Executive Summary : | Drops and bubbles are ubiquitous in natural and industrial processes alike, as they find important applications in key areas of global interest such as separation processes, food and pharmaceutical industries, biomedical devices, targeted drug delivery, among many others. Manipulation of droplet trajectories has therefore been an active area of research over the last several decades, leading to multiple aspects of droplet generation, their motion and shape deformation being studied by several researchers across the globe. One recently emerging area in this regard is the study of active droplets, which propel themselves forward by generating unbalanced interfacial forces driven by local chemical gradients around the drops. Active drops have been shown to have potential applications in cargo delivery, biomedicine, chemical detection, to highlight a few. Recent experimental and theoretical investigations on this topic reveal the complexity of the underpinning physico-chemical processes whilst also shedding light on the variety of intriguing trajectories that such a drop may possibly venture on. Despite such attention on active drops, the dynamics of active compound drops (or, double emulsions) has still remained an unresolved area of research. Compound drops find important applications in many areas, especially in drug and cell encapsulation that are used for targeted delivery, prolonged release and therapeutic treatments. Therefore, one infers that a confluence of compound drops and self-propulsion may lead to a paradigm shift in several biomedical remedial and detection processes, wherein active matter finds most of its applications. The purpose of this proposal is therefore to develop a fundamental framework for characterizing the motion of active compound drops using theoretical and numerical tools. In particular, we shall focus on two specific mechanisms of self-propulsion, namely, (1) solubilization of the outer shell leading to active motion, and (2) self-propulsion by the means of surfacic and bulk reactions. The numerical solutions will be carried out using expansions in orthogonal eigenfunctions and the theoretical analysis will involve the use of weakly non-linear asymptotic methods. Achievement of the project objectives would enhance our fundamental understanding of active propulsion and help advance applications such as drug and cell encapsulation, drug release, therapeutics as well as chemical detection. |