RHEOLOGY: Introduction, Concept of Viscosity & Newton's law of flow

 RHEOLOGY Part 1

Link for Video Demonstration, check YouTube 👇

https://youtu.be/06e-FOIXLqg

INTRODUCTION

Rheology is the science that concerns with the flow of liquids and the deformation of solids. Study of flow properties of liquids is important for pharmacists in the manufacturing of several dosage forms, viz., simple liquids, gels, ointments, creams and pastes. These systems change their flow behaviour when exposed to different stress conditions in the following situations:

(i) Manufacture of dosage form: Material undergo processes such as mixing, flowing through pipes, filling into the containers etc. Flow related changes influence the selection of mixing equipment. 

(ii) Handling of drugs for administration: The injectablility of the medicines, the pouring of the liquids from containers, extrusion behaviour of dosage forms. 

Thus, flow behaviour of liquids (on applying stress) is of great relevance in pharmacy. Performance of a product depends on the net effect of all the above mentioned processes. Therefore, flow properties are used as important quality control tools to maintain the superiority of the product and reduce batch to batch variations. For example, dextran 40 and dextran 110 injections are analysed by determining the viscosity ratios at 37°C (I.P).

CONCEPT OF VISCOSITY

Flow property of a simple liquid is expressed in terms of viscosity. Viscosity is an index of resistance of a liquid to flow. The higher the viscosity of a liquid, the greater is the resistance to flow. For example, coconut oil, honey, syrup all resist flow more in comparison to water or alcohol, thus pours slowly. On the molecular level, motion is transferred between molecules of a syrup at lower rate than for molecules of water.

NEWTON’S LAW OF FLOW

Consider a ‘block of liquid’ consisting of parallel layers of molecules, similar to a deck of cards as shown in figure. The bottom layer is considered to be fixed in place.

Fig 1: Pictorial representation of liquid at rest (a) and the changes produced on application of shear stress (b)

When force is applied horizontally on the top layer ‘A’, the liquid begins to flow. It assumes the shape shown in figure 1b. Arrows indicate the magnitude of flow velocity. Since force is applied on the top layer (A), it moves at greater velocity. While moving ahead, the first layer (A) induces flow in the second layer (B). The velocity of the second layer (B) is somewhat less than that of the first layer (A), because of the viscous drag offered by the third layer (C). Similarly, the velocity of the third layer (C) is less than that of the second layer (B), but higher than that of the fourth layer (D).This phenomena continue and the bottom layer (N) remain stationary. Thus, liquids resist flow when force is applied. This resistance is estimated and expressed as viscosity. 

When liquid flows through a pipe, under the conditions of streamline flow. Liquid layers that adhere to solid surfaces remain stationary. Other layers adjacent to the stationary layers move relative to it. This behaviour is pictorially represented below.

Mathematical derivation of viscosity

Shear stress is defined as the force per unit area, F’/A, which is applied to bring about the flow.

Shear stress, F= F’/A

Velocity gradient or rate of shear, dv/dr is defined as the change in the velocity, dv, with a change in distance, dr.

Rate of shear, G = dv/dr

Newton recognised that the higher the viscosity of a liquid, the greater the force per unit area (shearing stress) required to produce a certain rate shear.

The higher the viscosity of the liquid, the greater is the force per unit area required to produce a certain rate of shear. Hence, the relationship between shear stress and rate of shear is as follow:

Shear stress α rate of shear

F’/A α dv/dr

Or F’/A = ŋ dv/dr

Or F = ŋG ____eq.1

 In which ŋ is the coefficient of viscosity, and usually referred to as viscosity.

Or ŋ= F’/A  = F/G ____eq.2

                dv/dr

The basic unit of viscosity is poise (P) named after Jean Louis Marie poiseuille. Poise is defined as the shearing force (shear stress) required to maintain a relative velocity of 1cm/sec between two parallel planes, 1cm2 in area and 1cm apart. A more convenient unit for viscosity is the centipoises (cP) with 1cP being equal to 0.01 poise.

The centipoises is commonly used because water has a viscosity of 1.002 cP at 20°C.

The CGS unit for the poise are dyne sec cm-2 or gcm-1sec-1, while  the SI is units is Pascal-second (Pa-S)

1poise =100 centipoise =1 dyne sec cm-2 =1 gcm-1sec-1= 0.1 Pa-S