Physical Chemistry Third Edition

444 10 Transport Processes

10.2 Transport Processes

In a transport process, some quantity is transported from one place to another. The

principal transport processes are heat conduction, diffusion, and viscous flow. In heat

conduction, energy in the form of heat is transported. In diffusion, substances are

transported. In viscous flow, momentum is transported.

Variables to Specify the Rates of Transport Processes

The rates of nonequilibrium processes could be specified by time derivatives of inten-

sive variables, but other variables are customarily used. The rate of heat flow is cus-

tomarily specified by theheat flux, which is a vectorqin the direction of the flow of

heat and with magnitude equal to the quantity of heat in joules per square meter per

second passing through a plane perpendicular to the direction of heat flow. The rate of

diffusion of substanceiis specified by itsdiffusion flux, which is a vectorJithat has

the direction of the average velocity of the molecules of substanceiand a magnitude

equal to the net amount of the substance in moles per square meter per second passing

through a plane perpendicular to the direction of diffusion. In precise discussions of

diffusion one must specify whether the plane is stationary in the laboratory or is sta-

tionary with respect to the center of mass of a small portion of the fluid in the system,

etc. We will assume that our plane is stationary in the laboratory.

The rate of viscous flow is specified in a different way. Figure 10.1 shows an idealized

apparatus for the measurement of viscosity, which is the resistance of a fluid to shearing

flow. The fluid is confined between two large horizontal plates. The top plate is dragged

along parallel to its surface in theydirection, and the lower plate is fixed to a stationary

object with infinite mass. The moving plate puts a frictional force on the layer of fluid

next to it, transferring momentum to it, and this layer of fluid puts a frictional force on

another layer, transferring momentum to it, and so on. The momentum is eventually

transferred to the stationary object, which does not accelerate due to its infinite mass.

The speed of each layer is a little smaller than the speed of the layer that puts a force

on it, corresponding to a nonzero value to the rate of shear∂uy/∂z. In Figure 10.1,

arrows are used to indicate the magnitude of the flow velocity at different heights. This

kind of flow is calledlaminar flow(flow in layers). A flow that is not laminar is called

turbulent flow. We do not attempt to discuss turbulent flow. Although we could use

the momentum flux as a rate variable, it is customary to use as a rate variable the force

per unit area that must be exerted on the moving plate by an external agent to keep it

Movable plate

Stationary plate

Fluid

Force on plate

Fluid

velocity

vectors

Figure 10.1 An Idealized Viscosity Experiment.