The formation of discrete droplets in a capillary jet is one of the most important processes in fluid mechanics. For example, it underpins ink-jet printing and drug delivery. However, regardless of the specific application, droplets tend to form over a wide range of temporal frequencies from around a single droplet per second in the case of a leaky faucet to thousands of droplets per second in the case of an ink-jet printer. A thorough understanding of the physics behind this would therefore enable more accurate and more precise control over the droplet formation process and, in turn, over properties such as the droplet size distribution, the droplet velocity, and the droplet formation frequency.
Although the linear behavior of capillary jets has been well studied, their nonlinear behavior has not. This is why a systematic investigation of capillary droplet formation, from its inception to transition to nonlinear instability is needed. Furthermore, previous studies on the control of such jets have explored only open-loop control. Here we propose to apply closed-loop control, leveraging recent advances in machine learning to discover improved model-free control laws. Not only will this spur new pathways for the development of novel control strategies for such jets, but it will also provide much needed fundamental insight into the physics of self-excited flows in general.
A joint experimental and theoretical project is proposed in collaboration with SUSTech and the University of Liverpool. Starting at HKUST, students will design, build and commission a novel apparatus for investigating the droplet formation process in a round capillary jet subjected to closed-loop control based on machine learning. The actuator will be a piezoelectric diaphragm embedded within a nozzle chamber. The students will use a computer-controlled syringe pump to expel liquid at precise flow rates from a thin capillary tube until full jetting conditions are reached. Using a high-speed digital camera, the students will record backlit images of the jet at various flow and control conditions, and then post-process the images in Matlab to extract the dominant droplet formation frequencies, diameters and mode shapes. Furthermore, they will apply nonlinear time-series analysis to identify the dominant attractors in state space. The students will then analyze the data using non-dimensional parameters such as the Bond number, Reynolds number, Weber number and Ohnesorge number, in an effort to discover universal scaling laws for the droplet formation frequency. The students will build on previous experiments by using different mixtures of glycerol and water, thus enabling the shear viscosity to be systematically varied. They will also explore the effect of non-Newtonian rheology, by adding trace amounts of long-chain polymers (polyethylene oxide, PEO) to the base solvent to impart liquid elasticity, thus controlling the extensional viscosity, a key parameter in the droplet formation process.
On completing this UROP project, the students will be able to:
Design and perform thermofluids experiments.
Apply nonlinear time-series analysis to experimental data.
Apply the principles of machine learning for closed-loop control of self-excited flows.
Develop a theoretical framework to explain experimental observations in the context of nonlinear dynamics.