The detachment of a wall-bound pendant drop suspended in a sheared fluid and subjected to an external force field

The phase field approach is applied to numerically simulate the detachment of an isolated, wall-bound 2D pendant drop suspended in a fluid in a simple shear flow. The model has been previously employed to simulate several two-phase flow phenomena, assuming that the system consists of a regular, partially miscible mixture, with the drop and the continuous phase being in thermodynamic equilibrium with each other. In addition, it is assumed that the two phases are separated by an interfacial region having a non-zero characteristic thickness a, i.e., the interface is diffuse. In the creeping flow regime, the problem is described in terms of three non-dimensional numbers: the fluidity number N α as the ratio between capillary and viscous fluxes, the Bond number N B o as the ratio between external and capillary forces, and the Peclet number N P e as a non-dimensional shear rate. We find that, at large fluidity numbers and for small droplets (i.e., for d drop = d drop / a ≤ 45), the onset of the drop detachment can be described in terms of a master curve, with the critical macroscopic Bond number N B o (M) = N B o · d drop 2 decreasing monotonously with N P e · d drop 1.5 for five drop sizes in the micrometer range.