Modelling surfactant effects on the onset of spontaneous droplet breakup in both regular and irregular T-junction microchannels

A lattice Boltzmann method is adopted to investigate the breakup of surfactant-free and surfactant-laden droplets in both regular and irregular T-junction microchannels. During droplet neck contraction, the neck thinning shifts from inertia dominated to interfacial tension dominated, causing spontaneous rapid neck collapse due to Rayleigh–Plateau instability. For the regular rectangular microchannels, we find that the prerequisite for the spontaneous breakup of a surfactant-free droplet is that the local capillary pressure in the triggering area exceeds the Laplace pressure difference between the inside and outside of the droplet neck. Results show that the critical neck thickness $\delta _\textit{cr}^{*}$ for the droplet spontaneous breakup increases with increasing height-to-width ratio $\chi$ of the microchannel in both surfactant-free and surfactant-laden systems. The presence of surfactants decreases $\delta _\textit{cr}^{*}$ at the identified $\chi$ , while the surfactant effects are gradually enhanced as $\chi$ increases. Subsequently, a constriction section is incorporated into the upper microchannel wall to establish an irregular microchannel. As constriction depth (length) increases, $\delta _\textit{cr}^{*}$ linearly decreases (increases) in the surfactant-free system, while $\delta _\textit{cr}^{*}$ exponentially decreases (linearly increases) in the surfactant-laden system. Four empirical formulas are proposed to predict the values of $\delta _\textit{cr}^{*}$ under varying constriction depths and lengths in the two systems.