The interaction of fluids and electric fields is at the heart of natural phenomena such as the disintegration of raindrops in thunderstorms and many practical applications such as electrosprays, inkjet printing, lab-on-a-chip and microfluidics. Yet, despite the method is widely used in several applications, fundamental knowledge of the mechanisms of emulsion demixing by electric fields and, in particular, the influence of surface active agents on drops placed in electric fields, is limited. The surface active agents (surfactants) are compounds that lower the surface tension between liquids, they are often used in pharmaceutical and engineering applications but also naturally present in heavy oils, e.g., asphaltenes, resins, etc; consequently it is of crucial importance to develop an improved understanding of the complex physics involved. Nowadays, numerical methods can offer a powerful tool to study very accurately such physical systems. Nevertheless, modelling these micro-fluidic processes is a challenging task, especially in three dimensions, because of the complex multiscale physics involved: large surface to volume ratio, many-body interaction, moving geometries and transport of surface active agents and of surface charges.
I propose to develop novel numerical methods for accurate micro-fluidic simulations of 3D drops in Stokes flow; this computational tool will be based on a boundary integral formulation, will consider the particles in both free space and confined geometries and it will include the effects of surfactants and electric fields.
To validate the simulations as well as to guide the modeling efforts, I will collaborate with Prof. Vlahovska (Northwestern University), who will run experiments in her Applied Math Lab.
With the integration of mathematical modeling, computations, and experiments we anticipate both a much deeper understanding of the underlying physics as well as the discovery of new dynamical regimes and engineering opportunities.
The broader impact of this research, in addition to advancing basic knowledge on boundary integral methods and numerical tools for surface PDE, lies in the potential applications of the electrohydrodynamics to detect and separate particles, for mixing of viscous fluids, production of patchy particles with new surface patterns (e.g. belts, ribbons), and design of novel active materials (e.g., emulsions with effective viscosity tunable by electric field, or collection of Quincke drops spontaneously self-organizing into macroscopic directed motion). The proposed research will provide insights into new phenomena by elucidating the fundamental mechanisms of the instabilities associated with these electrodriven flows, and will generate new opportunities for technological applications involving smart soft materials with tunable properties.
The realization of this project will greatly benefit from my experience and expertise in boundary integral methods for microfluidics. I will start from this solid basis to complement and reinforce related ongoing projects in this field, to broaden my knowledge in novel shock-capturing numerical tools and to study unexplored behaviors of surfactant-laden emulsions in electric fields.
As the simulation tool progresses, the results will be compared to those of physical experiments for simpler set-ups. This will also give input to refinements in the simulation model. The most important use of simulations is that they can show the detailed dynamics inside the drops and at the drop surfaces, in a way that is impossible to do based on physical experiments. Systematic studies with different parameters and set-ups where the simulations play the role of a 3D microscope will yield an increased knowledge of the dynamics of the system. Improvements for droplet based microfluidics will be suggested based on this knowledge and directly tested in real systems. I will continue the ongoing collaboration with Prof. Vlahovska (Northwestern University) in a multifaceted way; Prof. Vlahovska indeed is currently working on the development of new asymptotic theories (time-dependent small perturbation theories) and running experiments that I will use for validating my numerical code and to develop semi-analytical solutions. Those results will be used to investigate the effect of the charge convection, to understand and quantify the physical mechanism(s) responsible for the complex dynamics observed.
With the integration of mathematical modeling, computations, and experiments we anticipate both a much deeper understanding of the underlying physics as well as the discovery of new dynamical regimes and engineering opportunities.