Hydrodynamic interaction of two deformable drops in confined shear flow

We investigate hydrodynamic interaction between two neutrally buoyant circular drops in a confined shear flow based on a computational fluid dynamics simulation using the volume-of-fluid method. The rheological behaviors of interactive drops and the flow regimes are explored with a focus on elucidation of underlying physical mechanisms. We find that two types of drop behaviors during interaction occur, including passing-over motion and reversing motion, which are governed by the competition between the drag of passing flow and the entrainment of reversing flow in matrix fluid. With the increasing confinement, the drop behavior transits from the passing-over motion to reversing motion, because the entrainment of the reversing-flow matrix fluid turns to play the dominant role. The drag of the ambient passing flow is increased by enlarging the initial lateral separation due to the departure of the drop from the reversing flow in matrix fluid, resulting in the emergence of passing-over motion. In particular, a corresponding phase diagram is plotted to quantitatively illustrate the dependence of drop morphologies during interaction on confinement and initial lateral separation.

Figure 1

Schematic of initial configuration and location of the drops in shear flow.

Figure 2

Drop deformation for four different meshes at Re = 0.2 and Ca = 0.2.

Figure 3

Comparison between simulation results and experiment data (Re = 0.02, Ca = 0.13, $\Delta y_0/a=0.43$): (a) deformation, (b) relative trajectory, (c) angle $\varphi$, (d) drop shape evolution.

Figure 4

Motion behaviors of two drops in a shear flow (Re = 0.2, Ca = 0.2): (a) passing over $(a/H=0.100)$, (b) reversing $(a/H=0.200)$, (c) drop velocity of passing over, (d) drop velocity of reversing.

Figure 5

Local transient pressure and velocity contours for passing-over motion ($a/H=0.100$, Re = 0.2, Ca = 0.2): (a) pressure contour, (b) velocity contour.

Figure 6

Local transient pressure and velocity contours for reversing motion ($a/H=0.200$, Ca = 0.2, Re = 0.2): (a) pressure contour, (b) velocity contour.

Figure 7

Effect of Re and Ca on drop trajectories $(\Delta x_0/a=6,\Delta y_0/a=0.8,a/H=0.075)$: (a) effect of Re (Ca = 0.2), (b) effect of Ca (Re = 0.2).

Figure 8

Effect of confinement on the flow field around two interactive drops under passing-over motions (Re = 0.2, Ca = 0.2): (a) $a/H=0.050$, (b) $a/H=0.075$, (c) $a/H=0.150$.

Figure 9

Effect of confinement on drop trajectories (Re = 0.2, Ca = 0.2, $\Delta x_0/a=6,\Delta y_0/a=1.2$).

Figure 10

Effect of confinement on drop deformation (Re = 0.2, Ca = 0.2, $\Delta x_0/a=6,\Delta y_0/a=1.2$).

Figure 11

Trajectories of drops in a confined shear flow ($a/H=0.150$, Re = 0.2, Ca = 0.2, $\Delta x_0/a=6$).

Figure 12

Effect of initial lateral separation on the two interactive drops (Re = 0.2, Ca = 0.2): (a) $\Delta y_0/a=0.4$, (b) $\Delta y_0/a=1.0$, (c) $\Delta y_0/a=1.6$.

Figure 13

Regimes of pairwise interaction at finite confinements $\left(\Delta x_0/a=6\right)$.