**High Knudsen Number Flow — Optical Diagnostic Techniques**

Tomohide Niimi

**1. Introduction**

Along with the development in micro‐ and nano‐technology with small characteristic length and high technology under high vacuum environments, it has been strongly desired to understand thermo‐fluid phenomena around a micro‐ and nano‐system such as a magnetic head slider of hard disk drive, micro thruster for micro satellite, semiconductor thin film fabrication system and so on. In cases where the characteristic dimension of the flow is of the order of the mean free path (about 60 nm at the atmospheric condition), we have to analyze the flows at the atomic or molecular level, because the continuum approach becomes invalid. The atomic or molecular gas flow had been used synonymously with the rarefied gas flow so far, but has to be applied also to the flow around the micro‐ and nano‐devices working under atmospheric conditions as mentioned above. We call these flows with large *Kn* ʺHigh Knudsen numberflowsʹʹ.As an indicator ofrarefaction of gas‐flows,the Knudsen number(*Kn*)is defined by the ratio of the mean free path (*λ*) divided by the characteristic dimension (*L*) of the flow. The flow regimes are classified on a scale of *Kn* number, as follows.

**•** *Kn* < 10‐<sup>3</sup> : *Continuum flow regime*

Compressible Navier‐Stokes equation with no‐slip boundary condition

**•** 10‐<sup>3</sup> < *Kn* < 10‐<sup>1</sup> : *Slip flow regime*

Compressible Navier‐Stokes equation with velocity slip and temperature jump at the boundary

**•** 10‐<sup>1</sup> < *Kn* < 10: *Transition flow regime*

Boltzmann equation, where intermolecular collisions should be taken into account

© 2013 Niimi; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Niimi; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **•** 10 < *Kn*: *Free molecular flow regime*

Boltzmann equation, where intermolecular collisions are negligible compared with inter‐ actions between the gas molecules and the walls

For high Knudsen number flows, we have to take into account the followings that may be neglected for the continuum flow regime. In the case of large *λ*, there appear the strong nonequilibrium phenomena because of few intermolecular collisions. For extremely small *L*, on the other hand, the flow field is strongly influenced by interaction of molecules with a solid boundary rather than intermolecular collisions.

Experimental analyses of thermo‐fluid phenomena related to the high Knudsen numberflows need the optical diagnostic techniques based on atoms or molecules, such as their emission and absorption of photons. However, the experimental techniques are behind on development compared with the molecular simulation techniques such as the molecular dynamic method (MD), the direct simulation Monte‐Carlo method (DSMC) and so on.

**Figure 1.** Principle of LIF

**Figure 2.** Supersonic free jet visualized by I2-LIF [1]

High Knudsen Number Flow — Optical Diagnostic Techniques 35

**Figure 3.** Interacting supersonic free jets visualized by I2-LIF [2]

In this chapter, the optical diagnostic techniques for the high Knudsen number flows are mainly described, such as laser induced fluorescence (LIF), resonantly enhanced multiphoton ionization (REMPI) and pressure‐sensitive molecular film (PSMF), and some experimental results obtained by the use of the techniques, i.e., applications of LIF to visualization ofrarefied gas flows including complicated shock wave system and to measurement of rotational temperature, establishment of a REMPI system and its application to detection of rotational nonequilibrium in highly rarefied gas flows, and development of the PSMF for micro gas flow measurements.
