Predicting the deposition spot radius and the nanoparticle concentration distribution in an electrostatic precipitator

Deposition of aerosol nanoparticles using an electrostatic precipitator is widely used in the aerosol community. Despite this, basic knowledge regarding what governs the deposition has been missing. This concerns the prediction of the size of the particle collection zone, but also, perhaps more importantly, prediction of the nanoparticle concentration distribution on the substrate, both of which are necessary to achieve faster and more precise deposition. In this article, we have used COMSOL Multiphysics simulations, experimental depositions, and two analytical models to describe the deposition. Based on that, we propose a simple equation that can be used to predict the size of the deposition spot as well as the particle concentration on the substrate. The equation we derive concludes that the size of the deposition spot only depends on the gas flow rate into the precipitator, and on the constant drift velocity of a particle in an electric field. The equation also displays that the deposited particle concentration is independent of the gas flow rate. Our general mathematical analysis has great applicability, as it can be used to model different geometries and different types of deposition methods than the one described in this article. We can therefore also propose that the drift velocity in this model easily could be replaced by another velocity acting on the particles at other deposition conditions, for instance, the thermophoretic velocity during thermophoretic deposition. This would result in the same dependence as presented in this article. Finally, we demonstrate analytically and through experiment that the particle distribution inside the spot will be homogenous and follows a top hat profile.