Recently I have been showing some of our rotational rheometer customers how to make high shear measurements on their instruments. This highlights some of the hard to define measurement constraints that rheometer users can have when pushing the practical limits of the instrument. I thought it would be useful to share some of the issues and potential solutions via our blog.
One of the advantages of using a rheometer, over a viscometer for example, is that a rheometer can more closely simulate conditions that a sample may undergo during application or processing. This is vitally important as complex materials can behave very differently depending on the conditions encountered during the process or application. This is typical of almost any application, but maybe the most extreme is expecting a material to behave like a solid under some conditions and flow like a liquid under others. One example is asphalt or bitumen road surfaces which are expected to behave like solid materials when we drive on them, even at high temperatures, but they are also designed to behave like liquids over longer time scales to avoid thermal cracking when temperatures drop during winter or at night.
Another example is topical creams or food items like mayonnaise, where we need “solid like” behavior under low stresses to give the requisite stability, texture and stand-up characteristics in the pot or on the plate. Yet these materials also need to flow like a liquid in order to be applied or dispensed from a bottle.
A single “viscosity” reading is not going to help answer the question of whether my sample is behaving like a solid or liquid and under what conditions. A rheometer, however, is able to replicate the shear conditions encountered in the bottle or tub as well as in use, and can help answer these important questions. For example, low frequency oscillation testing or creep testing can mimic long time scale/low stress conditions like those encountered during storage, while steady rotation at high speeds and small gaps can be used to simulate high shear processes such as rubbing. Measuring yield stress can also tell us what stress is required to go through the solid-liquid transition – for the solid structure to yield.
That’s why a rheometer is needed, to measure these contrasting material behaviours under process or application relevant conditions and hence optimize a formulation or process in the lab before scale up. If your sample is being sprayed, brushed or printed then there will be a corresponding shear rate or shear stress associated with the process. If known, it is possible to evaluate and compare material behave under these conditions on a rheometer. The examples cited are typically very high shear rates processes so we need to understand how these materials behave under such conditions.
High shear rate measurements are possible on a modern rotational rheometer but there are practical limitations which are often more do to with the sample rather than the ability of instrument to reach the desired shear rate. For example, the highest shear rates are achieved by using a high rotational velocity, combined with a small measurement gap. Malvern’s Kinexus rheometer can apply rotational velocities of 500 rad/s; more than other rotational rheometers. However, we just can’t use this speed with any geometry (measuring system), or else centrifugal forces will eject the sample out of the gap! Although this can be a sign of a good rheologist ☺️, we need to avoid this for high shear rate measurements.
To facilitate the use of these speeds, we also need to use a smaller measurement gap, hence the typical use of parallel plates, which have the flexibility of a changeable gap. The advantage is now two fold… the smaller gap keeps the sample between the plates at higher rotational speeds (due to the samples surface tension at the gap edge), and with shear rate being inversely proportional to gap, we also win here, as we can use lower rotational speeds.
But now, we have another practical consideration; how small in gap will the sample allow? As a rough rule of thumb, we use a measurement gap which is 5-10 times larger than the large(st) particle size (i.e. D95) in the sample. With a gap this size, the chance, even at higher rotational speeds, of the particles physically jamming together (like a traffic jam!) is slim so that we can ensure we are measuring the bulk material flow. This can limit the practical gap size that can be used in a measurement. It may be that these limitations are also present in the real application, if the gap dimensions are similar, or the real process may employ a higher shear velocity with a larger shear gap to achieve the same shear rate. Therefore, when replicating a high shear process it is important to consider whether the rheometer gap being used is of the same order as that encountered in the process, especially for small gaps where confinement of the microstructure may influence the resulting rheology.
There is also need to consider what the particle size and packing behavior is when under shear. Emulsions, for example, have soft deformable particles which can elongate and stream line under shear. This makes the equivalent particle size (in the direction of shear) effectively smaller! (Reference dispersion masterclass, on shape). It is also possible, that these extreme shear rates break down relatively strongly held flocs / aggregates of particles that would otherwise be quantified as the primary particle size.
So, it is common to apply very high shear rates with samples containing small particles, i.e. less than a micron on a rheometer using very small gaps… however we now have a different practical consideration: physical alignment, or rather parallelism of the measuring systems. A review of this practical limit (and the correction) is discussed in the article by Kravchuk and Stokes . Although we can command sub-micron gap changes with Kinexus, this doesn’t mean we can use gaps of this magnitude. The practical limiting factor is now how flat and parallel the upper and lower plates are. With development of Kinexus as a next generation rheometer these practical concerns were taken into consideration.
The plate cartridge system of Kinexus was designed from the outset with removable lower plates with consistent alignment being an absolute requirement. Not only does this allow the user to change the surface finish (roughened, serrated to prevent slippage), or use pedestal (diameter matched with the upper) plates to promote accurate (loading) trimming of tricky samples, but now ensures an increased accuracy in alignment and parallelism. For example parallelism, how “horizontal” the upper and lower plates are, is going to limit how small in gap we can go.
On Kinexus, our service engineers are all equipped with a dedicated “alignment kit” to ensure the best possible alignment on installation. The alignment kit is effectively, a special oversized lower plate (to increase any alignment errors and make them easier to correct) with a revolving micrometre attached to a measuring system shaft. These measurements are then used to adjust an alignment mechanism which is built in to every Kinexus cartridge to get the best possible alignment.
This all gets quite technical, but it basically means that with Kinexus we can minimise the gap error and minimise any corrections for a more accurate result. Alignment is still the physical limitation to any small gap measurement, and is usually corrected for by measuring a known viscosity sample at a few decreasing gaps. As detailed by Kravchuk and Stokes , this gap offset is more significant as the measurement gap decreases but can be accounted for.
Finally, consider the diameter of the plate. For the same angular velocity, at the same gap, the average shear rate the sample will see, increases linearly with upper plate diameter. Therefore to get the highest shear rate, use the largest plate. However, the larger the plate the greater the alignment errors so we need to find a balance. A 40mm plate is usually a good compromise and what I would typically use to get the best results.
One other bit of advice for these measurements; Kinexus cartridges all come with a thermal enclosure to maximise the temperature accuracy. However, for these high shear rate measurements this thermal enclosure can give another practical limitation, viscous heating, where heat generated within the sample cannot dissipate efficiently. Working without a thermal cover can therefore be useful BUT remember that centrifugal force limitation….Well, from experience, we also call the thermal enclosure the “shirt saver” ☺️ !