**4. Two dimensional flow problem**

### **4.1 Calculation model for 2D flow**

On the basis of the results described in the previous section, we have proposed a new method for the direct generation of monodisperse nanoparticles. This method makes use of interaction phenomena between the plume and shock wave arising in an ellipsoidal cell following laser ablation in ambient gas. The method is based on the hypothesis that monodisperse nanoparticles are instantaneously formed inside a narrow region constructed from a diffusion mixture of vapor and ambient gas during the interaction between a plume and shock wave. Such a region forms at one focal point of the ellipsoidal cell, while the plume is ejected from the other focal point with laser irradiation being accompanied by shock waves. Here, the ellipsoidal cell is used as an experimental device based on this principle to obtain uniformly sized nanoparticles, which does not require an additional size classifier like a differential mobility analyzer (Camata, R. P., 1996), and therefore is expected to show high efficiency (Iwata, Y., 2002).

The basic idea of the proposed device, illustrated in Figure 6, is as follows: the target material is exposed to a high-power pulsed laser; the ablated vapor suddenly expands due to high temperature; the expansion results in a propagating shock wave (Figure 6(a)); the vapor is fed by the ablation process for a period of the exposure of the pulse laser; the plume propagates toward the cell exit (Figure 6(b)); the ablation stops after a short duration, while the shock wave and the plume continue to propagate and start to interact (Figures 6(b) and 6(c)); and after the complex interaction between them, the monodispersed nanoparticles are produced and extracted through the cell exit (Figure 6(d)). During the interaction, it is important for the nanoparticles to grow to a certain size.

To investigate the effect of this new model, 2D calculations were performed. For the governing equations, we have chosen the axisymmetric, two-dimensional, compressible Navier–Stokes equations, because the experiments showed that the laser-ablated plume travels straight toward the cell exit with no distortion. The equations are solved by a finite

Fig. 5. Influence of distance between target and wall on nanoparticle growth. The circles

On the basis of the results described in the previous section, we have proposed a new method for the direct generation of monodisperse nanoparticles. This method makes use of interaction phenomena between the plume and shock wave arising in an ellipsoidal cell following laser ablation in ambient gas. The method is based on the hypothesis that monodisperse nanoparticles are instantaneously formed inside a narrow region constructed from a diffusion mixture of vapor and ambient gas during the interaction between a plume and shock wave. Such a region forms at one focal point of the ellipsoidal cell, while the plume is ejected from the other focal point with laser irradiation being accompanied by shock waves. Here, the ellipsoidal cell is used as an experimental device based on this principle to obtain uniformly sized nanoparticles, which does not require an additional size classifier like a differential mobility analyzer (Camata, R. P., 1996), and therefore is expected

The basic idea of the proposed device, illustrated in Figure 6, is as follows: the target material is exposed to a high-power pulsed laser; the ablated vapor suddenly expands due to high temperature; the expansion results in a propagating shock wave (Figure 6(a)); the vapor is fed by the ablation process for a period of the exposure of the pulse laser; the plume propagates toward the cell exit (Figure 6(b)); the ablation stops after a short duration, while the shock wave and the plume continue to propagate and start to interact (Figures 6(b) and 6(c)); and after the complex interaction between them, the monodispersed nanoparticles are produced and extracted through the cell exit (Figure 6(d)). During the interaction, it is

To investigate the effect of this new model, 2D calculations were performed. For the governing equations, we have chosen the axisymmetric, two-dimensional, compressible Navier–Stokes equations, because the experiments showed that the laser-ablated plume travels straight toward the cell exit with no distortion. The equations are solved by a finite

indicate the arrival time of the shock wave.

**4. Two dimensional flow problem** 

to show high efficiency (Iwata, Y., 2002).

important for the nanoparticles to grow to a certain size.

**4.1 Calculation model for 2D flow** 

volume method using the MUSCL-type total variation diminishing (TVD) scheme with a curvilinear generalized coordinate (Yaga, M., 2005, 2008; Fukuoka, F., 2008)

Fig. 6. Behavior of plume and shock wave in an ellipsoidal cell.
