Answer to the quiz question at PolymerProcessing.com

Answer to the September 15, 2000 Question

The Incompressibility Assumption

Perspective Meter:

In the analysis of polymer processing operations it is commonly assumed that polymer melts are incompressible, meaning that the density is constant independent of temperature and pressure. This considerably simplifies the calculation of velocity fields, flow rates, temperature distributions, etc. Whether or not it is appropriate to assume incompressibility depends, of course, on how much inaccuracy you are willing to tolerate.

The dependence of polymer melt densities on pressure and temperature are reasonably well known and this allows for a quick estimation of the error associated with the incompressibility assumption. Two excellent sources of information include Properties of Polymers by D.W. van Krevelen [Elsevier, New York, pp. 88-106 (1997)] and Polymer Handbook [John Wiley & Sons, New York, 4th Ed., pp. VI591-601 (1999)]. These references both provide the relevant PVT relationships and equations of state, including thermal expansion coefficients and compressibilities.

As an example, consider the compressibility of a polymer melt. Typical melt densities for many polymers are approximately 1000 kg/m3 (1 g/cm3). In addition, a reasonably representative change in density for a given change in pressure for a polymer melt is:

The pressure encountered by the melt in a process varies substantially from atmospheric to about 1.0E+7 N/m2 (1500 psi) in profile extrusion to in excess of 1.0E+8 N/m2 (15,000psi) in injection molding. The error associated with assuming incompressibility can be easily quantified by:

The errors can thus be summarized as:

delta P (psi)	% error	representative process
10	0.003 %	thermoforming
1000	0.3 %	profile extrusion
10,000	3.4 %	injection molding

Thus, in general the incompressibility assumption is good for low pressure processes; but probably not accurate for high pressure processes like injection molding.

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