An Asymptotic Analysis of Differential Electrical Mobility Classifiers

Abstract

An asymptotic analysis of balanced flow operations of differential mobility analyzers (DMAs) and a new class of instruments that includes opposed migration aerosol classifiers (OMACs) and inclined grid mobility analyzers (IGMAs) provides new insights into the similarities and differences between the devices. The characteristic scalings of different instruments found from minimal models are shown to relate the resolving powers, dynamic ranges, and efficiencies of most such devices. The resolving powers of all of the instruments in the nondiffusive regime of high voltage classifications, R nd , is determined by the ratio of the flow rate of the separation gas (sheath or crossflow) to that of the aerosol. At low voltage, when diffusion degrades the classification, the OMAC and the IGMA share an R nd factor advantage in dynamic range of mobilities over the DMA, although the OMAC also suffers greater losses because diffusion immediately deposits particles onto its porous electrodes. On the basis of this analysis, a single master operating diagram is proposed for DMAs, OMACs, and IGMAs. Analysis of this operating diagram and its consequences for the design of differential electrical mobility classifiers suggests that OMACs and IGMAs also have advantages over DMAs in design flexibility and miniaturization. Most importantly, OMACs and IGMAs may outperform DMAs for the currently difficult classification of particles with diameters less than 10 nm. On the other hand, DMAs are more amenable to voltage scanning-mode operation to enable accelerated size distribution measurements, whereas it is most convenient to operate OMACs and IGMAs in voltage stepping-mode operation.

The Multiple Monodisperse Outlet Differential Mobility Analyzer: Derivation of Its Transfer Function and Resolution

“…Equations 27 and 28, respectively). In the diffusion-limited regime, assuming that the transfer function of the MMO-DMA is Gaussian, we derive the diffusion-limited resolution R diff i for each outlet (Equations (97), (99), and (100)), using the approach followed by Flagan (1999) and Downard et al (2011). Combining the two limiting cases (i.e., for nondiffusing and for diffusing particles), we further derive an approximate resolution R approx i (Equations (107) and (108)) for balanced flows only, which can be applied over the entire range of particle mobilities and diffusional broadening parameters.…”

“…Flagan (1999) showed that for small particles, the resolution is proportional to the square root of the applied voltage. Downard et al (2011) extended this approach for the opposed migration aerosol classifiers (OMACs) and the inclined grid mobility analyzers (IGMAs), and showed that at low voltages both these instruments exhibit better resolution compared with that of the DMA. Using their approach, we derive here a general expression for estimating the resolution of the ith exit of the MMO-DMA for given operating conditions.…”

Design, simulation, and characterization of a radial opposed migration ion and aerosol classifier (ROMIAC)

“…Particles, the electrical migration of which is balanced by the cross-flow, are advected between the porous electrodes by a smaller sample flow. The performance of the OMAC is similar to that of the DMA, except that the voltage at which diffusion begins to degrade resolution is much lower, and scales as V / R nd (Downard et al 2011) rather than as V / R 2 nd as in the DMA (Stolzenburg 1988;Flagan 1999). Because the length scale over which diffusion must act to affect resolution is the entire channel width, b, in the OMAC, but only » bb in the DMA, the dynamic range of the OMAC can, in theory, be made much larger than that of any DMA of comparable resolving power and dimensions.…”

“…with r 2 D 0.96, shown in Figure 8h. An asymptotic analysis of the transfer function for an idealized, rectilinear OMAC (Downard et al 2011) supports the observed dependence of h trans on b. The experimental h trans values are compared with those predicted by Equation (25) in Figure 8i.…”

“…A consequence of this design is that both the flow and electric field in the classification region deviate from the ideal ones considered in the initial conceptual models (Flagan 2004;Downard et al 2011). The classifiedaerosol outlet port is located at the center of the grounded screen electrode.…”