (oscillatory measurements not covered in this blog post).
Possibilities In Process Analysis
When you need to control the viscosity (or other rheological properties) as part of quality control or process monitoring at the production line, you must do these measurements many times, every day. Therefore, conducting the measurements needs to be as easy and fast as possible to prevent this control from delaying the production process. Carrying out an efficient control can either be done as manual measurements in process labs or at small lab stations situated close to the production line or by automated analyzers integrated into the production facility. All the above methods are used for manual testing, while analyzers exist by integrating rotational viscometers (Inline versions of cylindrical geometries) or online, automated capillary rheometers (RheoStream®). For more details on the pros and cons of the different process analyzers, check out Fluidan’s blog, “How RheoStream Can Help You Even When You Have Given Up on Other Viscometers.”
Measuring More Complex Rheological Properties
Except for the viscometer with rotating rods, all the other rheometer types that I’ve mentioned can measure the viscosity at different well-defined shear rates. Such a shear rate dependence of the viscosity is a significant rheological property (see “Why Shear Rate Matters in Process Control”).
Many more rheological effects and properties exist, such as, e.g., viscoelasticity (oscillatory measurements), torsional viscosity, and elongational viscosity. They will not be covered in this article, as they are seldomly used to control liquid products.