The coalescence of two equal-sized drops in a two-dimensional linear flow

Abstract

A four-roll mill was used to experimentally investigate the coalescence of two equal-sized drops in general linear flows. The experimental system consisted of polybutadiene drops suspended in polydimethylsiloxane. Under the experimental conditions studied, the bulk-phase rheological properties of both fluids are Newtonian. We studied both head-on collisions for a purely extensional “hyperbolic” flow that always lead to coalescence, and collisions with a finite offset from the inflow axis for several different flow types produced in the four-roll mill. The experimental results have been 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. In head-on collisions, it was found experimentally that the product of the film drainage time and strain rate is independent of capillary number (Ca) and drop radius at very low Ca. This scaling behavior agrees qualitatively with theoretical predictions from the approximate small Ca theory. At higher values of Ca, this dimensionless drainage time varies as Ca3/2. This scaling is also consistent with theoretical predictions. For collisions with a nonzero offset from the head-on configuration, coalescence occurs only for capillary numbers below a critical value, Cac. Measurements were made of Cac as a function of the drop size and the flow type, for various values of the offset. The critical capillary number for coalescence was found to decrease with increasing offset, in qualitative agreement with predictions from the theoretical model. However, these Cac versus offset results do not agree quantitatively with the theoretical predictions. 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, for configurations with small but nonzero offsets, it is found experimentally that coalescence occurs earlier in the collision process. Thus, the actual time available for film drainage is shorter, and the critical capillary number is smaller than what is predicted by the model. At the same time, for larger offsets, it is shown experimentally that the collision and initiation of film drainage is delayed relative to what is predicted, and thus there are offset values where the model predicts that coalescence is possible, whereas, in fact, no coalescence is observed.

Multi-step synthesis of nanoparticles performed on millisecond time scale in a microfluidic droplet-based system

“…[27][28][29][30][31] At low values of the Capillary number, surface tension effects dominate and the interface between the stream and the passing droplet quickly dissipates. At high values of the Capillary number, shear forces dominate and oil cannot be displaced from the region between the droplet and aqueous stream as easily.…”

Coalescence and splitting of confined droplets at microfluidic junctions

“…Observations show that coalescence occurs when collisions are slow, corresponding to capillary numbers below a critical value of order Ca c z 10 À2 . Numerous experimental and numerical studies have characterized the film drainage time, the critical capillary number, and the angle at which droplets coalesce as a function of droplet size, [19][20][21] viscosity ratio, 19,20,22 overall droplet deformation, 23,24 and the offset of the collision. [25][26][27] In particular, Hu and co-workers 19 show that the critical capillary number for coalescence in a predominantly extensional flow when collisions are nearly head-on exhibits power law dependence on droplet radius a and viscosity ratio l h m d /m c , such that Ca c f (l) À0.41 AE 0.06 (2a) À0.82 AE 0.03 (1) where m d and m c represent the droplet phase and matrix phase liquids, respectively.…”

A numerical study on the dynamics of droplet formation in a microfluidic double T-junction

“…The merging will depend on the surfactant effects usually present in actual operation 43 and the viscous ratio affecting on the interfacial mobility. 44 This explains why the alternating process is easier to observe in experiments even though precisely symmetric conditions are imposed for the two dispersed flows. This merging process continues, with the phase discrepancy growing as well over time.…”