Generation of droplets via oscillations of a tapered capillary tube filled with low-viscosity liquids

Abstract

Droplet formation via the oscillations of a tapered capillary tube is experimentally and numerically investigated using incompressible, low-viscosity Newtonian liquids. As in many other common methods of droplet generation, this technique features a transient flow that is directed out of a nozzle. However, due to the interactions of the oscillations, the tube, and the fluids, the flow rate upstream of the nozzle cannot be directly obtained. In this study, the motion of the tube is measured under the activation of a specific waveform, and the flow inside the tube and drop formation are further numerically studied using a non-inertial reference system in which the tube is stationary. The mechanism of ejection is quantitatively explained by analyzing the temporal variation in the velocity and pressure distributions inside the tube. The dynamics of drop formation, the drop velocity, and the drop radius are studied as functions of the dimensionless groups that govern the problem, including the Ohnesorge number Oh, the Weber number We, the gravitational Bond number G, and various length scale ratios. The results show that droplets are generated due to the inertia of the liquid and velocity amplification in the tapered section. By influencing the balance between the viscous effect and inertial effect of the liquid along the entire tube, the length scale ratios affect the evolution of the transient flow at the nozzle and eventually influence the drop radius and velocity. For liquids with viscosities close to that of pure water, the critical Reynolds number, at which a drop can be generated, linearly depends on the Z number (the reciprocal of Oh) at the nozzle.