Towards a Standard Method for Estimating Fragmentation Rates in Emulsification Experiments

The fragmentation rate function connects the fundamental drop breakup process with the resulting drop size distribution and is central to understanding or modeling emulsification processes. There is a large interest in being able to reliably measure it from an emulsification experiment, both for generating data for validating theoretical fragmentation rate function suggestions and as a tool for studying emulsification processes. Consequently, several methods have been suggested for measuring fragmentation rates based on emulsion experiments. Typically, each study suggests a new method that is rarely used again. The lack of an agreement on a standard method has become a substantial challenge. This contribution critically and systematically analyses four influential suggestions of how to measure fragmentation rate in terms of validity, reliability, and sensitivity to method assumptions. The back-calculation method is identified as the most promising—high reliability and low sensitivity to assumption—whereas performing a non-linear regression on a parameterized model (as commonly suggested) is unsuitable due to its high sensitivity. The simplistic zero-order method is identified as an interesting supplemental tool that could be used for qualitative comparisons but not for quantification.

Kinematics of the viscous filament during the droplet breakup in air

The dripping regime in the vicinity of droplet breakup is analyzed concerning the evolution of the filament’s neck and its corresponding thinning velocity. Three flow regimes are observed as the relative time decreases: (i) a monotonous increase of the neck’s thinning velocity, where inertia and capillarity are balanced, (ii) a transition region characterized by the equilibrium between inertia, capillarity, and viscous forces, where the thinning velocity varies non-monotonically with the relative time and (iii) the final pinch-off regime, where velocity decreases or oscillates around a constant value. Based on the correlation between experimental data and numerics, the distribution of the zeta - coefficient (defined as the non-dimensional second invariant of the velocity gradient) on the droplet’s profile is used to quantify the ratio between elongation and rotation of the fluid at the interface. The regions dominated by extension, where pure elongation is located at zeta = 1 , are determined. One main result of this study is the confirmation that distribution of the zeta - coefficient is a relevant parameter to analyze and to quantify the breakup process. This result has the potential of developing novel techniques and more precise procedures in determining the interfacial rheology of viscous and complex fluids.

Explosive fragmentation of Prince Rupert’s drops leads to well-defined fragment sizes

Anyone who has ever broken a dish or a glass knows that the resulting fragments range from roughly the size of the object all the way down to indiscernibly small pieces: typical fragment size distributions of broken brittle materials follow a power law, and therefore lack a characteristic length scale. The origin of this power-law behavior is still unclear, especially why it is such an universal feature. Here we study the explosive fragmentation of glass Prince Rupert’s drops, and uncover a fundamentally different breakup mechanism. The Prince Rupert’s drops explode due to their large internal stresses resulting in an exponential fragment size distribution with a well-defined fragment size. We demonstrate that generically two distinct breakup processes exist, random and hierarchical, that allows us to fully explain why fragment size distributions are power-law in most cases but exponential in others. We show experimentally that one can even break the same material in different ways to obtain either random or hierarchical breakup, giving exponential and power-law distributed fragment sizes respectively. That a random breakup process leads to well-defined fragment sizes is surprising and is potentially useful to control fragmentation of brittle solids.

Simulation of liquid transfer between the plate and the groove

The transfer of the liquid from groove to plate is significantly affected by the breakup process of liquid bridge, which is the core problem of gravure. In this paper, many-body dissipative particle dynamics method (MDPD) is used to simulate the behaviors of the stretching liquid cylinder between the plate and the groove, and the influence of surface wettability, stretching velocity and groove structure on the liquid cylinder rupture and the transfer rate of liquid are studied. The results show that both of the slipping velocity of the contact line on the plate and the thinning velocity of the liquid cylinder determine the breakup state of the liquid bridges and the liquid transfer rate from the groove to the plate. In the cases with the same surface wettability, at high hydrophilicity surface, the transfer rate increases firstly and then decreases with the increase of the stretching velocity. In the cases with different surface wettability of the plate and the groove, reducing the stretching velocity and the inclination angle of the groove are helpful to pull the liquid out of the groove and increase the transfer rate, and it could also be achieved by increasing the wettability of the plate and decreasing the wettability of the groove. This study provides some new insights into the effects of surface wettability, stretching velocity and groove structure on the dynamics of breakup process and liquid transfer in stretching.

Investigation of the spray formation and breakup process in an open-end swirl injector

The spray formation and breakup process in an open-end swirl injector were studied through experiments and numerical simulations. A high-speed shadowgraph system and a high-speed backlight system were adopted to record the spray. Volume of fluid was used as the interface tracking method to capture the evolution process. The filling process of the liquid film inside the injector was captured. The air core formation process as observed in the experiments differed from that depicted by the numerical simulation results. The results revealed that the spray pattern of the cross-section at the tangential inlets also varied during the filling process. The evolution of the holes on the liquid film and ligaments was observed. It was determined that the liquid sheet repeatedly exhibited thinning, instability, shedding, breakup, and coalescence in the spray formation and breakup process. The spray pattern underwent the distorted pencil stage, onion stage, tulip stage, and fully developed stage with the increased injection pressure drop. The formation process of the open-end swirl injector also underwent these four stages under an injection pressure drop of 0.5 MPa.