Charge of clustered microparticles measured in spatial plasma afterglows follows the smallest enclosing sphere model

The plasma-induced charge of non-spherical microparticles is a crucial parameter in complex plasma physics, aerosol science and astrophysics. Yet, the literature describes this charge by two competing models, neither of which has been experimentally verified or refuted. Here we offer experimental proof that the charge on a two-particle cluster (doublet) in the spatial afterglow of a low-pressure plasma equals the charge that would be obtained by the smallest enclosing sphere and that it should therefore not be based on its geometrical capacitance but rather on the capacitance of its smallest enclosing sphere. To support this conclusion, the size, mass and charge of single particles (singlets) and doublets are measured with high precision. The measured ratio between the plasma-afterglow-induced charges on doublets and singlets is compared to both models and shows perfect agreement with the predicted ratio using the capacitance of the smallest enclosing sphere, while being significantly dissimilar to the predicted ratio based on the particle's geometrical capacitance.