Modelling the passive breakup of a surfactant-contaminated droplet in a T-junction microchannel

A lattice Boltzmann method is used to explore the effect of surfactants on the unequal volume breakup of a droplet in a T-junction microchannel, and the asymmetry due to fabrication defects in real-life microchannels is modelled as the pressure difference between the two branch outlets ( Δ P^ ). We first study the effect of the surfactants on the droplet dynamics at different dimensionless initial droplet lengths ( l₀^ ) and capillary numbers ( Ca ) under symmetric boundary conditions ( Δ P^ = 0 ). The results indicate that the presence of surfactants promotes droplet deformation and breakup at small and moderate l₀^ values, while the surfactant effect is weakened at large l₀^ values. When the branch channels are completely blocked by the droplet, a linear relationship is observed between the dimensionless droplet length ( ld^ ) and dimensionless time ( t^ ), and two formulas are proposed for predicting the evolution of ld^ with t^ for the two systems. We then investigate the effect of the surfactants on the droplet breakup at different values of Δ P^ and bulk surfactant concentrations ( ψ b ) under asymmetric boundary conditions ( Δ P^ ≠ 0 ). It is observed that, as Δ P^ increases, the volume ratio of the generated droplets ( V₁/V₂ ) decreases to 0 in both systems, while the rate of decrease is higher in the clean system, i.e. the presence of surfactants could cause a decreased pressure difference between the droplet tips. As ψ b increases, V₁/V₂ first increases rapidly, then remains almost constant and finally decreases slightly. We thus establish a phase diagram that describes the V₁/V₂ variation with Δ P^ and ψ b .