| The present study experimentally investigates the coalescence of two equal-sized drops in general linear flows using a four-roll mill. The experimental system consists of Polybutadiene drops suspended in Polydimethylsiloxane matrix. Both fluids exhibit Newtonian behavior under the experimental conditions. We measure three parameters that describe the coalesce process: the critical capillary number below which coalescence is always possible and above which coalescence is not possible, the time it take for the two drops to coalesce after they have made apparent contact, and the position (angle) of the two drops when coalescence occurs. In so doing, we study the dependence of coalescence on six parameters that characterize the experimental conditions: drop diameter, flow type, capillary number, initial offset from the inflow axis of the drops, viscosity ratio and molecular weight of the matrix fluid. The experimental results are then compared with approximate theoretical predictions of coalescence, based on an asymptotic theory for small capillary number, where the drops are spherical apart from a small planar deformation at the frontal surfaces between the two drops.; The results show that the scaling relationships of drainage time vs. capillary number, drainage time vs. flow type, critical capillary number vs. diameter, and critical capillary number vs. offset show a good agreement between the scaling theories and the experiments at moderate offset values. However, for large offset values, there are collisions for which the scaling theory predicts that coalescence is possible but no coalescence is observed. Moreover, in the model the minimum film thickness occurs when the two-drop pair has rotated to the angle at which the external flow just begins to pull them apart. However, it was found that the coalescence angle at the critical capillary number can vary from values close to the inflow axis to values past the angles where the drops are being pulled apart by the external flow depending on both viscosity ratio and offset. We discuss possible mechanisms responsible for the above observations.; Also, it was found that coalescence is affected by the molecular weight of the matrix above a threshold molecular weight even when all the hydrodynamic parameters that characterize the experimental conditions are kept constant. Specifically, the critical capillary number increases with increasing molecular weight of the matrix. Assuming that slip at the polymer-polymer interface is the mechanism responsible for this observed trend, a three-layer drainage model is proposed. The predictions of the model show a good agreement when compared against the experimental results. Furthermore, the presence of a slip layer is corroborated by demonstrating that the molecular weight dependence can be mitigated by introducing compatibilizers on the interface. |
