Dynamics of liquid drops coalescing in the inertial regime

Bridge Radius Evolution during Coalescence of Ferrofluid Droplets Suspended in a Nonmagnetic Outer Fluid

Understanding the droplet coalescence/merging is vital for many areas of microfluidics such as biochemical reactors, drug delivery, inkjet printing, oil recovery, etc. In the present study, we carried out numerical simulations of two magnetic droplets suspended in a nonmagnetic fluid matrix and coalescing under the influence of an external magnetic field. We observed that the applied magnetic field played a key role in the merging dynamics of the magnetic droplets. When the two droplets make the first contact with each other, a microscopic liquid bridge forms between the two and grows rapidly in the lateral direction until it coalesces into one. The temporal evolution of the neck radius with the onset of coalescence gives the growth rate of the liquid bridge. In the present study, parameters such as magnetic Bond number, magnetic susceptibility, and the viscosity ratio of the outer ambient fluid to droplet fluid were varied, and the bridge radius growth rate was assessed. The current study aims to discern how parameters such as magnetic Bond number, magnetic susceptibility, and the viscosity ratio influence the growth rate of the liquid bridge that forms between the droplets during coalescence. It is observed that the growth rate of the bridge radius is significantly affected by the change in magnetic Bond number and magnetic susceptibility for a high viscosity ratio. In contrast, for low viscosity ratio cases, the influence of magnetic Bond number and magnetic susceptibility on the rate of bridge growth is negligible. This unveils the implicit relationship among the three aforementioned parameters. Furthermore, we observe that the spatial structure of the neck region varied with the viscosity ratio and affected the rate of expansion of the neck radius. This study reveals how a magnetic influence can manipulate the structure of the neck region of two merging droplets and in turn affect the growth rate.

Dynamics of Droplet Coalescence on Hydrophobic Fibers in Oil: Morphology and Liquid Bridge Evolution

Although droplet self-jumping on hydrophobic fibers is a well-known phenomenon, the influence of viscous bulk fluids on this process is still not fully understood. In this work, two water droplets' coalescence on a single stainless-steel fiber in oil was investigated experimentally. Results showed that lowering the bulk fluid viscosity and increasing the oil-water interfacial tension promoted droplet deformation, reducing the coalescence time of each stage. While the total coalescence time was more influenced by the viscosity and under-oil contact angle than the bulk fluid density. For water droplets coalescing on hydrophobic fibers in oils, the expansion of the liquid bridge can be affected by the bulk fluid, but the expansion dynamics exhibited similar behavior. The drops begin their coalescence in an inertially limited viscous regime and transition to an inertia regime. Larger droplets did accelerate the expansion of the liquid bridge but had no obvious influence on the number of coalescence stages and coalescence time. This study can provide a more profound understanding of the mechanisms underlying the behavior of water droplet coalescence on hydrophobic surfaces in oil.

Coalescence of Microscopic Polymeric Drops: Effect of Drop Impact Velocities

In this paper, we employ the direct numerical simulation (DNS) method for probing three-dimensional, axisymmetric coalescence of microscale, power-law-obeying, and shear-thinning polymeric liquid drops of identical sizes impacting a solid, solvophilic substrate with a finite velocity. Unlike the cases of drop coalescence of Newtonian liquid drops, coalescence of non-Newtonian polymeric drops has received very little attention. Our study bridges this gap by providing (1) the time-dependent, three-dimensional (3D) velocity field and 3D velocity vectors inside two coalescing polymeric drops in the presence of a solid substrate and (2) the effect of the drop impact velocity (on the solid substrate), quantified by the Weber number (We), on the coalescence dynamics. Our simulations reveal that the drop coalescence is qualitatively similar for different We values, although the velocity magnitudes involved, the time required to attain different stages of coalescence, and the time needed to attain equilibrium vary drastically for finitely large We values. Finally, we provide detailed simulation-based, as well as physics-based, scaling laws describing the growth of the height and the width of the bridge (formed due to coalescence) dictating the 3D coalescence event. Our analyses reveal distinct scaling laws for the growth of bridge height and width for early and late stages of coalescence as a function of We. We also provide simulation-based coalescence results for the case of two unequal sized drops impacting on a substrate (nonaxisymmetric coalescence) as well as results for axisymmetric coalescence for drops of different rheology. We anticipate that our findings will be critical in better understanding events such as inkjet or aerosol jet polymer printing, dynamics of polymer blends, and many more.

Dynamic measurements and simulations of airborne picolitre-droplet coalescence in holographic optical tweezers

We report studies of the coalescence of pairs of picolitre aerosol droplets manipulated with holographic optical tweezers, probing the shape relaxation dynamics following coalescence by simultaneously monitoring the intensity of elastic backscattered light (EBL) from the trapping laser beam (time resolution on the order of 100 ns) while recording high frame rate camera images (time resolution <10 μs). The goals of this work are to: resolve the dynamics of droplet coalescence in holographic optical traps; assign the origin of key features in the time-dependent EBL intensity; and validate the use of the EBL alone to precisely determine droplet surface tension and viscosity. For low viscosity droplets, two sequential processes are evident: binary coalescence first results from the overlap of the optical traps on the time scale of microseconds followed by the recapture of the composite droplet in an optical trap on the time scale of milliseconds. As droplet viscosity increases, the relaxation in droplet shape eventually occurs on the same time scale as recapture, resulting in a convoluted evolution of the EBL intensity that inhibits quantitative determination of the relaxation time scale. Droplet coalescence was simulated using a computational framework to validate both experimental approaches. The results indicate that time-dependent monitoring of droplet shape from the EBL intensity allows for robust determination of properties such as surface tension and viscosity. Finally, the potential of high frame rate imaging to examine the coalescence of dissimilar viscosity droplets is discussed.