Aerodynamic focusing of 5–50 nm nanoparticles in air

Abstract

An aerodynamic lens consisting of several thin plate orifices has been widely used to focus 30–300 nm nanoparticles. However, there is a big challenge in focusing sub-30 nm particles in air mainly due to flow instability in the lens. Here, we propose a new design of the aerodynamic lens consisting of three converging–diverging orifices to resolve the challenge. Through a series of numerical simulation from single- to multi-lens, we determined a specific design for sub-optimal focusing of 5–100 nm aerosol particles while keeping the air flow stable and free of shock formation. The final multi-lens assembly was revealed to be quite successful.

Introduction

Aerodynamic focusing has been widely used to produce a tightly collimated nanoparticle beam in a variety of application fields, such as an efficient inlet for aerosol mass spectrometry (Cho & Lee, 2007; Huffman et al., 2005; Kane & Johnston, 2000; Lee, Cho, & Lee, 2008; Lee, Miller, Kittelson, & Zachariah, 2006; Lee, Park, & Zachariah, 2005; Noble & Prather, 2000) and material syntheses of three-dimensional microstructures (Akedo, Ichiki, Kikuchi, & Maeda, 1998), direct-write fabrication (Akhatov, HOey, Swenson, & Schultz, 2008), implantation of large metal ions (Carrol, Hall, Palmer, & Smith, 1998), and ultra-smooth thin films (Haberland et al., 1995). An aerodynamic lens (ADL) consisting of a series of thin-plate (T-P) orifices, first invented by Liu, Ziemann, Kittelson, & McMurry (1995a), Liu, Ziemann, Kittelson, & McMurry (1995b), has been extensively demonstrated to produce a narrower beam of particles in a wider size range with less transport loss than a capillary (Murphy & Sears, 1964) or a sonic/supersonic nozzle (Crujicic, Zhao, Tong, DeRosset, & Helfritch, 2004;.Jen, Pan, Li, Chen, & Cui, 2006; Rafreshi et al., 2002; Whalen, 1987).

Despite these great benefits, there is a big challenge in focusing sub-30 nm aerosol particles, mainly due to their small inertia and high diffusivity. In respect to growing significances of the sub-30 nm nuclei-mode aerosols such as their promising physico-chemical properties and adverse health effect (Lee et al., 2006), a need for an efficient ADL enabling to focus such small particles is rapidly growing too. The gas flow in the ADL is generally restricted to be continuum and subsonic for focusing the nanoparticles. Regarding these constraints, Wang, Kruis, and McMury (2005) suggested an inequality indicating a minimum focusable size of particles d_p,min as

$$d_p\ge \frac{8S{t}_0}{M{a}^{*}K{n}^{*}{\rho }_p}\left(1+\frac{\pi \alpha }{8}\right)\mu \sqrt{\frac{M}{R{T}_1\gamma }}=d_{p,\mathit{min}}\propto \frac{S{t}_0}{M{a}^{*}K{n}^{*}}\sqrt{M}$$

where the upper limit of Knudsen number Kn* was assumed to be 0.1 for the continuum regime, the optimal particle Stokes number St₀ ranged from 0.6 to 1.0 for the T-P orifice (Lee et al., 2008; Wang & McMury, 2006), the critical Mach number Ma* was proportional to the flow discharge coefficient across the T-P orifice C_d (≤0.6; refer to Wang, Kruis, et al. (2005) for the remaining un-described symbols that will not be used in the following).

They attempted to reduce the d_p,min by using a lighter carrier gas than air, i.e., reducing the molecular weight of carrier gas M in Eq. (1) and could moderately focus 5–50 nm aerosol particles with a minor change in design with respect to Liu et al. (1995a)'s one. To the best of our knowledge, this is the only available design for aerodynamically focusing sub-30 nm particles. It should be however noted that their promising design works only in He, not in air, mainly due to the constraint of the Mach number (Wang, Kruis, et al., 2005) and the requirement for minimizing flow instability induced by recirculation downstream of the orifice (Wang & McMury, 2006). Since it is impossible to replace the air with He for the environmental aerosols, there still remain a great need for a new design to focus such aerosols in air.

Thus returning to Eq. (1), we attempted to decrease the d_p,min by increasing the Ma* and decreasing the St₀. The constraint of the subsonic flow was originally suggested to prevent a shock formation between the orifices which degrades the focusing performance of the T-P orifice. (Wang, Kruis, et al., 2005) Of particular interest is to note that a converging–diverging (C–D) nozzle, well known in aerospace disciplines, has been designed for a shock-free operation even at supersonic flow. In comparison to the T-P orifice, the C–D orifice normally offers superior benefits, e.g., a minimal flow recirculation downstream of the orifice (Wang & McMury, 2006), much lesser pressure drop across the orifice, and the greater discharge coefficient C_d(∼1.0) (Whalen, 1987).

These benefits enable the C–D orifice to operate with the minimized flow instability at higher Ma. For this reason, it is in principle expected that the d_p,min can be reduced below 10 nm (see Eq. (1)). However, the diverging part of the C–D orifice might increase the length of lens system as well as the residence time of particles, which gives rise to a greater diffusive broadening of particle beam. To circumvent this possibility, the length of C–D orifice should be minimized under the constraints to remain gas flow stable and shock-free. We first show the differences in aspects of flow instability and shock formation when flowing air across the C–D and T-P orifices. We then introduce geometric designing factors of a single C–D orifice and their effects on aerosol focusing. Next we prove this idea with an example that illustrates the use of a new three-stage C–D-type aerodynamic lens to focus 5–50 nm aerosol nanoparticles with a minimal transportation loss.