When comparing simulation results to measurements it is important to understand whether pressure or number density is the relevant quantity to compare. In the vacuum industry it is common to use the ideal gas law to relate the pressure, p, to the number density, n:

where kB is the Boltzmann constant, and T is the absolute temperature. Equation 2-1 is not rigorously true in a molecular flow. The derivation of the ideal gas law assumes that molecules arrive at a surface from random directions (at high pressure this is true because of collisions between the molecules). Provided highly directional effects such as molecular beaming are absent from a molecular flow, Equation 2-1 holds approximately in many circumstances (it is possible, for example, to compare the pressure with nkBT in some of the model examples and often the two values are within 10% of each other). A counterexample that demonstrates when this relationship completely fails is provided by the Rotating Plate example in the Molecular Flow Module’s Applications Libraries.

COMSOL Multiphysics defines pressure as the normal force acting on a surface and number density as the number of molecules per unit volume. Unfortunately it is common practice in the vacuum industry to lump both of these quantities together under the concept of pressure. Many vacuum gauges that operate at low pressures actually measure number density (in the COMSOL Multiphysics sense) but are calibrated to give readings in units of pressure. For these gauges it is appropriate to compare the quantity nkBT from a simulation with the pressure that the gauge reads.

A practicing engineer needs to answer the question: “Does my gauge actually measure pressure or number density?”. Ref. 2 discusses how the common types of vacuum gauge operate and classifies gauges as direct or indirect. Direct gauges usually measure the displacement of a wall, which is directly related to the pressure in a COMSOL Multiphysics simulation. Indirect gauges measure the “pressure” indirectly, via a gas property. Many indirect gauges are so-called ionization gauges, in which the gas is ionized by some mechanism, and the ion current generated by an electric field is measured. For these gauges, the quantity nkBT is appropriate for comparison with experimental gauge readings. Other indirect gauges operate on other principles that make it harder to associate them with either a pressure or a number density directly. For example, Pirani and thermocouple gauges measure the heat loss from a wire in the gas. Although this process could be modeled in detail by the Free Molecular Flow interface, it is often more practical to exercise engineering judgment when comparing simulation results with data from these types of gauges. Table 2-1 classifies common vacuum gauges in terms of the quantity they measure.