Introduction to Transport Coefficients

There are a number of excellent references on transport properties, for example, by Hirsch-felder, Curtiss, and Bird [178], Bird, Stewart, and Lightfoot [35], and Reid, Prausnitz, and Poling [332], In addition to providing theoretical background, these references also give tabulated values of transport properties of many chemical compounds. The best of source of transport property data is probably the NASA Technical Report by Svehla [389]. 

An experiment to measure the viscosity of a fluid is shown schematically in Fig. 12.1. In this experiment the fluid is confined between two parallel plates. The bottom plate is held stationary, and the top plate, at a distance a away in the z direction, moves at constant velocity U in the x direction. The thin layer of fluid adjacent to each wall assumes the velocity of that wall that is, the gas at height z = 0 has zero velocity, and the layer of gas at z — a moves with x velocity u = U. At steady state, a linear velocity profile is set up across the gas, with the upper and lower limits just mentioned. Therefore the velocity gradient du/dz has the value Ula across the channel. It is found that that the force required to maintain the constant velocity of the upper plate is proportional to the area of the plates and the velocity U, and is inversely proportional to the separation a. Thus the retarding force of the fluid per unit area (of the plates) is proportional to the velocity gradient du/dz  

Upper plate moves with constant velocity, U 

As a layer of gas at one velocity is pulled across an adjacent layer of gas at a slightly different velocity, gas in the faster layer tends to be slowed down by the interaction, and gas in the faster layer tends to speed up. There is velocity or, more precisely, momentum transfer between the layers. Thus it takes a force to maintain the velocity gradient across the fluid. (Recall the definition that force is the time rate of change of momentum.) Fundamentally, the viscosity is a transport property associated with momentum transfer. 

Viscosities for liquids and gases vary with temperature, although in functionally different ways. Except for very high pressures, viscosity varies weakly with pressure, and the pressure dependence is often neglected. These variations are discussed later in the chapter. 

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