Replace the spoon with a cylinder of known size
A spoon brings its edges, the liquid surface and the cup walls into the measurement. Two concentric cylinders give the liquid a defined space. The inner bob rotates inside a stationary cup. Liquid at each solid surface follows that surface, so adjacent layers slide past one another across the annular gap. This relative motion is shear.
The motor holds a chosen speed. A sensor in the shaft measures torque, the turning moment needed to maintain that motion. In a spring instrument, an elastic connection between two parts of the shaft twists slightly, and sensors read their relative angle. Speed and torque answer separate questions: how fast is the bob turning, and how much turning effort does it require?
Sources: [2]
Compare resistance with deformation rate
A narrow gap puts the same change in surface velocity into a smaller distance. The liquid layers then slide past their neighbours more rapidly. Shear rate measures this velocity change across the fluid. Torque, together with the bob radius and wetted area, gives shear stress: tangential force per unit area. Viscosity compares stress with shear rate.
A Newtonian reference liquid supplies a useful first example. At a fixed temperature, within its Newtonian range, doubling the shear rate doubles the stress. The motor works harder, and the viscosity stays the same.
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Rising torque can accompany shear thinning
Imagine a fourfold increase in shear rate that produces only twice the stress. The torque rises, but stress divided by shear rate falls to half its earlier value. That behaviour is shear thinning. A graph of torque alone can conceal it because the speed is changing at the same time.
One speed cannot settle the question. Two liquids can require the same torque at a particular speed even if one is Newtonian and the other thins under shear. Their curves separate as the speed changes. Retaining a whole sweep reveals how resistance grows, instead of treating one turning effort as a complete description of the liquid.
Consider a bob with a radius of 12.5 millimetres, a cup with an inner radius of 13.5 millimetres and a wetted bob length of 40 millimetres. For a Newtonian reference viscosity of 0.1 pascal seconds at an angular speed of two radians per second, the ideal side-wall torque is about 110 micronewton metres. The inner-wall shear rate is about 28 per second. Double the speed and both quantities double. Their ratio still gives the same viscosity. These are calculated teaching values with end effects omitted.
A longer bob would also require more torque because more surface touches the liquid. That extra turning effort would appear even with the same liquid, speed and gap. The known radius and wetted length let the instrument convert the total torque into stress before comparing it with shear rate. Geometry is part of the measurement.
A wider annulus adds another complication. The stress falls from the inner cylinder toward the cup, and a non-Newtonian liquid redistributes the shear rate across that stress gradient. The usual Newtonian cylinder conversion then gives a nominal rate. Correcting the inner-wall rate requires a material model and measurements over a range of speeds.
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Keep calibration and temperature with the reading
The sensor initially reports an angle or a count. Viscosity appears after calibration and geometric conversion. An unloaded zero measurement and a reference liquid of known viscosity connect sensor counts to torque. The cylinder dimensions and reference temperature must accompany that calibration.
An increasing-speed sweep followed by a decreasing-speed sweep can reveal whether the material depends on its recent history. An instantaneous shear-thinning model retraces the same curve. Some real samples need time to rebuild an internal structure after shearing, so the two sweeps can separate. Sample preparation and resting time then matter to the measured result.
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A shallow cone makes shear nearly uniform
A cone and plate arrange the gap differently. Farther from the centre, the shallow cone moves faster and sits farther above the lower plate. At a small cone angle, these changes nearly compensate, so most of the sample experiences the same shear rate.
A real cone has a flattened tip with a known clearance. That central disc also contributes to the torque conversion. The sample must fill the gap to the defined outer edge for the measurement to correspond to that radius. A different cone angle or truncation belongs with the new calibration and result.
Sources: [1]