Merging, spreading and jumping nanodroplets
Perumanath Dharmapalan, Sree Hari
Droplet-based systems appear in various aspects of our daily lives: in understanding the process of atmospheric storm cloud formation -involving very large length and time scales; in determining the shelf life of emulsion-based products such as mayonnaise - involving intermediate scales; and in design and optimization of next-generation micro/nano-fluidic devices such as nanopipe cooling materials - operating at much smaller scales. There are clear differences in the dominant physics that underpins their functioning, when these systems scale from macro to nano. As a result, many of the experimental observations at micro/nano-scales are often counter-intuitive and fascinating. Some such examples relevant to future nano-engineered technologies include: order of magnitudes higher water flow rate through nanotubes than predicted by traditional theories, passive water droplet transport to hotter regions on a heated surface and faster evaporation rates from nanoscale menisci. In this thesis, unconventionally large and computationally expensive molecular dynamics simulations are used to study problems involving nanodroplets, which have a wide range of engineering applications. The novelty in this work includes: (a) the investigation of previously unexplored realms of nanoscale interfacial fluid flows using high-fidelity molecular simulations and (b) uncovering the theoretical and fundamental explanation of how molecular motion affects the nanodroplet dynamics of three problems: merging, spreading and jumping nanodroplets. In the first problem, coalescence of two water droplets is studied, focusing on the first contact and growth of the bridge that connects both droplets. Many mathematical models in the literature host a `singularity' in the beginning of coalescence, where calculated quantities like velocity and pressure diverge at this point. Such singularities are unphysical, and what happens in reality is investigated in more detail in this thesis. The thermal motion of constituent molecules is found to have substantial impact not only in initiating coalescence, but also in developing the liquid bridge in the initial stages. For large droplets, a hydrodynamic instability develops owing to the attraction between confronting interfaces of the droplets as they approach each other. However, no evidence of such instability is observed at the nanoscale. Instead, the first contact happens because of the interfacial thermal fluctuations on droplets' surfaces meeting from opposite sides. Thereafter, coalescence proceeds in an observed `thermal regime', where, as molecular simulations show, the bridge grows as a result of gradual cohesion of the confronting interfaces of the droplets due to collective molecular jumps. This continues until a `thermal length scale' is achieved, which is found to scale as square-root of the size of the coalescing droplets. Only after these molecular-driven processes finish does the bridge evolve in the manner that we had previously understood. The relevance of the observed molecular thermal motion on droplet-droplet interactions is tested on droplet-surface interactions and found to extend also to these problems with small variations in the observed physics. When a liquid wets a solid surface, which is essential for applications in coating technologies, agriculture and printing, to name a few, a regime of contact line motion, which is very similar to the thermal regime in coalescence, is found to precede the contact line motion that we have traditional understood. The extent of this regime not only scales as square-root of the droplet size, but also depends on the attraction from the underlying wall. The dependence of this length scale on the equilibrium contact angle is explained based on the local profile of the droplet near the wall when the first contact happens. In this `thermal-vdW regime', the interfacial molecules of the droplet get deposited directly on to the surface, before it gives way to the traditional picture of contact line motion, where the molecules at the three-phase-zone hop over the potential energy landscape above the wall atoms. The existence of this new regime of droplet wetting on atomically smooth surfaces is further validated by comparison of the contact line motion with what is described by the molecular kinetic theory, with which the late stage dynamics closely match. The third problem combines the droplet-droplet and droplet-surface interactions and investigates the molecular physics of coalescence-induced jumping of nanodroplets from non-wetting surfaces, which is relevant for heat transfer and self-cleaning applications. Here, the effect of molecular thermal motion and ambient gas rarefaction on the jumping speed of a droplet is investigated. While the presence of an outer gas reduces the jumping speed by introducing an additional dissipation mechanism into the system, the interfacial thermal fluctuations make the jumping of nanodroplets a stochastic process. An analytical model of drag from outer gas is developed explaining the reduction of the jumping speed with respect to that in near-vacuum conditions. The thermal-capillary waves on the droplet surface renders the jumping speed to be statistically distributed with smaller droplets having wider and skewed distributions. It is shown that the jumping dynamics of nanodroplets is governed not just by Ohnesorge number as previously thought, but also by Knudsen number and thermal fluctuation number. Despite their increased importance at the nanoscale, this is the first time that the effect of thermal capillary waves is properly quantified in studies concerning the dynamics of nanodroplets. Moreover, this thesis is intended to inspire the reader to look at many other traditional problems with singularities from a fundamental molecular perspective. It may be the case that the thermal regime of droplet coalescence and the thermal-vdW regime of droplet spreading are two special classes of a larger set of interface evolution dynamics and this requires further systematic molecular investigations and quantifications. Furthermore, the models developed in this thesis can be integrated in CFD simulations in the future as better initial/boundary conditions. Coupled with insights from the theoretical analyses presented throughout this thesis, the results can be used to study many natural systems and to predict performance characteristics of futuristic micro/nano-fluidic devices, which employ nanodroplets for heat-transfer and various other emerging technologies such as self-cleaning and anti-icing surfaces.