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Graphical abstract Abstract The mixing of binary droplets is of paramount importance in microfluidic systems. In order to reveal the mixing mechanism of two free droplets suspended in the immiscible phase, we have developed a novel experimental setup to study the internal mixing in coalescing droplets with varying interfacial tension differences and droplet sizes. It is confirmed that the interfacial energy of droplets supports the jet flow and liquid bridge expansion during the coalescence of droplets. The increase of interfacial tension difference can increase the intensity of jet flow accompanied with slower liquid bridge expansion, which enhances the mixing of droplets. The decrease of droplet size can increase the initial velocity of jet flow. However, the intensity of jet flow decreases due to the rapid expansion of the liquid bridge, which results in weaker internal mixing. On this basis, a Reynolds number incorporating the jet velocity and droplet size is proposed to characterize the vortex size, which represents the degree of droplet mixing. This study presents an effective approach for enhancing the mixing of droplets. [ABSTRACT FROM AUTHOR]

Droplets banding is critical to emulsion separation under ultrasonic irradiation as it can greatly improve the separation efficiency. In this paper, the formation process of droplets banding under ultrasonic standing waves was precisely captured by high-speed microscopic photography; by processing the images, the droplets banding characteristics, including the banding formation time and banding interval, were extracted. Then the effects of acoustic intensity, frequency, droplet size, and physical properties of oil and water on the droplets banding characteristics were discussed in details. The results show that the range of acoustic intensities, within which the droplets banding can form, increases with the increase of the frequency; a maximum allowable acoustic intensity exists for banding formation, which also increases with the frequency. The banding formation time, which increases with increasing oil viscosity but decreases with droplet size, is found to be hardly affected by the oil-water interfacial tension. In addition, the banding interval is only related to the frequency, which closely corresponds to the half wavelength. [ABSTRACT FROM AUTHOR]

• Droplet response mode depends on electric capillary number and viscosity ratio. • Liquid bridge growth is dominated by interface tension instead of electric stress. • Dimensionless liquid bridge radius is linear with the conical angle. Deformation and coalescence behaviors of water droplets in viscous fluid under a direct current electric field are investigated with experiments and numerical simulations. An electro-hydrodynamic model is developed based on fluid dynamics equations and electrostatic equations. A coupled level set and volume of fluid method is proposed to capture the dynamic interface. The numerical results are validated to be in good accordance with classic results in the literature. The effects of electric capillary number Ca and viscosity ratio λ on droplet deformation and coalescence are systematically analyzed. Two different droplet response modes are obtained, namely overdamping response and underdamping response. The conversion of response modes is discussed with the (Ca, λ) phase diagram. Moreover, the distributions of electric field and flow field before and after the droplets contact are compared and analyzed. Numerical results show the time evolution of liquid bridge is dominated by the interfacial tension and viscosity of continuous phase. The electric stress is extremely weak at the liquid bridge and has a slight influence on evolution of liquid bridge. The correlation formula between dimensionless liquid bridge radius and conical angle during the growth of liquid bridge is regressed. These results are helpful for the optimization of electro-coalescence process. Image, graphical abstract [ABSTRACT FROM AUTHOR]