Breakage of Single Droplets in 2-D Inertial Flows

Abstract

Droplet break-up research has traditionally focused on droplets in: 1) generally uniform flow fields (constant strain rates or constant turbulence dissipation rates) that are easier to characterize and study, and in 2) highly complex flow fields generated by mixing devices in which the evolution of an entire droplet population with time is of interest. The current work adds to the existing body of knowledge by investigating the effect of short-term high-intensity deformation events on the break-up of single large droplets in both turbulent and inertial laminar flows. This approach consists of two components: high-speed imaging of droplets as they pass through a 2-D slit orifice and CFD simulations of the orifice flow field. The experimental trajectories of the droplets are combined with the CFD-generated flow field to determine the deformation history of the droplet prior to break-up.

In turbulent 2-D orifice flows, droplets and bubbles on the order of the macroscale of turbulence were studied. For these large droplets and bubbles, it was found that the product of strain rate magnitude and un-deformed diameter (essentially the velocity difference across the droplet) was a more suitable velocity scale. A new form of locally-derived, trajectory-dependent Weber number, consisting of the maximum average strain rate magnitude over an exposure time equal to 0.04 multiplied by the Stokes particle relaxation time, was used to develop a break-up probability model that can be applied to the break-up of both liquid droplets and gas bubbles. The model adds weight to the break-up interpretation of Levich (1962); break-up occurs due to the internal pressure fluctuations overcoming the interfacial stresses of the deformed droplet.

In inertial laminar 2-D orifice flows, the break-up of water droplets in oil was studied at two viscosity ratios. The recommended local Weber number was again based on the maximum average strain rate magnitude over a particular exposure time, but this exposure time was instead 8 multiplied by the oscillation time scale. Using the maximum length achieved by the droplet as the length scale was also found to better represent the potential for break-up. With these modifications, and an associated capillary number-based model for predicting the drop draw ratio, two local Weber number thresholds were defined. First, the threshold for break-up is at Welocal = 30. Second, the threshold for producing large daughter droplets, termed fracturing in this work, is at Welocal = 1,000. Between these thresholds, droplets may fracture or undergo a mechanism termed erosion in this work, where a small number of tiny droplets break off from the main body of the droplet. Both of these break-up types are based on an elongative end-pinching mechanism.