Semi-solid and liquid drug products display complex rheological behaviors, which have significant impact on patient compliance, product manufacturability and stability.
Aside from Ketchup or toothpaste, there are ample examples of semi-solid and liquid dosage forms where the rheology plays a delicate role in product characteristics. For instance, a medicated shampoo should be easily poured out of a bottle, nevertheless it needs to be viscous enough to stay in patient’s hand before application. It is crucial to understand and measure the rheological properties in order to design manufacturing processes to achieve desirable finished products.
What is Yield Point?
Yield point is an inherent property of a material which demonstrates the resistance to flow under stress owing to the microscopic structure of the material. In the shampoo example, yield point is the moment when the shampoo starts to move or flow, either by gravity force or hand squeeze.
Temperature, pressure, time scale, material relaxation and other factors can influence the measurement of yield point. For example, a product may lose its microscopic structure after repeated shaking or vibration due to transportation or usage. As a result, the yield point may change significantly compared to the unshaken product. For all practical purpose, yield point cannot be quantitatively measured. What can be measured is the yield stress and yield strain.
What is Yield Stress?
Yield stress is defined as the minimum shear stress exerted to the material to induce flow. Shear stress (σ, units of Pa) is the ratio of external force (F, units of N) to the applied area (A, unit of m²):
σ = F / A
Yield strain is the material deformation (or shear strain) resulting from the applied stress prior to the start of flow. Yield strain can be characterized as the relative change in the length of the material at the yield point.
Unlike the viscosity which is measured under a defined shear rate, both yield stress and yield strain (i.e. shear stress and shear strain at yield point at which the shear rate is essentially zero), are difficult to quantitatively measure using a simple viscometer.
Measurement of Yield Stress
There are many yield stress measurement methods, including stress ramp, dynamic stress, extrapolation of flow data, incremental creep test, etc. One of the easiest ways to determine the product yield stress/yield point is the stress ramp method. The stress ramp method applies a gradually increased shear stress to the material until the material flows. The method measures the torque value using a rheometer.
Either a vane spindle or cone-and-plate setup can be used. The test material is equilibrated at a constant temperature prior to testing. The resistance of the material to movement is measured by observing increasing torque values as the spindle or cone rotates. At the yield point, the material starts to flow and the torque value reaches maximum. The other commonly used method is extrapolation of flow curve. This can be achieved by measuring either shear stress or viscosity with gradually increased shear rate, i.e. increased spindle speed in a viscometer.
After plotting the flow curve using shear rate as the variable on x-axis and shear stress on the y-axis, one can obtain a good approximation of yield stress by measuring the y-intercept of the regression of this curve.
Without a sophisticated rheometer, a simple qualitative sliding method can be employed to have rapid comparison of yield point between different products, which are applied on a flat plate. Then the plate is tilted to increased angles. The products start sliding under gravity once angle reaches certain level. The difference of yield point can be quickly assessed with minimal cost and resource.
Practical Use of Yield Stress Determination
There are many practical data can be generated by studying product yield stress. A number of examples are listed as follows:
- Pourability: Yield stress will provide quantitative comparison among different formulations to assess the pourability. Some minute changes in formulation may have significant impact on pourability.
- Shaking and Vibration: Mechanical stress can have an immediate impact on the microstructure of a product. Testing the yield point and yield stress after
shaking or vibration provides a quick assessment on the effect of mechanical stress.
Relaxation and Recovery: A time scale study to repeatedly test yield point can determine how quickly the product restores to its original microstructure after it is put on rest.
Temperature: Higher the temperature, lower the yield stress. Typical application of temperature profile of yield stress will identify any possible increase or decrease within normal temperature range.
Determination of yield stress and yield point is an important part of product flow behavior and rheological properties. It provides a good understanding of product formulation, structure of the system, and application properties. Often, yield to flow is the first impression that a product conveys to the patient or user: a product may be considered good quality if it is properly dispensed from the bottle. With various instruments and technology available to product development, one should not yield to “Yield Stress”.