**2. Laser Induced Fluorescence (LIF)**

Some atoms and molecules emit fluorescence when irradiated by a laser beam whose wave‐ length corresponds to an absorption line of molecules, as shown in Figure 1. In Figure 2 [1], LIF of iodine molecules (I2) seeded in argon gas was applied to visualization of a flow field of a supersonic free jet issued from a sonic nozzle with exit diameter of 0.5 mm into a vacuum chamber, clearly showing the barrel shock waves and Mach disk. Figure 3 shows an example of the visualization of complicated flowfield structure and shock wave systems of two interacting supersonic free jets [2] by using I2‐LIF. NO‐LIF has been also employed to visualize the low density high speed flows [3].

A method for planar measurement of rotational temperature using two‐line I2‐LIF was proposed forthe rarefied gas flows [4]. If the fluorescence intensities at a point in the flow field are designated by *F1* and *F2* when the iodine molecules in the rotational levels *Jʹʹ<sup>1</sup>* and *Jʹʹ<sup>2</sup>* are excited, respectively, the ratio *F1* / *F2* depends on rotational temperature and two rotational quantum numbers, *Jʹʹ<sup>1</sup>* and *Jʹʹ2*. Therefore, once two absorption lines are selected, the rotational temperature can be deduced from the ratio of the fluorescence intensities.

Figures 4 are typical images of a supersonic free jet visualized by the use of irradiation of laser beams with different wavelengths corresponding to the respective absorption lines. These

**Figure 1.** Principle of LIF

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

Biomedical Engineering

34

measurements.

actions between the gas molecules and the walls

boundary rather than intermolecular collisions.

**2. Laser Induced Fluorescence (LIF)**

the low density high speed flows [3].

(MD), the direct simulation Monte‐Carlo method (DSMC) and so on.

Boltzmann equation, where intermolecular collisions are negligible compared with inter‐

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

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

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

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

Some atoms and molecules emit fluorescence when irradiated by a laser beam whose wave‐ length corresponds to an absorption line of molecules, as shown in Figure 1. In Figure 2 [1], LIF of iodine molecules (I2) seeded in argon gas was applied to visualization of a flow field of a supersonic free jet issued from a sonic nozzle with exit diameter of 0.5 mm into a vacuum chamber, clearly showing the barrel shock waves and Mach disk. Figure 3 shows an example of the visualization of complicated flowfield structure and shock wave systems of two interacting supersonic free jets [2] by using I2‐LIF. NO‐LIF has been also employed to visualize

A method for planar measurement of rotational temperature using two‐line I2‐LIF was proposed forthe rarefied gas flows [4]. If the fluorescence intensities at a point in the flow field are designated by *F1* and *F2* when the iodine molecules in the rotational levels *Jʹʹ<sup>1</sup>* and *Jʹʹ<sup>2</sup>* are excited, respectively, the ratio *F1* / *F2* depends on rotational temperature and two rotational quantum numbers, *Jʹʹ<sup>1</sup>* and *Jʹʹ2*. Therefore, once two absorption lines are selected, the rotational

Figures 4 are typical images of a supersonic free jet visualized by the use of irradiation of laser beams with different wavelengths corresponding to the respective absorption lines. These

temperature can be deduced from the ratio of the fluorescence intensities.

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

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

images are obtained at the same pressure condition: source pressure *Ps* = 16kPa and back‐ ground pressure *Pb* = 100Pa. It can be seen that the fluorescence intensity distributions are very different, depending on the absorption lines. If using two images among them, we can deduce the temperature distribution two‐dimensionally as shown in Figure 5.

**3. Resonantly Enhanced Multi‐Photon Ionization (REMPI)**

free jet to detect the non‐Boltzmann distribution of the rotational levels.

to the resonant state (*a*<sup>1</sup>

**Figure 6.** (2+2) N2-REMPI process.

relevant processes. In this process, nitrogen molecules at the ground state (*X*<sup>1</sup>

To measure the rotational population in rarefied supersonic nitrogen free jets and finally to confirm the non‐Boltzmann distribution of the rotational levels experimentally, a REMPI (Resonantly Enhanced Multi‐Photon Ionization) method has been applied to detection of nitrogen ions directly as an ion current. REMPI is known to have high detection sensitivity, which allows obtaining the signal under the very low number density condition. Here the principle of REMPI is introduced and the (2+2) N2‐REMPI is applied to a supersonic nitrogen

Figure 6 depicts the schematic energy level diagram for (2+2) N2‐REMPI, illustrating the

by additionaltwo‐photon energy. Since four photons participate in this process,the ion current is proportional to the fourth power of laser flux in principle. However, when the laser flux is sufficiently high so that almost all the excited molecules are ionized, the ion current is proportional to square of laser flux, because the REMPI process reflects the two‐photon transition process from the ground to the resonant state. In other words, the REMPI spectrum reflects directly the rotational population in the ground state of neutral molecules, so the rotational temperature can be deduced from the REMPI spectra, provided that the flow is in equilibrium, that is, the rotational energy distribution follows the Boltzmann distribution.

The REMPI technique is applied to detection of the rotational non‐equilibrium in a nitrogen free‐molecular flow. All experiments are carried out in a vacuum chamber evacuated by a turbomolecular pump and a dry pump as a backing pump, allowing an oil‐free vacuum environment. Nitrogen gas is issued from a sonic nozzle with *D* = 0.50mm diameter, and expanded into the chamber. Stagnation temperature is kept at 293 K and source pressures P0 is set at 30 Torr (3.9 × 103 Pa) to 1 Torr (1.3 × 102 Pa). A Nd:YAG‐pumped dye laser operated

Π*g*) by two‐photon absorption. Then the excited molecules are ionized

*Σg* +

High Knudsen Number Flow — Optical Diagnostic Techniques 37

) are excited

**Figure 4.** Supersonic free jets visualized by I2-LIF with different wavelengths. P and R means P- and R-branches, respec‐ tively, and the number the rotational energy level [4].

**Figure 5.** Two-dimensional temperature distribution of a supersonic free jet [4].
