Modelling the effect of aerosol polydispersity on unipolar charging and measurement in low-cost sensors

Low-cost ultrafine aerosol sensors are experimentally calibrated with controlled aerosol sources to provide metrics such as surface area, lung-deposited surface area, mean particle size and/or total concentration from one or more electrical current measurements. However, an aerosol with a large standard deviation in particle size provides a significantly different signal from a monodisperse aerosol with the same median particle size. In this paper, we investigate the effect of particle polydispersity on measurements in devices which employ unipolar charging. The conservation equations are solved for particle/ion charging and transport (convection, diffusion and electrical transport) in laminar, steady-state, incompressible flow. Lognormal particle size distributions are represented by over 10² coupled conservation equations for multiple size bins and discrete charge states and solved numerically for the first time. Modelling results show that integrated electrical current from a polydisperse particle distribution can be represented by a monodisperse distribution characterised by the count mean diameter (d¯; unipolar diffusion charging) or diameter of the average surface (d_s¯; photoelectric charging) and total concentration, for a large range of particle distributions and operating conditions offering a convenient simplification for the interpretation of ultrafine particle measurements. The simplification reduces the number of simultaneous conservation equations required, thereby reducing computation time by up to 57 times for a polydisperse particle distribution represented by 16 discrete size bins. The method of analysis is useful to both users and developers of low-cost ultrafine particle sensors to understand the effect of particle polydispersity on measurements.