Design of a Slot Nanoparticle Virtual Impactor

A novel design for a nanoparticle slot virtual impactor is proposed. Compressible flow through the slot impactor is simulated using the CFD code FLUENT, and the corresponding particle trajectories are studied. The variation of the impactor performance with design parameters is also investigated. The design is optimized for a specific application where the virtual impactor serves as a preconcentrator. However, the design proposed is suitable for any application that requires concentration of ultrafine particles at high volumes. Additionally, the design developed in this work can be used for size selection by simply varying the operating pressure of the instrument. The 50% cut-off diameter varies from 13 nm to 200 nm as the operating pressure is increased by a factor of 20, without affecting the minor to total flow ratio significantly.

*Currently with Framo Engineering, PO Box 174 Sandsli, N-5862 Bergen, Norway.

INTRODUCTION AND MOTIVATION

Most mass spectrometry instruments are limited by the mass flow rate of the inlet. To overcome this problem, the sampling mass flow is split into a major and minor flow by a bend in the flow stream—the high inertia particles fail to turn and are therefore concentrated in the minor flow. Such a device is commonly termed as a virtual impactor if the minor flow is the focus of the instrument or a dichotomous sampler if both the major and minor flows are important. The study of virtual impactors has been carried out for many years. The first virtual impactor was proposed about 40 years ago by Hounam and Sherwood (1965). The round jet virtual impactors and samplers have been the focus of several studies (Marple and Chien 1980; Loo and Cork 1988). Ravenhall et al. (1982) and Forney et al. (1982) studied the two dimensional slit impactor. High volume slit impactors with low cut-points and small pressure drops were subsequently developed (Sioutas et al. 1994a; Sioutas 1994b; Ding and Koutrakis 2000; Kim et al. 2004).

The design of a virtual impactor with a cut-off particle diameter less than 1 micron has proven to be a technological challenge (Sioutas et al. 1994b). Nanoparticle impactors have been the focus of very few studies (e.g., Chutmanop et al. 2000; Furuuchi 2001). The inertial separation of particles is primarily governed by the Stokes number, which is proportional to the gas dynamic ratio M ²/Re (M and Re are the jet Mach number and Reynolds numbers, respectively) (Fernández de la Mora et al. 1990). Therefore, inertial separation of very small particles requires operation at either small Reynolds numbers or high Mach numbers. The former limits pumping capabilities and cost; therefore operation at high Mach number is the practical approach for ultrafine separation (Fernández de la Mora et al. 1990). The high velocity inertial impactors of Biswas and Flagan (1984) provide some guidelines for operation at high Mach numbers. Recently, Tsai and Lin (2000) extended the particle trap impactor approach to reduce particle bounce problems. More recently, Lee et al. (2003) developed a nanoparticle virtual impactor and studied the dependence of design parameters on its performance.

In this work we wish to integrate the approach of Lee et al. (2003) and Sioutas et al. (1994b) to design a high volume nanoparticle slot virtual impactor. Further, we demonstrate one of the several applications where it is used as a pre-concentrator to enhance instrument efficiency.

The multiple lens assembly (Liu et al. 1995a, 1995b) is appropriate for focusing a wide particle size range and the capped cone inlet (Middha and Wexler 2003) is appropriate for focusing a narrow particle size range. Both of these geometries have high transmission rates; yet, they suffer from the drawback that they need to be operated at very low pressures, limiting the mass flow rate through the instrument, to prevent separation and concomitant mixing after the lenses; low pressures produce low Reynolds numbers which prevent separation. In particular, the Liu et al. (1995a,b) geometry works only up to an operating pressure of 2 torr (∼0.0026 atm). Therefore, there is a need for elements that concentrate particles in the flow stream during their transition from ambient pressures to the lower pressures in the focusing elements.

In the current work, we wish to use a high volume, low cut-point, transonic virtual impactor as an upstream concentrator to enhance the focusing of any downstream focusing element. It is similar in concept to the Liu et al. (1995a,b) lenses and the matched slots (Middha and Wexler 2005), but is able to operate at high pressures also and therefore enhances the operation of existing geometries at a multitude of pressures. Additionally , this work seeks to develop a slot virtual impactor that can be used to produce as small a cut-point as desired for any application. Noone et al. (1988) developed a counterflow virtual impactor with an adjustable range of particle cut-size by adjusting the flow rate. Recently, Dhaniyala and co-workers (2003) developed a counterflow virtual impactor for sub-micron particle cut-size by operating at sub-atmospheric pressures. This works seeks to extend the range to nanoparticles by varying the operating pressure of the instrument, the operating pressure being close to atmospheric pressure. This work also seeks to understand and identify the parameters that govern focusing in a high-velocity virtual impactor.

DESIGN CONSIDERATIONS

As described earlier, focusing of particles in aerodynamic lenses depends on upstream concentration of particles entering the assembly. A virtual impactor placed upstream of either the lens assembly or the capped cone assembly pre-concentrates particles and thus improves efficiency of the system. However, the design of a virtual impactor for this purpose needs to satisfy certain constraints that include: (a) The mass flow rate through the minor stream equals the mass flow rate through the downstream assembly, (b) The 50% cut-off particle diameter of the virtual impactor, D _p,50, defined as the geometrical diameter of particle corresponding to 50% concentration efficiency (defined in equation 1), is larger than the optimum particle diameter focused by the downstream assembly, (c) The minor flow pressure must be equal to the operating pressure of the downstream element, and (d) The virtual impactor should concentrate particles into the minor flow by a factor of 10 or more.

DESIGN PARAMETERS

The particle concentration efficiency, η, is defined as follows (Tsai and Lin 2000):

The cut-off characteristics of an impactor are expressed in terms of the Stokes number which is defined as (Flagan 1982):

where ρ _p is the particle density, U is the average jet velocity, W is the slot width, D _p is the focused particle diameter, and μ is the viscosity of carrier gas and its variation with temperature is given by (Willeke 1976)

where μ₀ is the viscosity of air at T ₀ = 296.2 K and C _c is the Cunningham correction factor which accounts for the non-continuum Stokes drag on the particle. The Cunningham correction factor can be expressed to a good degree of accuracy by a linear correlation given by (Mallina et al. 2000):

where Kn = 2λ/D _p is the particle Knudsen number and λ is the mean free path of air which depends on temperature and pressure as (Willeke 1976):

where T is measured in Kelvin and p in atmospheres.

Calculation of the Stokes number is a challenge for transonic flows (Lee et al. 2003) due to the significant variation in temperature and pressure in the impactor domain. The Stokes number has been calculated in different manners by different researchers (Flagan 1982; Hering 1987; Fernández de la Mora et al. 1990). The Stokes number calculated in this work is based on the pressure, temperature and actual fluid velocity at the exit of the orifice, marked as plane A in Figure 1, Figure 2, and Figure 3, which are obtained from the CFD solver in a manner similiar to the one used by Fernández de la Mora for real impactors in the transonic regime (Fernández de la Mora et al. 1990). Further, the dimensionless parameter determining particle separation is √Stk ₅₀ corresponding to the 50% cut-off particle diameter, D _p,50 defined earlier.

FIG. 1 A 2D view of a symmetric half of the slot virtual impactor.

FIG. 2 2D symmetric section of the improved virtual impactor where the major is tilted more towards the minor.

FIG. 3 2D view of the novel slot impactor where the major and minor flows are parallel.

The Reynolds number is another important parameter governing the flow field in an impactor. The Reynolds number has been calculated in the slot virtual impactor as:

where ρ is the density of the carrier gas.

SOLUTION STRATEGY

To validate the aforementioned enhancement in inlet efficiency through the use of virtual impactors, commercially available CFD software FLUENT (version 6.0) was used to simulate the fluid flow and the particle motion in a virtual impactor. The dimensions were optimized to satisfy the mass flow rate and the operating pressure conditions.

The grid was generated using GAMBIT, a preprocessor tool provided by FLUENT. Only a symmetric half of the geometry was simulated; and a structured quadrilateral mesh was generated for the flow domain . The skewness of the mesh elements was maintained below 0.8 in the entire domain and the aspect ratio of the elements was less than 10. The mesh was made denser close to the regions with large gradients in velocities and coarser in the regions with small velocity gradients to improve computational efficiency. The inlet was modeled as a pressure inlet and both the minor and major streams were modeled as pressure outlets. The particle trajectories were solved in a Lagrangian frame of reference by integrating the force balance. A user-defined Stokes law for the non-continuum drag force was used with a linearized version of the Cunningham correction factor as described earlier. The particles were assumed to be spherical and of unit specific gravity. The numerical simulations neglect Brownian diffusion and Saffman lift forces.

AXISYMMETRIC IMPACTOR

Traditionally, axisymmetric elements have been used as virtual impactors. Therefore, the first design of the impactor considered in this work was an axisymmetric round jet virtual impactor. However, it was found that an axisymmetric virtual impactor could not serve all the requirements mentioned above. In particular, a single axisymmetric virtual impactor cannot match both the Stokes number and the flow rate criteria. This is due to the fact that only one free parameter, the nozzle size, determines the mass flow rate and the particle size focused. We can scale the axisymmetric impactor appropriately to match the critical particle diameter of the downstream assembly but this leads to a small minor flow rate. In order to maintain the large sampling flow of the downstream assembly, several axisymmetric virtual impactors in parallel are required. This design presents operational difficulties, as many virtual impactors must perform in the same fashion for the entire assembly to have the desired characteristics.

PROPOSITION OF A SLOT IMPACTOR

As described above, lots of axisymmetric virtual impactors are required to maintain the high throughput through the downstream assembly, which is difficult to control. To overcome these difficulties, a slot virtual impactor can be used; a slot is equivalent to several axisymmetric constrictions in parallel. Herein, an additional parameter, the slot length, helps to adjust the mass flow rate and match the particle focusing at the same time (Sioutas et al. 1994a; Middha and Wexler 2005). The constraints on the design are similar to those of the axisymmetric virtual impactor.

RESULTS AND DISCUSSION

Straight Slots

The symmetric half of the geometry of the straight slot virtual impactor considered in this work is shown in Figure 1. It should be noted that a priori calculations show that in order to match the flow rate of the downstream assembly, the length of the slot impactor (the dimension in the plane of the paper) is much larger than the width. Therefore, a two-dimensional simulation of the geometry is sufficient. The inlet width was chosen to be 0.2 mm for this work. The ratio of the dimension of the minor branch to the inlet, W ₂/W ₁, was chosen to be 1.2 as previous studies (Marple and Chien 1980; Loo and Cork 1988) have shown that a ratio larger than 1 works well for improving the collection efficiency of the instrument. The minor stream pressure was set at 0.0026 atm (to match the operating pressure of the downstream element) and the major stream was modeled at vacuum conditions to satisfy the constraints mentioned earlier. The ratio of the major flow dimension to the slot width, S/W ₁, was chosen to be 7 to ensure a high major flow rate, and hence a small minor flow rate. A shock was seen in the major branch, which is desired for matching mass flow rate as well as particle focusing. However, it was found that for these dimensions, the ratio of the minor flow rate was much larger than 10% of the total flow rate. It is possible to decrease the ratio by increasing S, but this happens at the cost of increasing the cut-off diameter. Therefore, there is a trade-off in choosing the dimensions of this geometry.

Improved Designs

A careful analysis of the flow in the previous geometry showed that, although W ₂ is much smaller than S, the majority of the flow continues into the minor branch because the flow close to the axis carries the majority of the momentum. To overcome this problem, a new geometry, shown in Figure 2, was explored where the major branch is inclined towards the minor. In this geometry, the streamlines do not have to negotiate the sharp turn that is required in the previous design to enter the major branch and it was hypothesized that this would result in a larger fraction of the flow going into the major flow stream.

This geometry was simulated in an identical manner as before, using FLUENT. As described in the previous section, it was sufficient to consider a 2D model of the design. The dimensions of the instrument were the same as in the designs described above. Indeed this geometry resulted in ratio of the minor flow to total flow of 10%. Additionally, the efficiency does not vary with minor outflow pressure as long as the upstream pressure is much higher than the major and minor flow pressures, which agrees with previous observations (Biswas and Flagan 1984).

The angle of inclination was varied to scan for the best performing geometry. Table 1 shows the variation ofD _p,50, √Stk, Re and minor to total flow ratio as the angle of inclination is increased from 0 to 90 degrees. The ratio of minor flow to total flow decreases and the cut-off diameter does not change significantly as the angle of inclination of the major flow is increased from 0 to 90 degrees.

TABLE 1 Concentration characteristics of slot virtual impactor of Figure 2 (S/W ₁ = 7, W ₂/W ₁ = 1.2, Upstream pressure = 1 atm., Minor branch pressure = 0.0026 atm., Major branch pressure: Vacuum)

Inclination of major branch to minor branch	50% cut-off particle diameter (nm)	Stokes Number √Stk	Ratio of minor flow rate and total flow rate	Reynolds number Re
90°	210	0.78	0.14	4526
45°	220	0.79	0.1	4112
0°	200	0.85	0.095	4174

The geometry corresponding to a 90-degree inclination where the the major stream is tilted towards the minor entirely so that both flows are parallel, is depicted in Figure 3, which is similar to the axisymmetric geometry investigated by Lee et al. (2003). Figure 4a and Figure 4b show the pressure and temperature variation in the impactor domain for this geometry. Notice that the shock is spread over both the major and minor flow streams which aids particle separation. Figure 5 shows the concentration efficiency as a function of the particle diameter, which is similar to that observed by Sioutas et al. (1996) and Tsai and Lin (2000). Also notice that the concentration characteristics do not vary with minor outflow pressure as long as the upstream pressure is much higher than the major and minor flow pressures, which agrees with previous observations (Biswas and Flagan 1984). The 50% cut-off particle diameter for this geometry is 200 nm. The minor flow rate was slightly smaller than the previous geometry. Therefore, this geometry is able to satisfy all our constraints by appropriate scaling.

FIG. 4 (a) Contours of pressure in the slot impactor of Figure 3 at an upstream pressure of 1 atm and minor stream pressures of 0.0026 atm. (b) Contours of temperature in the slot impactor of Figure 3 at an upstream pressure of 1 atm and minor stream pressures of 0.0026 atm.

FIG. 5 Concentration efficiency of the slot impactor shown in Figure 3 at an upstream pressure of 1 atm and minor stream pressures of 0.0026 atm (filled triangles) and 0.026 atm (empty squares).

This geometry performs the best among the designs considered. We further optimized the geometry by searching for the best dimensional ratios S/W ₁ and W ₂/W ₁ and angle θ. These results are summarized in Table 2. It can be seen from Table 2 that the 50% cut-off particle diameter and hence cut-off Stokes number increased as the major flow dimension increases, which is similar to the findings of Marple and Chien (1980). The minor flow rate was found to follow the opposite trend, that is, the largest minor flow rate was seen for the smallest value of S. Hence, as the ratio of minor to total flow decreases, the cut-off diameter increases, which is similar to the observation of Marple and Chien (1980). This, therefore, presents a trade-off between the concentration ratio and particle cut-off diameter.

TABLE 2 Variation of the cut-off particle diameter and minor flow rate with different geometric parameters for the design depicted in Figure 3 (Upstream pressure = 1 atm, Minor branch Pressure = 0.0026 atm, Major branch Pressure: vacuum)

S/W 1	W 2/W 1	θ (in degrees)	50% cut-off particle diameter (nm)	Ratio of minor flow rate and total flow rate
5	1.2	45	150	0.14
7	1.2	45	200	0.095
10	1.2	45	210	0.075
7	1.4	45	165	0.115
7	1.8	45	140	0.15
7	1.2	0	200	0.095
7	1.2	30	200	0.095
7	1.2	60	145	0.17

It can be seen from Table 2 that there is a similar trade-off when increasing the minor flow dimension, W ₂, with respect to the slot width, W ₁. The cut-off particle diameter decreases and the minor to total flow ratio increases as the ratio is increased which is in agreement with the observations of other researchers (Loo and Cork 1988; Sioutas et al. 1994b). Table 2 also shows the variation in cut-off diameter and minor to total flow ratio with the angle θ (see Figure 3). It can be observed that the cut-off diameter and the ratio of the minor flow to total flow is almost independent of θ if the angle is below 45 degrees, beyond which the cut-off diameter decreases slightly but the minor flow increases significantly. This can be explained on the basis of change in the flow characteristics; as the angle increases the recirculation region decreases and then the flow reattaches causing the minor flow stream to increase and the cut-off diameter to decrease. Therefore to satisfy the constraints mentioned earlier, a value of θ less than or equal to 45 degrees must be selected.

Further, the upstream pressure of the virtual impactor was varied. Table 3 presents a summary of the cut-off particle diameters and the ratio of the minor to total flow at three different pressures. It can be seen from the table that the virtual impactor design can be used to concentrate particle sizes from 13 nm to 200 nm by varying the operating pressure by a factor of 20 without affecting the minor to total flow ratio significantly. Hence, the virtual impactor can be used for size selection by simply varying its operating pressure and without altering the geometry of the instrument.

TABLE 3 Variation of the cut-off particle diameter and minor flow rate with the upstream pressure for the design depicted in Figure 3 (S/W ₁ = 7, W ₂/W ₁ = 1.2, θ = 45°, Minor branch pressure = 0.0026 atm, Major branch pressure: vacuum)

Upstream Pressure (in atm.)	50% cut-off particle diameter (nm)	Ratio of minor flow rate and total flow rate
1	200	0.095
0.25	65	0.11
0.05	13	0.14

Therefore, we have designed a slot virtual impactor that is able to deliver an arbitrary cut-off particle diameter, while being able to drastically increase the concentration of the particles, thus enabling a large increase in the efficiency of the aerosol inlets.

CONCLUSIONS

The goal of this work was to design an improvement over the current inlet geometries for enhanced transmission of particles. The best existing inlet geometries, viz., Liu et al. (1995) aerodynamic lenses and capped cone assembly (Middha and Wexler 2003), are not optimal because they suffer from small operating pressures and thus limited mass flow rates. A slot virtual impactor upstream of the inlet assemblies was proposed. An axisymmetric design is not feasible due to the inherent single degree of freedom associated with the geometry. To overcome this shortcoming, a slot geometry for the virtual impactor was proposed. The flow through the slots was simulated and their particle concentration characteristics were subsequently studied. Further, the slot geometry was optimized in terms of its geometric parameters to obtain a highly concentrated minor flow stream. The optimal geometries were found to work very well as they were able to reduce the minor flow rate to obtain the required concentration factor of 10. The best geometries investigated by this work had a minor to total flow ratio of 10 and particle cut-off diameter of 200 nm at an upstream pressure of 1 atm. It was further shown that the slots could be used for a wide range of operating pressures of the downstream assemblies, as the focusing characteristics did not change between a minor pressure of 0.0026 and 0.026 atm. It was also demonstrated that the virtual impactor can be used for size selection by simply varying its upstream pressure. Therefore, we have been able to design a slot virtual impactor that is able to deliver a small cut-off particle diameter, while being able to drastically increase the concentration of the particles, thus enabling a large increase in the efficiency of the aerosol inlets. Also, it is capable of matching any desired mass flow rate of the downstream assembly by simply adjusting the slot length.

This work was supported by the EPA supersite programs via funding to the Pittsburgh and Baltimore supersites.

Notes

*Currently with Framo Engineering, PO Box 174 Sandsli, N-5862 Bergen, Norway.