Fluids are often regarded as continua in most treatments of heat and mass transfer in engineering. This treatment makes it possible to introduce the concept of fluid (liquid or gas) density at a point. On this basis, the mass density of a liquid, ρ, is simply the mass of a liquid contained in a macroscopic volume, whereas the amount-of-substance density, , represents the amount (number of moles) of a liquid contained in the same volume. The density of a liquid is a relatively strong function of temperature at constant pressure, but a relatively weak function of pressure at constant temperature. This is because, in the liquid phase, the molecules that comprise the liquid move around largely in the well region of the Van der Waals Forces between them. Thus, increases in molecular energy cause an expansion as the molecules stray further out into the relatively-weak attractive region of the potential. However, as the pressure is increased, the tendency for the molecules to be pushed further together is opposed by the strong repulsive forces between molecules.
A particularly simple Equation of State for the description of the density of liquids is due originally to van der Waals, expressed as:
which recognizes the existence of attractive forces between molecules at large distances and repulsive ones at short distances. As discussed under Density of Gases, the parameters a and b in this equation can be estimated from critical constants. However, this is not a particularly satisfactory method since it can lead to large errors.
For several pure fluids, empirical equations of state of very high accuracy are available. These equations have been fitted to a set of experimental data that have been critically evaluated and are thermodynamically consistent with other thermodynamic quantities [de Reuck and Craven (1993)]. For the majority of fluids, such equations are not available and one must then have recourse to methods of density estimation. These methods can be based upon refinements of the van der Waals equation of state, such as that due to Redlich and Kwong or Benedict, Webb and Rubin [Bett et al., (1975)]. However, all of these methods require a knowledge of some experimental information on the fluid in question. In the absence of such methods, entirely empirical procedures for the extraction of the liquid phase density, such as those listed by Reid et al. (1977), must be employed.
For liquid mixtures, it is sometimes sufficiently accurate for many purposes to assume that there is no volume of mixing, so that the density of the mixture can be written as:
where the are the amount-of-substance fractions. For systems with strong specific interactions, this is often a poor approximation and more sophisticated methods are required [Rowlinson and Swinton (1982)].
Bett. K. E., Rowlinson, J. S., and Saville, G. (1975) Thermodynamics for Chemical Engineers, Athlone Press, London.
de Reuck, K. M. and Craven, R. J. B. (1993) International Thermodynamic Tables of the Fluid State—12. Methanol, Blackwell Scientific, London.
Reid, R. C., Prausnitz, J. M., and Sherwood, T. C. (1977) The Properties of Gases and Liquids, 3rd ed., McGraw-Hill, New York.
Rowlinson, J. S. and Swinton, F. L. (1982) Liquids and Liquid Mixtures, 3rd ed., Butterworths, London.