# Rheology in Pharmacy

Rheology is the study of flow properties of matter, which addresses the viscosity characteristics of solution and colloidal systems. In pharmacy, rheology primarily focuses on liquids and semisolids (e.g., creams, ointments, and gels).

Rheological properties are important considerations in the manufacturing, analysis, and use of several dosage forms, including solutions, emulsions, suspensions, pastes, lotions, suppositories, parenteral injectable drug products, and intravenous infusions.

In addition, viscosity is an important consideration as a critical material attribute (CMA) and critical (in-process) material attribute (CMA) for pharmaceutical manufacturing.

#### Newtonian and Non-Newtonian Flow (Newton's Law of Viscosity)

Depending on the flow characteristics, there are two general categories of materials - Newtonian and non-Newtonian. Newtonian flow is characterized by constant viscosity, regardless of the shear rates applied. Non-Newtonian flow is characterized by a change in viscosity characteristics with increasing shear rates. Non-Newtonian flow includes plastic, pseudo-plastic, and dilatant flow.

The Newton law of flow relates parallel layers of liquid: with the bottom layer fixed, when a force is placed on the top layer, the top plane moves at constant velocity, and each lower layer moves with a velocity directly proportional to its distance from the stationary bottom layer.

The velocity gradient, or rate of shear (dv/dr), is the difference of velocity dv between two planes of liquid separated by the distance dr. The force (F′/A) applied to the top layer that is required to result in flow (rate of shear, G) is called the shearing stress (F).The relationship can be expressed:

F′/A = η × (dv/dr)

Where η is the viscosity coefficient or viscosity. This relationship is often written:

η = F/G

Where,

F = F′/A and

G = dv/dr.

The higher the viscosity of a liquid, the greater the shearing stress required to produce a certain rate of shear. A plot of F versus G yields a rheogram. A Newtonian fluid will plot as a straight line with the slope of the line being η.

Non-Newtonian substances are those that fail to follow the Newton equation of flow. Example materials include colloidal solutions, emulsions, liquid suspensions, and ointments. There are three general types of non-Newtonian materials: plastic, pseudo-plastic, and dilatant.

The viscosity of non-Newtonian materials is determined using a viscometer capable of producing differing shear rates, measuring the shear stress, and plotting the results. Other types of flow not detailed here include thixotropic, antithixotropic, and rheopexic. Thixotropic flow is used to advantage in some pharmaceutical formulations. It is a reversible gel–sol transformation.

Upon setting, a network gel forms and provides a rigid matrix that will stabilize suspensions and gels. When stressed (by shaking), the matrix relaxes and forms a sol with the characteristics of a liquid dosage form for ease of use. All of these unique flow types can be characterized by studying their respective rheograms.

Reference: Ansel’s Pharmaceutical Dosage Forms and Drug Delivery Systems