Condensation particle counters: Exploring the limits of miniaturisation

The measurement of airborne particles continues to attract increased interest for the detection and characterisation of air pollution, emissions, fire detection, occupational and climate impacts. Concerted efforts have reduced the size and cost of optical counters that have enabled widespread sensor deployment. Currently the World Health Organisation (WHO) enforces particle regulations that are mass-based which has resulted in an influx of low-cost portable optical particle counters (OPCs) calibrated to mass standards and widely utilised for research and personal monitoring. However, OPCs are incapable of measuring particles with diameters d(p) less than or similar to 300 nm which misses ultrafine particles (<= 100 nm) that often represent the majority of particles by number concentration. Condensation particle counters (CPCs) capable of measuring ultrafine particle number concentration with high instrument sensitivity, accuracy and precision have recently been targeted for miniaturisation. Herein, we explore the limitations of the miniaturisation of a CPC growth chamber (CPC-GC). Results presented in this work use water, but equivalent expressions can be obtained for other working fluids or design criteria using the same methods. Scaling analysis considers phenomenological constraints of supersaturation, heat transfer, particle penetration and droplet growth to establish limits during miniaturisation. The results showed that optimal thermal and saturation conditions are similar where the optimum device aspect ratio is L* >= L-min,L-s* = 1.68 Re + 7.98 and L* >= L-min,L-th* = 1.78 Re + 8.02 respectively L* is the non-dimensional aspect ratio and L-min* is the minimum non-dimensional device length required as a function of the flow Reynolds number Re. Higher Reynolds numbers lead to a convection-dominated regime, where the saturation and temperature profiles take a parabolic shape. As the Reynolds number approaches unity, the reduced mass and thermal Peclet numbers result in vapour and heat diffusing upstream of the condenser, creating ellipsoidal saturation and temperature profiles. To achieve a satisfactory performance, the heat and mass transport within the CPC-GC must be convection-dominated, leading to a minimum value of Re greater than or similar to 2. Desired penetration P >= 0.9 for particles with an initial diameter d(p)(init) = 10 nm is achieved by designs with an aspect ratio, L* <= L-max,L-p* = 2.5 Re. Together, these constraints define an allowable range of aspect ratios for a CPC-GC as a function of the Reynolds number. The final size of the grown droplets can be controlled by varying the interaction residence time tau(int), defined as the time a particle spends in the supersaturation profile. Having defined a target final droplet size for optical detection, and hence having fixed tau(int), the aspect ratio necessary to achieve the desired growth is a function of the Reynolds number and of the dimensional radius of the CPC-GC (R-i(cpc)) according to: L-growth * = gamma Re/(R-i(cpc))(2) with gamma = 2 tau(int)nu, where v is the kinematic viscosity of air. Selecting a value of R-i(cpc) such that the line for L-growth* falls in the centre of the allowable operating region defined above will optimise the dimensional CPC-GC for the selected design criteria. Limits from this model were used to realising a prototype successfully tested experimentally against a reference commercial CPC within a laboratory environment. The outcome of the present work enables designers and researchers with a toolkit to optimise the next generation of high performance miniaturised CPC-GC designs.