What is Shear Rate and Why is it Important?

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Shear rate is the rate at which a fluid is sheared or “worked” during flow. In more technical terms, it is the rate at which fluid layers or laminae move past each other. Shear rate is determined by both the geometry and speed of the flow. If someone quickly rubs a very thin layer of ointment, cream, or lotion on the skin, for example, then the shear rate may be much higher than if that material is slowly squeezed out of its tube. Figure 1 shows an example of simple shear, in which one plate moves parallel to another.

Figure 1 – Example of simple shear, in which one plate moves parallel to another.

Viscosity is the resistance to flow. In this case, there is some friction between the layers. Therefore, as the upper plate moves with speed or velocity v₂ equal to V, cm/s, some of that motion is transferred downward from layer to layer, until the stationary plate is reached. The stationary plate has speed or velocity v₁ equal to zero. The distance between plates is x, cm. Therefore, the shear rate in this case is

 (1)

where ẏ is the shear rate, reciprocal seconds, denoted s^-1 or 1/s.

Figure 2 shows a force, F, dynes, applied to the top fluid layer. This is translated downward through the layers. The shear stress, τ, is the force per area, dynes/cm².

The viscosity, η, is the relationship between the shear stress and the shear rate.

(2)

Figure 2 – Simple shear between two parallel plates.

Simple liquids, at constant temperature and pressure (and without chemical reactions or phase changes occurring), have a constant viscosity. These are called Newtonian liquids. The viscosity remains constant with changing shear rate. However, most fluids are non-Newtonian, that is, their viscosities are a function of shear rate. Therefore, changing the geometry, such as the distance between the two plates, above, and/or the speed of flow, may significantly change the viscosity. We refer to the “apparent viscosity” or η_A in this case.

Shear rate is thus important because it may significantly affect the viscosity of many materials. This, in turn, must be considered when designing pumping, mixing, and spraying systems. It is important in designing various materials for consumer use, whether the products are pharmaceutical creams, ointments, or other. A high viscosity may help an ointment stay in place once it is applied, while a lower viscosity may help a cream spread more easily.

The pharmaceutical industry manufactures and tests a wide variety of commercially important products. Material behavior is often non-Newtonian. To reduce costs, many users try to test smaller quantities of materials. Cone-plate or cone-and-plate geometry may be used in this case, because it provides welldefined shear rates and typically requires small sample amounts. Figure 3 shows a cone-plate rheometer.

Figure 3 – Left: cone-plate rheometer. Right: sample cup and cone spindle, with Vernier dial for gap-setting.

A pharmaceutical cream and ointment were tested using the HBDV3TCP rheometer, with the CPA-40Z cone spindle and CPA-44PYZ sample cup (AMETEK Brookfield, Middleboro, MA). This particular geometry requires only 0.5 mL of sample. The sample cup’s water jacket was connected to a bath to maintain the proper experimental temperature. All experiments were run at conditions ensuring on-scale readings. Since the ointment was far more viscous than the cream, slower speeds—lower shear rates—were used, given the instrument’s spring torque range and the cone used.

Figure 4 presents data for the above samples. The cream data are in red, while the ointment data are in blue.

Figure 4 – Pharmaceutical cream (red) and ointment (blue); apparent viscosity, cP, versus shear rate, s-1, at 25 °C.

The apparent viscosity of each sample decreases greatly with increasing shear rate. Viscosity increases as the shear rate decreases again, but to values less than those measured in the initial, increasing-rate ramp. This response is thixotropy. Structure in the material breaks down over time and needs time to recover. The non-Newtonian behavior, in these cases, is useful—the viscosity decreases as the materials are rubbed on the skin, for example, easing application. Stopping the rubbing, and ceasing the shearing, allows the viscosity to increase, helping the ointment or cream to stay on the area.

Some pharmaceutical customers use the multispeed or “speed ramp” tests as an initial R&D tool. A simpler procedure may then be provided to the QA/QC lab. One example is the use of cone-plate geometry to test a sample at one speed, waiting a few minutes before taking the data point. Shearing the material for some time helps to break down the structure; the viscosity readings decrease and then plateau after some time. Therefore, more consistent readings may be taken from sample to sample, after a suitable shearing time. Representative data are shown for the ointment in Figure 5. The data show that the viscosity plateaus within about 2 minutes for this material. Therefore, an appropriate, single-point QC test may be to shear each ointment sample at 1 rpm for 2 minutes before recording a reading.

Figure 5 – Thixotropy: apparent viscosity, cP, decreasing with increasing time, minutes, at a constant speed of 1 rpm for a pharmaceutical ointment at 25 °C.

Conclusion

Shear rate is important because it may significantly affect the viscosity and therefore the processability and applicability of various materials. In the example given here, higher shear rates during rubbing result in lower viscosities and thereby allow ointments and creams to be more easily spread by the user.

Stopping the rubbing, equivalent to a very low or essentially “zero” shear rate, allows the material to recover to a higher viscosity, and helps ensure the product will stay on the skin. Viscosity measurements at various shear rates help quantify similarities or differences between various pharmaceutical ointments and creams, for example. The cone-plate rheometer provides a convenient tool for testing small amounts of pharmaceutical products at different shear rates. Proper equipment selection may allow significantly different materials to be tested with one instrument and geometry, merely by changing the testing speed or shear rate.

David Moonay is sales engineer, rheology laboratory supervisor, AMETEK Brookfield, Instrumentation & Specialty Controls Division, 11 Commerce Blvd., Middleboro, MA 02346, U.S.A.; tel.: 800-628-8139/508-946-6200; e-mail: [email protected]; www.brookfieldengineering.com