Discussion on measurement mechanism of pressure-sensitive paints

The pressure-sensitive paint (PSP) is a very useful tool to measure pressure distributions on surfaces. In general, a measured pressure distribution by the paint shows good agreement with that by pressure taps. The paint is considered to represent the thermodynamic pressure. Recently, the paint has been adopted to rarefied gas flows and micro/nanoflows, i.e. high Knudsen number regime, and exhibited feasibility of pressure measurement in wide range of flows. In this study, we have discussed the physical meaning of luminescent intensity emitted from the paint through high Knudsen number regime measurements. It is known that a pressure tap shows good agreement with surface pressure and not with thermodynamic pressure in this regime, because of the temperature jump. High Knudsen number flow is required to be treated as a molecular flow; thus we discussed the PSP measurement mechanism by the molecular kinetic theory. The pressure profile of PSP was examined by a DSMC numerical result, and it was verified that PSP indicates the surface pressure. The temperature sensitivity was also investigated analytically in detail in continuum flow regime to discuss the suggestion that "PSP measures pressure, not density" [H. Bell, E.T. Schairer, L.A. Hand, R.D. Mehta, Surface pressure measurements using luminescent coatings, Annu. Rev. Fluid Mech. 33 (2001) 155-206]. From these analyses, however, we suggest that PSP measures a number flux of oxygen molecules toward the surface. The effect of a macroscopic flow against PSP in high Knudsen number flow is also discussed.