When the rate of shear is progressively increased and plotted against the resulting shear stress, various types of behaviors can be observed. One might assume that if the rate of shear were reduced after reaching the desired maximum, the downcurve would match the upcurve. In other words, the downcurve would be identical to and superimposable on the upcurve. While this is true for Newtonian systems, the downcurve for non-Newtonian systems can be displaced relative to the upcurve. In shear-thinning systems (also known as pseudoplastic systems), the downcurve is often displaced to the left of the upcurve. This indicates that the material has a lower consistency at any given rate of shear on the downcurve compared to the upcurve. This behavior suggests a breakdown of structure, resulting in shear thinning. The structure does not immediately reform when the stress is removed or reduced. This phenomenon is known as thixotropy.

Thixotropy can be defined as “an isothermal and comparatively slow recovery, on standing, of a consistency lost through shearing.” As defined, thixotropy applies only to shear-thinning systems. Typical rheograms for plastic and pseudoplastic systems exhibit this behavior (Fig.1).

# Description Thixotropic Behavior

Thixotropic systems usually consist of asymmetric particles that form a loose three-dimensional network within the sample through numerous points of contact. At rest, this network imparts some rigidity to the system, making it resemble a gel. When shear is applied and flow begins, this structure breaks down as contact points are disrupted and particles align. This leads to a gel-to-sol transformation and shear thinning. Once the stress is removed, the structure begins to reform. This is a gradual process as particles come into contact through random Brownian motion.

Rheograms of thixotropic materials depend heavily on the rate of shear increase or decrease and the duration at any given shear rate. The sample’s previous shear history significantly influences its rheologic properties. For instance, if the shear rate is increased from point a to point b and then decreased back to point e, it typically forms a hysteresis loop abe. If the shear rate is held constant at point b for a time (t1 seconds), the consistency decreases. This decrease depends on the shear rate and duration. As a result, a different loop, abce, forms when the shear rate decreases.

Holding the shear rate constant for a longer period (t2 seconds) would produce loop abcde. Thus, the rheogram of a thixotropic material is not unique and depends on the sample’s rheologic history and the method used to obtain the rheogram, which is crucial for quantitative measurement of thixotropy.

## Measurement of Thixotropy

Quantitative measurement of thixotropy can be approached in several ways. The most notable characteristic of a thixotropic system is the hysteresis loop formed by the upcurves and downcurves of the rheogram. The area within this hysteresis loop has been proposed as a measure of thixotropic breakdown. This area can be easily obtained using a planimeter or other suitable techniques. For plastic (Bingham) bodies, two common methods are used to estimate the degree of thixotropy.

### The First Method to Estimate the Degree of Thixotropy

The first method involves determining structural breakdown over time at a constant rate of shear. The required rheogram for this estimation is shown in (Fig. 2), and the steps to obtain it have already been described. From this rheogram, a thixotropic coefficient, B, representing the rate of breakdown with time at a constant shear rate, is calculated as follows:

$$ B=\frac{U_1-U_2}{\ln({\displaystyle\frac{t_2}{t_1}})} $$

where U1 and U2 are the plastic viscosities of the two downcurves after shearing at a constant rate for t1 and t2 seconds, respectively. The choice of shear rate is arbitrary. A more meaningful, though time-consuming, method for characterizing thixotropic behavior involves measuring the fall in stress over time at several shear rates.

### The Second Method to Estimate the Degree of Thixotropy

The second approach is to determine the structural breakdown due to increasing shear rate. This method is illustrated in (Fig.3), where two hysteresis loops are obtained with different maximum shear rates, v1 and v2. In this case, a thixotropic coefficient, M, which represents the loss in shearing stress per unit increase in shear rate, is calculated as follows:

$$ M=\frac{U_1-U_2}{\ln({\displaystyle\frac{v_2}{v_1}})} $$

where M is in dynes sec/cm², and U1 and U2 are the plastic viscosities for two separate downcurves with maximum shearing rates of v1 and v2, respectively. One criticism of this technique is that the rates of shear, v1 and v2, are chosen arbitrarily. The value of M will depend on these selected shear rates because they influence the downcurves and, consequently, the calculated values of U.

**Reference**:

- Sinko, P. (2011). Martin’s Physical Pharmacy and Pharmaceutical Sciences. Baltimore, : Lippincott Williams & Wilkins, a Wolters Kluwer business.