Non-equilibrium thermodynamics of a coagulating aerosol: Relating the self-preserving size distribution to entropy

For an evolving aerosol solely undergoing coagulation, an asymptotic form of a self-preserving distribution (SPD), uncorrelated with the initial state, is achieved after sufficient time. To better understand the existence of this state, we hypothesize that non-equilibrium theory can be applied to the SPD formation that has almost entirely been studied via kinetic relations. This study is the first known work to investigate the thermodynamic principles underlying aerosol coagulation, based on the existing definition of colloidal entropy and the self-similar state observed in grain growth. We use molecular dynamics models along with definitions of entropy for an aerosol undergoing collisions and coalescence that includes kinetic entropy, surface entropy and configurational entropy. We find that aerosols have high surface and configurational entropy changes, but note that the SPD can persist in scenarios characterized by non-coalescing particles (minimal surface entropy change) and homogenous mixing (no configurational entropy change). Thus, kinetic entropy alone is the dominant thermodynamic driver of SPD formation. A scaled entropy production (σ_N,scaled) is introduced and shown to remain constant once an aerosol has achieved an SPD. Applying non-equilibrium flux and force approaches, we find a linear flux-force relationship when the coagulation starts with a polydisperse aerosol and σ_N,scaled approaches a minimum value at SPD. Conversely, aerosols evolving from an initial monodisperse distribution to the polydisperse SPD exhibit a non-linear flux-force relationship and σ_N,scaled approaches a maximum value at SPD.