Physics for Geologists, Second edition

Stress and strain 91
Figure 9.1 Newton's concept of viscosity (seen in section). When the upper plate
moves relative to the lower, the lubricant between them is assumed
to have adhered to each plate, and to have sheared linearly between
them.
Coefficient of viscosity: absolute or dynamic viscosity
Consider a liquid between two closely-spaced parallel plates (Figure 9.1) of
which the top plate is moving with constant velocity, V, relative to the lower
plate. Fluid adheres to each plate. The velocity of the fluid against the upper
plate is V, while the fluid adhering to the lower plate does not move. Between
the two, it is reasonable to assume that successive layers slip relative to those
below and above it, so that the velocity is linearly distributed between the
two plates. This is Newton's concept of viscosity, and it is called newtonian
viscosity.
The coefficient of viscosity, q, is defined as the ratio of shear stress to the
rate of shear strain:
In words, the coefficient of viscosity is the tangential force per unit area that
maintains unit relative velocity between two parallel planes unit distance
apart.
The coefficient of viscosity is also known as absolute or dynamic viscosity.
The SI unit is newton second per square metre (N s rnp2). Other units are the
poise, P, which is grams per centimetre second (gcm-l s-l) in units of mass,
length and time or dynes second per square centimetre in units of force,
length and time. The poise is named after the French physician, J.-L.-M.
Poiseuille (1799-1869) whose interest in blood flow led to a beautiful series
of experiments on flow through small pipes.
If the viscosity remains constant throughout the fluid, and at different
strain rates, the fluid is said to be newtonian. Non-newtonian fluids are
those with variable viscosity.
Copyright 2002 by Richard E. Chapman