Yatin Darbar

Background: I graduated from the University of Birmingham with an MSci in Mathematics in 2019. During this time I specialised in applied mathematics, with the fluid mechanics modules being by far my favourite. This led to me doing my final year research thesis within the field of fluid dynamics. Specifically I investigated the static and quasi-static figures of equilibrium of a liquid bridge.

Research Interests: Currently my I am using my first year of the CDT to immerse myself in all the facets of research that fluid dynamics spans, this will help me identify the area of research I can make the best contribution. Ideally I would like to undertake a PhD project that has direct application and relevance to industry or the natural world.

Why I chose the CDT in Fluid Dynamics: After taking a year out of education to work, the CDT’s MSc + PhD approach appealed to me because it gave me the chance to consolidate the knowledge of fluid dynamics I gained during my undergraduate studies, but also allowed me to study topics that are outside my original discipline of mathematics. In addition to this the number different schools from the University that are in collaboration with the CDT meant that I would be in a perfect position to find the area of research that I wish to pursue.

PhD Project Title: Mixing Dynamics during Coalescence of Complex Fluids

Chemical reactions in coalescing droplets are used in many emerging technologies to create new materials in–situ. However for a chemical reaction to occur effective mixing between droplets is required. Asymmetries in droplet geometries and material properties permit the possibility of better mixing in coalescing droplets through the action of advective mixing. Advective mixing increases the internal interface area between the coalesced droplets, which increases the area in which diffusion can act across in order to homogenise the droplet. Hence, improving advective mixing can increase the efficiency of a chemical reaction instigated by droplet coalescence.
In addition, transport phenomena such as heat transfer and the chemical reaction themselves provide mechanisms in which the mixing can be engendered due to disparities in material properties on either side of the thermal or reaction front. The overarching purpose of the project is elucidate the mechanisms of mixing in coalescing droplets that undergo chemical reactions. Of particular interest is extending current simulation methods in order to explore mixing across various length scales relevant to contemporary applications, such as Reactive Inkjet
Printing (RIJ). Within these applications droplets can range from millilitre to picolitre in volume, which represents a range in length scales that spans four orders of magnitude.
Due to the small nature of droplets used in these applications, experiments concerning the internal dynamics of droplets are usually undertaken with millilitre sized droplets, since it is much easier to probe the internal dynamics of these droplets. Current visualisation methods lack the resolution to image the detailed structures inside coalescing droplets smaller than millilitre sized.   Advection and diffusion begin to balance at the smallest length scales, however it is hard to recreate this balance in experiments where millilitre sized droplets must be used.
To overcome this limitation in this research project a numerical simulation method will be created to explore the effect of diffusion, material parameters, heat transfer and chemical reactions on mixing across the multiple scales that are relevant to RIJ applications.  The latest version of the OpenSource computational fluid dynamics software OpenFOAM will be used to create a numerical model capable of capturing the dynamics of droplet coalescence. Additions to the source code will be developed in order to incorporate the physics of heat transfer and chemical reactions into the model. In-house experiments will form a basis for validation of the numerical method before it is used to explore the full parameter space.