An investigation of the evaporation of a droplet on a solid surface: Evaporation, self-assembly of colloidal deposits, and interfacial heat transfer

The high, fast and local heat transfer associated with the deposition and evaporation of a single droplet on a flat substrate has potential applications in spray evaporative cooling. Controlled evaporation of colloidal droplets can be used to manufacture nanowires, explosive crystalline layers and DNA spots for gene expression analysis. The physics of this phenomenon is a complex interplay of fluid dynamics in the presence of a severely deforming free surface, wetting line motion, convective and conductive heat transfer, mass transfer due to evaporation and advection-diffusion of particles inside the droplet. The main objective of this thesis is to deliver a numerical modeling to investigate the interplay of the transport phenomena for the droplet impact and evaporation, for the case of a pure liquid or a colloidal solution. Comparisons of numerical results with available or in house experiments are made wherever possible. Chapter 1 describes some industrial applications involving droplet deposition and evaporation, together with the associated transport phenomena and objectives of the thesis.;In chapter 3, the self-assembly of micro and nanoparticles during the evaporation of drops containing colloidal particles on a solid substrate is investigated numerically and experimentally. The finite-element numerical model described in chapter 2 is extended to handle particles transport inside the drop. Instead of tracking individual particles, we propose and successfully implement a continuum advection-diffusion equation to track the particle concentration. For the first time, the interaction of the free surface of the drop with a growing peripheral deposit is modeled based on wetting angle criteria. In case of electrically charged particles, DLVO interactions arise between the particles and the substrate: these are taken into account in the numerical model. Numerical results for evaporation times, deposit shape and flow field are in very good agreement with published experimental and theoretical results. We also performed transient visualization experiments of water and isopropanol drops loaded with polystyrene microspheres. Measured evaporation times, deposit shape and sizes, and flow fields were found in very good agreement with the numerical results. Different flow patterns caused by the competition of Marangoni loops and radial flow are shown to determine the deposit shape to be either a ring-like pattern or a homogeneous bump. Our results also show that the pH of the solution controls the deposit shape, which exhibit ring-like or more uniform patterns. We explain the transition between these patterns by considering how electrostatic and van der Waals forces modify the particle deposition process. We finally propose a phase diagram that explains how the shape of a colloidal deposit results from the competition between three flow patterns: a radial flow driven by evaporation at the wetting line, a Marangoni recirculating flow driven by surface tension gradients, and the transport of particles towards the substrate driven by DLVO interactions. This phase diagram explains three types of deposits often observed experimentally, such as a peripheral ring, a small central bump, or a uniform layer.;Chapter 4 and 5 are focused on investigating the transient temperatures at the interface between the droplet and the solid substrate. Chapter 4 describes a numerical investigation on the influence of liquid properties and interfacial heat transfer during microdroplet deposition onto a glass substrate. The motivation of this study is to select fluids for the interfacial temperature study described in chapter 5. Numerical results are used to predict the droplet spreading and temperature history of microdrops of four liquids, namely eutectic lead-tin solder, water, isopropanol and FC-72. The magnitude and rates of spreading for all four liquids are simulated and compared. Among the liquids, the spreading of FC-72 is the largest because of its larger Weber number. For isothermal impact, our simulations with water and isopropanol show very good agreement with experiments published in literature. For non-isothermal impacts, the transient drop and substrate temperatures are expressed in a non-dimensional way. The influence of imperfect thermal contact at the interface between the drop and the substrate is assessed for a realistic range of interfacial Biot numbers. Water and isopropanol drops are recommended for the laser based temperature measurements described in chapter 5.;Chapter 5 describes a novel laser-based measurement technique to measure temperature at the droplet-substrate interface. A measurement setup is built and the measurement technique is used in a combined experimental and numerical study of droplet impact and evaporation. The temporal and spatial resolution provided by the laser measurement are 100 mus and 20 mum, respectively. The respective impact and evaporation of micro- and nanoliter isopropanol droplets on a heated fused silica substrate are investigated. High-speed visualizations are performed to provide matching thermal contact resistance and wetting parameters for the numerical modeling. Our results describe and explain temperature oscillations at the drop-substrate interface during the early stages of impact. For the first time, a full simulation of the impact and subsequent evaporation of a drop on a heated surface is performed, and excellent agreement is found with the experimental results. Our results also shed light on the influence of wetting on the heat transfer during evaporation.;Chapter 2 describes the numerical model developed in the thesis for the evaporation of droplets of simple fluids. Comparison between numerical and experimental results are also provided for the evaporation of nanoliter water drops. First, we describe an in-house state-of-the-art finite element modeling based on the full Navier-Stokes and energy equation in Lagrangian coordinates. The Lagrangian scheme allows a very precise tracking of the free surface deformation and the associated Laplace stresses on the liquid-gas boundary. The numerical modeling that was originally developed to simulate thermofluidic phenomena during the droplet impact and solidification is modified to simulate the evaporation of a drop on a heated surface. At the free surface of the drop, the hydrodynamic and thermodynamic vapor-liquid jump conditions are respectively applied to account for mass and heat transfer during evaporation. A modeling is provided for the thermal Marangoni stresses along the free surface. The diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet-air interface. Numerical results for the microdroplet evaporation are presented for three substrate temperatures ranging from ambient to 122°C. Streamlines and temperature contours illustrate the fluid dynamics and heat transfer during the evaporation of the microdroplet. Comparisons with high-speed visualizations of the droplet evaporation are made, in terms of the evolution of the volume, wetting angle and wetted radius of the drop.;Finally, chapter 6 describes the conclusion of the thesis and proposes future work directions.