<div> <p>The distribution of local water vapor in the surrounding air has been shown to be the driving mechanism for several phase change phenomena during dropwise condensation and condensation frosting. This thesis uses reduced-order modeling approaches, which account for the effects of the vapor distribution to predict the droplet growth dynamics during dropwise condensation in systems of many droplets. High-fidelity modeling techniques are used to further probe and quantify the heat and mass transport mechanisms that govern the local interactions between a freezing droplet and its surrounding ambient, including neighboring droplets. The relative significance of these transport mechanisms in the propagation of frost are investigated. A reduced-order analytical method is first developed to calculate the condensation rate of each individual droplet within a group of droplets on a surface by resolving the vapor concentration field in the surrounding air. A point sink superposition method is used to account for the interaction between all droplets without requiring solution of the diffusion equation for a full three-dimensional domain. For a simplified scenario containing two neighboring condensing droplets, the rates of growth are studied as a function of the inter-droplet distance and the relative droplet size. Interactions between the pair of droplets are discussed in terms of changes in the vapor concentration field in the air domain around the droplets. For representative systems of condensing droplets on a surface, the total condensation rates predicted by the reduced-order model match numerical simulations to within 15%. The results show that assuming droplets grow as an equivalent film or in a completely isolated manner can severely overpredict condensation rates.</p> <p>The point superposition model is then used to predict the condensation rates measured during condensation experiments. The results indicate that it is critical to consider a large number of interacting droplets to accurately predict the condensation behavior. Even though the intensity of the interaction between droplets decreases sharply with their separation distance, droplets located relatively far away from a given droplet must be considered to accurately predict the condensation rate, due to the large aggregate effect of all such far away droplets. By considering an appropriate number of interacting droplets in a system, the point sink superposition method is able to predict experimental condensation rates to within 5%. The model was also capable of predicting the time-varying condensation rates of individual droplets tracked over time. These results confirm that diffusion-based models that neglect the interactions of droplets located far away, or approximate droplet growth as an equivalent film, overpredict condensation rates.</p> <p>In dropwise condensation from humid air, a full description of the interactions between droplets can be determined by solving the vapor concentration field while neglecting heat transfer across the droplets. In contrast, the latent heat released during condensation freezing processes cause droplet-to-ambient as well as droplet-to-droplet interactions via coupled heat and mas transfer processes that are not well understood, and their relative significance has not been quantified. As a first step in understanding these mechanisms, high-fidelity modeling of the solidification process, along with high-resolution infrared (IR) thermography measurements of the surface of a freezing droplet, are used to quantify the pathways for latent heat dissipation to the ambient surroundings of a droplet. The IR measurements are used to show that the crystallization dynamics are related to the size of the droplet, as the freezing front moves slower in larger droplets. Numerical simulations of the solidification process are performed using the IR temperature data at the contact line of the droplet as a boundary condition. These simulations, which have good agreement with experimentally measured freezing times, reveal that the heat transferred to the substrate through the base contact area of the droplet is best described by a time-dependent temperature boundary condition, contrary to the constant values of base temperature and rates of heat transfer assumed in previous numerical simulations reported in the literature. In further contrast to the highly simplified descriptions of the interaction between a droplet and its surrounding used in previous models, the model developed in the current work accounts for heat conduction, convection, and evaporative cooling at the droplet-air interface. The simulation results indicate that only a small fraction of heat is lost through the droplet-air interface via conduction and evaporative cooling. The heat transfer rate to the substrate of the droplet is shown to be at least one order of magnitude greater than the heat transferred to the ambient air.</p> <p>Subsequently, the droplet-to-droplet interactions via heat and mass exchange between a freezing droplet and a neighboring droplet, for which asymmetries are observed in the final shape of the frozen droplet, are investigated. Side-view infrared (IR) thermography measurements of the surface temperature for a pair of freezing droplets, along with three-dimensional numerical simulations of the solidification process, are used to quantify the intensity and nature of these interactions. Two droplet-to-droplet interaction mechanisms causing asymmetric freezing are identified: (1) non-uniform evaporative cooling on the surface of the freezing droplet caused by vapor starvation in the air between the droplets; and (2) a non-uniform thermal resistance at the contact area of the freezing droplet caused by the heat conduction within the neighboring droplet. The combined experimental and numerical results show that the size of the freezing droplet relative to its neighbor can significantly impact the intensity of the interaction between the droplets and, therefore, the degree of asymmetry. A small droplet freezing in the presence of a large droplet, which blocks vapor from freely diffusing to the surface of the small droplet, causes substantial asymmetry in the solidification process. The droplet-to-droplet interactions investigated in thesis provide insights into the role of heat dissipation in the evaporation of neighboring droplets and ice bridging, and open new avenues for extending this understanding to a system-level description for the propagation of frost.</p> </div> <br>

Droplet evaporation is ubiquitous to multitude of applications such as microfluidics, surface patterning and ink-jet printing. In many of the process like food processing tiny concentrations of suspended particles may alter the behavior of an evaporating droplet remarkably, leading to partially viscous and partially elastic dynamical characteristics. This, in turn, may lead to some striking mechanical instabilities, such as buckling and rupture. In this thesis, we provide a comprehensive physical description of the vaporization, self-assembly, agglomeration and buckling kinetics of sessile nanofluid droplet pinned on a hydrophobic substrate in various configurations. We have deciphered five distinct regimes of droplet lifecycle. Regime I-III consists of evaporation induced preferential agglomeration that leads to the formation of unique dome shaped inhomogeneous shell with stratified varying density liquid core. Regime IV involves capillary pressure initiated shell buckling and stress induced shell rupture. Regime V marks rupture induced cavity inception and growth. We provide a regime map explaining the droplet morphology and buckling characteristics for droplets evaporating on various substrates. Specifically, we find that final droplet volume and radius of curvature at buckling onset are universal functions of particle concentration. Furthermore, flow characteristics inside the heated and unheated droplets are investigated and found to be driven by the buoyancy effects. Velocity magnitudes are observed to increase by an order at higher temperatures with self-similar flow profiles. With an increase in the surface temperature, droplets exhibit buckling from multiple sites over a larger sector in the top half of the droplet. In addition, irrespective of the initial nanoparticle concentration and substrate temperature, hydrophobicity and roughness, growth of daughter cavity (subsequent to buckling) inside the droplet is found to be controlled by the solvent evaporation rate from the droplet periphery. The results are of great significance to a plethora of applications like DNA deposition and nanofabrication. In the next part of the thesis, we deploy the droplet in a rectangular channel. The rich physics governing the universality in the underlying dynamics remains grossly elusive. Here, we bring out hitherto unexplored universal features of the evaporation dynamics of a sessile droplet entrapped in a 3D confined fluidic environment. Increment in channel length delays the completion of the evaporation process and leads to unique spatio-temporal evaporation flux and internal flow. We show, through extensive set of experiments and theoretical formulations, that the evaporationtimescale for such a droplet can be represented by a unique function of the initial conditions. Moreover, using same theoretical considerations, we are able to trace and universally merge the volume evolution history of the droplets along with evaporation lifetimes, irrespective of the extent of confinement. These results are explained in the light of increase in vapor concentration inside the channel due to greater accumulation of water vapor on account of increased channel length. We have formulated a theoretical framework which introduces two key parameters namely an enhanced concentration of the vapor field in the vicinity of the confined droplet and a corresponding accumulation lengthscale over which the accumulated vapor relaxes to the ambient concentration. Lastly, we report the effect of confinement on particle agglomeration and buckling dynamics. Compared to unconfined scenario, we report non-intuitive suppression of rupturing beyond a critical confinement. We attribute this to confinement-induced dramatic alteration in the evaporating flux, leading to distinctive spatio-temporal characteristics of the internal flow leading to preferential particle transport and subsequent morphological transitions. We present a regime map quantifying buckling & non-buckling pathways. These results may turn out to be of profound importance towards achieving desired morphological features of a colloidal droplet, by aptly tuning the confinement space, initial particle concentration, as well as the initial droplet volume. These findings may have implications in designing functionalized droplet evaporation devices for emerging engineering and biomedical applications.

Droplets as precursor are extensively applied in diverse fields of science and engineering. Various contributions are provided previously towards analysis of single phase and multi-phase droplets of single and multiple components. This thesis describes modelling of multi-phase (nano fluid) droplet vaporization. The evaporation of liquid phase along with migration of dispersed particles in two-dimensional plane within droplet is detailed using the governing transport equations along with the appropriate boundary and interface conditions. The evaporation model is incorporated with aggregate kinetics to study agglomeration among nano silica particles in base water. Agglomeration model based on population balance approach is used to track down the aggregation kinetics of nano particles in the droplet. With the simulated model it is able to predict different types of final structure of the aggregates formed as observed in experimental results available in literature. High spatial resolution in terms of agglomeration dynamics is achieved using current model. Comparison based study of aggregation dynamics is done by heating droplet in convective environment as well as with radiations and using different combination of heating and physical parameters. The effect of internal flow field is also analysed with comparative study using levitation and without levitation individually. For levitation, droplet is stabilized in an acoustic standing wave. It is also attempted to study the transformation of cerium nitrate to ceria in droplets when heated under different environmental conditions. Reaction kinetics based on modified rate equation is modelled along with vaporization in aqueous cerium nitrate droplet. The thermo physical changes within the droplet along with dissociation reaction is analysed under different modes of heating. The chemical conversion of cerium nitrate to ceria during the process is predicted using Kramers' reaction velocity equation in a modified form. The model is able to explain the kinetics behind formation of ceria within droplet at low temperatures. Transformation of chemical species is observed to be influenced by temperature and configuration of the system. Reaction based model along with CFD (computational fluid dynamics) simulation within the droplet is able to determine the rate of chemical dissociation of species and predict formation of ceria within the droplet. The prediction shows good agreement with experimental data which are obtained from literature.