Non-Newtonian Fluid Systems

When we think of common liquids like water or honey, we are dealing with Newtonian fluids, where viscosity remains constant regardless of the force (shear rate) applied. However, a vast and complex group of materials—including most pharmaceutical, cosmetic, and food products—are Non-Newtonian fluids.

A Non-Newtonian fluid is one that does not follow Newton's law of viscosity. In these systems, the relationship between applied shear stress and the resulting strain rate (rate of flow) is non-linear and can even be time-dependent. This means their viscosity is not a single constant value but changes with how vigorously they are handled.

Non-Newtonian systems are broadly classified into Time-Independent (viscosity depends only on the shear rate) and Time-Dependent (viscosity depends on both shear rate and the duration of shearing) flow behaviors.

⏳ Time-Independent Non-Newtonian Flow

These systems show three main types of behavior, classified by how their viscosity changes as the shear rate is increased.

1. Plastic Flow (Bingham Bodies)

Materials exhibiting plastic flow are known as Bingham Bodies.

Yield Value ( $f$ ): A Bingham body does not begin to flow until a specific minimum shear stress, called the yield value ( $f$ ), is exceeded. At stresses below this value, the substance acts as an elastic solid.
Flow Curve: The flow curve does not pass through the origin; rather, it intersects the shear stress axis at the yield value.
Equation: Once flowing, the relationship is described by the Plastic Viscosity (U):

U = \frac{F - f}{G}

Where F is the shear stress and G is the strain rate.

Examples: Highly flocculated suspensions, such as some concentrated paint or toothpaste.

2. Pseudoplastic Flow (Shear-Thinning)

Pseudoplastic fluids are the most common type of Non-Newtonian system in pharmacy.

Behavior: The apparent viscosity decreases with an increasing rate of shear. This is why they are often called shear-thinning systems.
Flow Curve: The consistency curve starts at the origin (no yield value).
Mechanism: As shearing stress increases, large, randomly arranged molecules (like polymers) begin to align their long axes in the direction of flow. This alignment reduces internal resistance, allowing them to flow more easily at higher forces.
Examples: Natural and synthetic gums (Tragacanth, Methylcellulose), polymer solutions, and common fluids like blood and milk.

3. Dilatant Flow (Shear-Thickening)

Dilatant systems are the opposite of pseudoplastic systems.

Behavior: They exhibit an increase in resistance to flow (viscosity increases) with increasing rates of shear. They are called shear-thickening systems.
Mechanism: These systems typically consist of suspensions with a high concentration (around 50% or greater) of small, deflocculated solids. At low shear, the small particles are efficiently packed with minimal void volume. When high stress is applied, the compact arrangement breaks up, increasing the void volume and causing the system to increase in volume (dilate). The limited vehicle is insufficient to lubricate the now-disorganized, tightly packed particles, dramatically increasing resistance.
Examples: Cornstarch and water mixtures (Oobleck), wet sand, and some high-concentration ceramic suspensions.

⏱️ Time-Dependent Non-Newtonian Flow: Thixotropy

Thixotropy is a crucial time-dependent flow property observed only in shear-thinning systems (Plastic and Pseudoplastic).

Definition: Thixotropy is the isothermal and comparatively slow recovery, on standing, of a consistency (viscosity) lost through shearing.
Mechanism: When a thixotropic material is sheared (e.g., shaken), its internal structure breaks down, and viscosity decreases (shear-thinning). When the shearing stops, the material slowly rebuilds its structure over time, and its viscosity returns to its original high value.
Pharmaceutical Application: This property is highly desirable in pharmaceutical formulations like suspensions and emulsions for topical or oral use:

High Viscosity at Rest: Ensures stability and prevents sedimentation during storage.
Low Viscosity Upon Shaking/Pouring: Allows for easy pouring and administration (controlled drug delivery).