“…As the particle ages, BC may collapse to a more compact structure (Zhang et al, 2008;Lack et al, 2014;Peng et al, 2016;Bhandari et al, 2019). A larger D f has often been used to represent BC with more compact structure (Liu and Mishchenko, 2005;Kanngießer and Kahnert, 2018;Cheng et al, 2014;Luo et al, 2019Luo et al, , 2023Luo et al, , 2024. Previous studies have shown that aged BC can sometimes have a D f of about 2.3 -2.6, assuming a fractal structure for aged BC (Adachi et al, 2010(Adachi et al, , 2007Chen et al, 2016).…”