Predicting material flow behavior involves testing the substance over a range of shear rates relevant to how it is processed in manufacturing or how it is used by the consumer. Ointments, for example, coat human body parts like skin, scalp, hair, lips, eyeballs, and finger/toe nails. The coating action, once applied to the surface, spreads the ointment as it is rubbed into place. Relevant viscosity tests employ shear rates that mimic this type of spreading action.
Shear rate is explained in Figure 1 as the velocity of whatever causes the spreading action divided by the thickness of ointment layer that gets deposited. Numerical values ranging from 50 to 5,000 sec-1 represent the spectrum of shear rate values to consider when devising tests to evaluate flow behavior.
Squeezing the ointment out of the tube is another type of flow behavior that should be tested for acceptable performance. The unfortunate situation that we are all familiar with is not being able to get the ointment out of the tube, no matter how hard you squeeze. Quantifying this behavior requires a test measurement known as “yield stress” determination. It establishes the amount of force needed to initiate flow of material out of the tube.
Another common problem is watching the ointment squirt out so fast that half the tube is empty before you realize what’s happening. This indicates that there is insufficient thickening agent in the formulation to give the ointment enough “body” to prevent flow behavior similar to that of a pourable liquid.
Worth noting is recent focus by pharmaceutical marketing departments on product packaging to make sure that the customer experience is acceptable in all respects. This includes providing user friendly tubes that open easily and expel controlled amounts of ointment that fall in line with recommendations of the physician.
Figure 2 shows the type of instrument known as the “cone/plate rheometer,” which is typically used by R&D to characterize flow behavior of ointments. Test material is placed on the flat metal plate and cone spindle is brought down into contact with the ointment, causing a spreading action. Sample material flows out to the circumference of the cone spindle and perhaps beyond if there is too much sample volume. Excess material is removed and the instrument is ready to run tests.
Cone spindles look like they have a flat bottom, but there is a slight angle between 0.5 and 2 degrees relative to horizontal. Because the geometry is precisely defined and there is a known “gap” between the sample plate and rotating surface of spindle, shear rate and shear stress values are calculated using the equations in Figure 3. These equations, embedded in the instrument firmware, allow the operator to run tests that mimic human actions for spreading ointment with shear rates that range from 50 to 5,000 sec-1.
Measuring yield stress can be accomplished by one of two methods. The first is to gradually increase the torque applied to the spindle until rotational movement is detected. The torque value at which rotation commences is called the “yield stress.” The second is to run a shear rate ramp from a low rotational speed to a high speed, then use a math model to find a best fit line through the shear stress vs. shear rate data.
The point of intersection for the best fit line with zero shear rate is the yield stress, because there is no flow movement at this shear rate value. Numerical values for yield stress measured in scientific units of Pascals (Pa) correlate with the squeezing force on the tube required to initiate ointment flow.
Figure 4 shows graphical data for a yield stress test using the first method, with controlled torque or stress applied by the instrument in Figure 1. Shear rate is plotted on the y-axis, shear stress on the x-axis. The instrument runs in controlled torque mode and applies gradually increasing torque to the cone spindle in contact with the ointment sample on the temperature controlled plate. Note that shear rate values are zero until shear stress is slightly below 100 Pa.
Shear rate gradually increases as shear stress ramps from 100 to 200 Pa. Then shear rate increases rapidly, indicating that the ointment is starting to flow readily. If this test becomes the QC method, then it is likely that R&D would specify 100 to 200 Pa for the expected range in which flow would start. Any yield stress values outside this range determine that the ointment is too thin or too thick respectively.
If the second method were used, shear stress vs. shear rate data may be analyzed by the Herschel-Bulkley math model, for example. The yield stress value obtained from this approach would be the best fit line thru the log-log plot of shear stress vs. shear rate data. Intersection of the line with the [shear stress] y-axis would be the yield stress value, which may be similar to or differ somewhat from the value obtained in the first method.
Viscosity “flow curves” are generated by testing the ointment over a range of shear rates, using the shear rate ramp mentioned above. Typical flow behavior for ointments exhibits very high viscosity values at low shear rates and decreasing viscosity values as the shear rate increases. “Pseudoplastic,” or “shear thinning,” is the term used to describe this phenomenon.
Figure 5 shows a viscosity flow curve for a commercially available ointment on a log-log plot of viscosity vs. shear rate. Below 10 sec-1 in shear rate, viscosity is around 10 Pa·s, which is equivalent to 10,000 cP. As shear rate increases to 10,000 sec-1, viscosity reduces to almost 0.1 Pa·s, or 100 cP. The observation is that viscosity reduces dramatically with increasing shear rate.
This controlled stress rheometer, like the instrument shown in Figure 1, provides an advantage when performing these tests because it operates in both controlled shear stress (torque) mode as well as controlled shear rate (rotational speed) mode. The stress mode is especially advantageous when measuring highly viscous materials because the torque applied to the spindle is increased gradually until movement commences.
This is a preferred method for testing flow behavior to simulate the startup torque conditions on a pump motor when processing the ointment or the squeezing action needed to expel ointment from a tube. Should you consider this type of instrument for your laboratory, you will be impressed with not only the resulting data, but also the speed and efficiency with which the controlled stress instrument completes the testing.
About the Authors:
Robert. G. McGregor is Director, Global Marketing & High End Lab Instrument Sales, and David J. Moonay, Ph.D. is Sales Engineer, Rheology Laboratory Supervisor, at AMETEK Brookfield, Instrumentation & Specialty Controls Division., 11 Commerce Blvd., Middleboro, MA 02346; (508) 946-6200.