Recent microfluidic experiments by Bremond, Thiam & Bibette (Phys. Rev. Lett., vol. 100, 2008, paper no. 024501), along with simulations by Yoon et al. (Phys. Fluid, vol. 19, 2007, paper no. 102102) and near-contact experiments and simulations by Manica et al. (Langmuir, vol. 24, 2008, pp. 1381-1390), have demonstrated that two droplets can coalesce as they are separating rather than upon their collision. We analyse the experimental microfluidic flow configuration for the approach to contact with a two-dimensional model: we apply a lubrication analysis followed by the method of domain perturbation to determine the droplet deformation as a function of time. We find the approximate shape for the deformed droplet at the time of contact. In particular, for droplets of radius R, moving apart according to h0(t) = h0(0) + αt2, where 2h0(t) is the separation distance, we define a non-dimensional arameter A = 4 C μ R2α1/2/πγ[h0 (0)]3/2, where μ is the viscosity of the continuous phase; γ is the interfacial tension; and C depends on the viscosity ratio between the droplets and the continuous phase. Our model suggests that there exists a critical value Acrit = 16/33/2 ≈ 3.0792, below which separation is unlikely to facilitate the coalescence of the droplets. The predictions are in good agreement with available experimental data.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering