Merging, spreading and jumping nanodroplets

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

Contaminant removal from nature’s self-cleaning surfaces

Many organisms in nature have evolved superhydrophobic surfaces that leverage water droplets to clean themselves. While this ubiquitous self-cleaning process has substantial industrial promise, experiments have so far been unable to comprehend the underlying physics. With the aid of molecular simulations, here we rationalize and theoretically explain self-cleaning mechanisms by resolving the complex interplay between particle–droplet and particle–surface interactions, which originate at the nanoscale. We present a universal phase diagram that consolidates (a) observations from previous surface self-cleaning experiments conducted at micro-to-millimeter length scales and (b) our nanoscale particle–droplet simulations. Counterintuitively, our analysis shows that an upper limit for the radius of the droplet exists to remove contaminants of a particular size. We are now able to predict when and how particles of varying scale (from nano-to-micrometer) and adhesive strengths are removed from superhydrophobic surfaces

Rolling and sliding modes of nanodroplet spreading : molecular simulations and a continuum approach

Molecular simulations discover a new mode of dynamic wetting that manifests itself in the very earliest stages of spreading, after a droplet contacts a solid. The observed mode is a “rolling” type of motion, characterized by a contact angle lower than the classically assumed value of 180°, and precedes the conventional “sliding” mode of spreading. This motivates the development of a novel continuum framework that captures all modes of motion, allows the dominant physical mechanisms to be understood, and permits the study of larger droplets

Rolling and sliding modes of droplet spreading : molecular simulations and a continuum approach

Molecular simulations discover a new mode of dynamic wetting that manifests itself in the very earliest stages of spreading, after a droplet contacts a solid. The observed mode is a “rolling” type of motion, characterized by a contact angle lower than the classically assumed value of 180°, and precedes the conventional “sliding” mode of spreading. This motivates the development of a novel continuum framework that captures all modes of motion, allows the dominant physical mechanisms to be understood, and permits the study of larger droplets

Molecular physics of jumping nanodroplets

Next-generation processor-chip cooling devices and self-cleaning surfaces can be enhanced by a passive process that require little to no electrical input, through coalescence-induced nanodroplet jumping. Here, we describe the crucial impact thermal capillary waves and ambient gas rarefaction have on enhancing/limiting the jumping speeds of nanodroplets on low adhesion surfaces. By using high-fidelity non-equilibrium molecular dynamics simulations in conjunction with well-resolved volume-of-fluid continuum calculations, we are able to quantify the different dissipation mechanisms that govern nanodroplet jumping at length scales that are currently difficult to access experimentally. We find that interfacial thermal capillary waves contribute to a large statistical spread of nanodroplet jumping speeds that range from 0 - 30 m/s, where the typical jumping speeds of micro/millimeter sized droplets are only up to a few m/s. As the gas surrounding these liquid droplets is no longer in thermodynamic equilibrium, we also show how the reduced external drag leads to increased jumping speeds. This work demonstrates that, in the viscous-dominated regime, the Ohnesorge number and viscosity ratio between the two phases alone are not sufficient, but that the thermal fluctuation number (Th) and the Knudsen Number (Kn) are both needed to recover the relevant molecular physics at nanoscales. Our results and analysis suggest that these dimensionless parameters would be relevant for many other free-surface flow processes and applications that operate at the nanoscale

Droplet coalescence is initiated by thermal motion

The classical notion of the coalescence of two droplets of the same radius R is that surface tension drives an initially singular flow. In this Letter we show, using molecular dynamics simulations of coalescing water nanodroplets, that after single or multiple bridges form due to the presence of thermal capillary waves, the bridge growth commences in a thermal regime. Here, the bridges expand linearly in time much faster than the viscous-capillary speed due to collective molecular jumps near the bridge fronts. Transition to the classical hydrodynamic regime only occurs once the bridge radius exceeds a thermal length scale lT∼√R

Contaminant Removal from Nature’s Self-Cleaning Surfaces

This dataset contains molecular dynamics LAMMPS set-up files for simulating droplets removing contamination particles on highly wetting surfaces, such as those on nature's cicada wings or lotus leaves. It relates to the article Sreehari Perumanath, Rohit Pillai and Matthew K. Borg (2023). "Contaminant Removal from Nature’s Self-Cleaning Surfaces". Nano Letters (accepted)

Molecular physics of jumping nanodroplets

Perumanath, Sree Hari. (2020). Molecular physics of jumping nanodroplets, [dataset]. University of Edinburgh. https://doi.org/10.7488/ds/2851

Unraveling the Regimes of Interfacial Thermal Conductance at a Solid/Liquid Interface

The interfacial thermal conductance at a solid/liquid interface (G) exhibits an exponential-to-linear cross-over with increasing solid/liquid interaction strength, previously attributed to the relative strength of solid/liquid to liquid/liquid interactions. Instead, using a simple Lennard-Jones setup, our molecular simulations reveal that this cross-over occurs due to the onset of solidification in the interfacial liquid at high solid/liquid interaction strengths. This solidification subsequently influences interfacial energy transport, leading to the cross-over in G. We use the overlap between the spectrally decomposed heat fluxes of the interfacial solid and liquid to pinpoint when “solid-like energy transport” within the interfacial liquid emerges. We also propose a novel decomposition of G into: i) the conductance right at the solid/liquid interface and ii) the conductance of the nanoscale interfacial liquid region. We demonstrate that the rise of solid-like energy transport within the interfacial liquid influences the relative magnitude of these conductances, which in turn dictates when the cross-over occurs. Our results can aid engineers in optimizing G at realistic interfaces, critical to designing effective cooling solutions for electronics among other applications. This data set contains the MD simulation files and post-processing codes to reproduce our results. The dataset is related to the publication by Abdullah El-Rifai, Sree Hari Perumanath Dharmapalan, Matthew K. Borg and Rohit Pillai (2024), "Unraveling the Regimes of Interfacial Thermal Conductance at a Solid/Liquid Interface", Journal of Physical Chemistry C, https://doi.org/10.1021/acs.jpcc.4c0053

Rolling and Sliding modes of Droplet Spreading: Molecular Simulations and a Continuum Approach

These dataset contains representative files to be able to reproduce the molecular dynamics (MD) and continuum model (CM) simulations we published in the manuscript entitled: 'Rolling and Sliding Modes of Nanodroplet Spreading: Molecular Simulations and a Continuum Approach' by Perumanath, Chubynsky, Pillai, Borg, and Sprittles published in Physical Review Letters (2023). In this dataset, the molecular simulations (using the LAMMPS software) discover a new mode of dynamic wetting that manifests itself in the very earliest stages of spreading, after a droplet contacts a solid. The observed mode is a `rolling' type motion, characterized by a contact angle lower than the classically-assumed value of 180 degrees, and precedes the conventional `sliding' mode of spreading. This motivated the development of a novel continuum framework within the COMSOL software that captures all modes of motion, allows the dominant physical mechanisms to be understood and permits the study of larger droplets