tfer-pma.

A particle mass analyzer
transfer function
evaluator.

Introduction

This web app examines the transfer function of particle mass analyzers, like the centrifugal particle mass analyer (CPMA) or aerosol particle mass analyzer (APM). We refer the reader to Sipkens et al. (2020) for more information on the underlying analytical transfer functions. A supporting repository with code to evaluate the PMA transfer functions is available here — including Matlab, Python, and Javacsript versions. A separate Matlab version, which can be imported into larger projects is also available here (e.g., this package is imported into bidias).

APM (aerosol particle mass analyzer) conditions are achieved when ω21 = 1. Typcialy CPMA (centrifugal particle mass analyzer) conditions are achieved when ω21 = 0.9696. Another interesting condition occurs when doubling the length to 40 cm, a scenario that can (very, very roughly) approximate two devices in series. In this case, diffusion is much larger, resulting in smooth, Gaussian-like curves even for m* ≈ 5 fg with distinct charging peaks.

We note that Case 1S, following from the approach proposed Ehara et al. (1996), results in various anomalies. For example, in the default app settings, there is an anomaly for the z = 1 transfer function, which appears as a linear increase in the transfer function for m/m* > 2 (enable Case 1S below to see this). This artifact is a consequence of solving for the equilibrium raidus and demonstrates a limitation of that approach. Other anomalies include problems with calculating the uncharged (z = 0) contributions. The method is generally stable for the ω21 = 1, the case originally intended by Ehara et al. (1996).

Visualization & controls

The default view shows contributions from integer charge states z = 1 through 3. All cases correspond to uniform flow — for parabolic transfer functions see Sipkens et al. (2020). A few preset conditions:

  1. APM conditions
  2. CPMA conditions
  3. Ehara, Fig. 8c (uniform flow only)
  4. Olfert and Collings, Fig. 5a (Couette CPMA curve)

Classifier and particle properties

Inner radius cm
Outer radius cm
Length cm

Flow rate LPM
ω21

Dm
ρeff,100 kg/m³

Integer charge states




Include charging?
Wiedensohler, z = 3
Gopalakrishnan, z < 3

Include Case 1S?
(Removed for clarity)

Setpoint

Setpoint mode

Mass setpoint fg
Resolution

Angular speed
ω =
1802
rad/s
ω =
17,203
RPM
Voltage
V =
12.26
V
Resolution
Rm =
5.00
Mobility diameter @ (m*, 2m*, 3m*) nm
(
26.59
,
35.17
,
41.42
)
Specific mass @ (m*, 2m*, 3m*) kg/C
(
0.06241
,
0.1248
,
0.1872
)
0.01.02.03.04.0+0+1+2+3+4z =
12340.050.100.150.200.250.00.20.40.60.81.01.2Particle mass over setpoint mass, m/m*Specific mass, s [kg/C]Transfer function, Ω

Legend

Case 1S (Ehara et al., Olfert and Collings)Case 1C (Recommended over Case 1S)Case 1C + DiffusionCase W1 (Only when ω2/ω1 = 1, where it is exact)Case W1 + Diffusion (Only when ω2/ω1 = 1)