VISCOSITY. All bodies, whether solids, liquids or gases, oppose a resistance to deformation or relative displacement of portions of the body against one another. This resistance may be of different kinds; it may, for instance, increase as the velocity with which parallel planes a fixed distance apart are displaced relatively to each other increases, and in that case, which is of great importance in nature, it is said to be due to viscosity. The definition will become clearer when we consider the viscosity of liquids, which is readily observed and was the first in point of time to be investigated both mathe matically and experimentally.
The Viscosity of Liquids.— We imagine two indefinitely ex tended parallel plates A and B (fig. I) between which a liquid is contained, and keep plate A moving in its own plane with a constant velocity v, indicated by the length of the arrow, while plate B remains at rest. The liquid in contact with A moves with it, while that in contact with B stands still; as the velocity in the liquid changes continuously, we can imagine it to consist of thin sheets or laminae, each moving with the velocity indicated by the arrows in fig. I. A certain force must be applied to A to keep the velocity v constant, and Newton made the assumption that this force was proportional to the area of the plates and to the velocity with which adjoining laminae passed over each other, in other words to the velocity gradient, v/d. These assumptions are purely intuitive, but all subsequent investigations have fully con firmed them. Other things being equal, the force varies greatly in different liquids, and to make comparison possible, it is usual to state the force required per unit area to keep A moving with unit velocity when d = unit distance and the space between the plates is filled with a particular liquid; this quantity is called the coefficient of viscosity of the liquid. The units generally employed in physics for force, length and time are used to express viscosity coefficients, viz., the dyne, centimetre and second.
Two parallel plates with a liquid between them constitute an arrangement from which we can easily deduce a definition of the viscosity coefficient, but one which cannot be realized experi mentally. Arrangements are, however, possible which fulfil the essential condition that the liquid should behave as if it consisted of thin laminae each moving with a constant velocity—a type of motion which is, for that reason, called "laminar." We can, for instance, "roll up" the two parallel planes of fig. 1 into two concentric cylinders and rotate the outer one with constant velocity, while the inner one is at rest (fig. 3). Each circle in the ring of liquid then rotates with a constant velocity; the inner cylinder tends to follow the mo tion and from the torque exerted on it the coefficient of viscosity can be deduced.
Laminar motion is also set up when a liquid flows through a cylindrical tube of small bore and sufficient length, as long as the velocity does not exceed a cer tain limit. The liquid flows as if it consisted of thin concentric tubes, each moving with a con stant velocity which increases from the wall towards the axis (fig. 2). The coefficient of viscosity can be deduced from the dimensions of the tube and the quantity of liquid forced through it in unit time by a known pressure.
It is, finally, possible to determine the coefficient of viscosity of a liquid by observing the velocity with which a small sphere of known diameter and mass falls in it. It was shown by Stokes that a small sphere falling in a viscous medium soon attains a constant velocity (in a medium offering no resistance its velocity is uniformly accelerated) given by the following equation: in which the symbols mean: v the velocity of fall per second, r the radius of the sphere,p and p' the density of the sphere and of the liquid respectively, g the acceleration of gravity =98I and t the coefficient of viscosity. Other things being equal, the coefficient of viscosity and the velocity of fall are inversely proportional.