Regimes and Breakup Model of Head-On Collisions of Unequal-Sized Water Nanodroplets

The difference in diameters of unequal-sized water nanodroplets can significantly alter the collision regimes, and a quantitative model for predicting nanodroplet breakup remains unclear. This study employs molecular dynamics simulations to investigate the head-on collisions of unequal-sized nanodroplets. The interactions during head-on collisions are analyzed over a broad spectrum of Weber numbers and size ratios, allowing for a comprehensive characterization of the collision regime diagram. Binary nanodroplet collisions are characterized by coalescence and breakup regimes. Further exploration reveals that the coalescence regime in topological changes involves three distinct modes: coalescence following regular deformation (CRD), coalescence following reverse encapsulation (CRE), and coalescence after experiencing holes (CEH), and the breakup regime can be categorized into three distinct modes: rim-ring fragmentation (RF), partial breakup (PB), and divergent splattering (DS). The average film thickness at the minimum flattened state is found to scale as <i>h</i>_min ∼ <i>We</i>^-1/2 during the regular deformation regime of colliding equal-sized water nanodroplets; however, this scaling does not hold in the breakup regime due to the influence of thermal fluctuations, which induce fluctuations and perforations in the spreading sheet. The mechanism of spreading sheet puncture is clarified as a short-wavelength instability amplified by thermal fluctuations. Based on the dispersion relation characterizing the instability of a nanoscale liquid film, the critical liquid film thickness for sheet puncture follows a scaling law, <i>h</i>_cri ∼ α(λ_t + 2<i>h</i>_t), where α = 1.5 is a fitting parameter, λ_t is the nanoscale critical wavelength associated with the short-wavelength instability, and <i>h</i>_t is the characteristic length determined by the competition between thermal fluctuations and surface tension. Furthermore, an analysis model based on energy balance is proposed to determine the binary water nanodroplet breakup by utilizing the Reynolds and Ohnesorge numbers as fundamental parameters. This model expression accurately quantifies the transition between coalescence and breakup regimes, hence providing valuable guidance for nanodroplet interaction applications.