Rheology

 

The term rheology from the Greek rheo (to flow) and logos (science), was suggest by Bingham and Crawford to describe the flow of liquids and the deformation of solids. Viscosity is an expression of the resistance of a fluid to flow, the higher the viscosity, the greater is resistance.

When classifying materials according to types of flow and deformation, it is customary to place them in one of two categories. Newtonian or non-Newtonian systems. The choice depends on whether or not their flow properties are in accordance with Newton’s law of flow.

Consider a ‘block’ of liquid consisting of parallel plates of molecules. If the bottom layer is fixed in place and the top plane of liquid is moved at a constant velocity, each lower layer will move with a velocity directly proportional to its distance from secondary bottom layer.

A block of liquid consisting of parallel plates of molecules

The difference of velocity, dv, between two planes of liquid separated by an infinitesimal distance, dr, is the velocity gradient or rate of shear, dv/dr. The force per unit area, F’/A, required to bring about flow is called the shearing stress and is given the symbol F.

 

Newtonian System

Newtonian was the first to study flow properties of liquid in a quantitative way. He recognized that the higher the viscosity of a liquid, the greater is the force per unit area (shearing stress) required to produce a certain rate of shear. Rate of shear is given the symbol G. Hence, rate of shear should be directly proportional to  shearing stress, or,

                 F'/A = n dv/dr

where, n is the coefficient of viscosity, usually referred to simply as viscosity. 

equation is frequently written as, 

            n= F/G

where F = F'/A, and G = dv/dr

A representative flow curve, or rheogram, obtain by plotting F versus G for a Newtonian system. As implied by equation, a straight line passing through the origin is obtained. 

                                           Rheogram for Newtonian flow system

The unit of viscosity is the poise, defined as the shearing force required to produce a velocity of 1cm/ sec between two parallel planes of liquid each 1cm2 in area and separated by a distance of 1 cm. 

The cgs units for poise are dyne sec cm-2 or g cm-1 sec-1. These units are readily obtained by a dimensional analysis of the viscosity coefficient. rearranging equation to ,

n = F'dr/Adv = dynes* cm/ cm2 * cm/sec = dyne sec/cm2 = g * cm/sec2 * sec /cm2 = g/cm sec