A Model for a Spreading and Melting Droplet on a Heated Substrate

We develop a model to describe the dynamics of a spreading and melting droplet on a heated substrate. The model, developed in the capillary-dominated limit, is geometrical in nature and couples the contact line, trijunction, and phase-change dynamics. The competition between spreading and melting is characterized by a single parameter KT that represents the ratio of the characteristic contact line velocity to the characteristic melting (or phase-change) velocity. A key component of the model is an equation of motion for the solid. This equation of motion, which accounts for global effects through a balance of forces over the entire solid-liquid interface, including capillary effects at the trijunction, acts in a natural way as the trijunction condition. This is in contrast to models of trijunction dynamics during solidification, where it is common to specify a trijunction condition based on local physics alone. The trijunction dynamics, as well as the contact angle, contact line position, and other dynamic quantities for the spreading and melting droplet, are predicted by the model and are compared to an isothermally spreading liquid droplet whose dynamics are controlled exclusively by the contact line. We find that in general the differences between the dynamics of a spreading and melting droplet and that of an isothermally spreading droplet increase as KT increases. We observe that the presence of the solid phase in the spreading and melting configuration tends to inhibit spreading relative to an isothermally spreading droplet of the same initial geometry. Finally, we find that increasing the effect of spreading promotes melting

Solidification of liquid metal drops during impact

Hot liquid metal drops impacting onto a cold substrate solidify during their subsequent spreading. Here we experimentally study the influence of solidification on the outcome of an impact event. Liquid tin drops are impacted onto sapphire substrates of varying temperature. The impact is visualised both from the side and from below, which provides a unique view on the solidification process. During spreading an intriguing pattern of radial ligaments rapidly solidifies from the centre of the drop. This pattern determines the late-time morphology of the splat. A quantitative analysis of the drop spreading and ligament formation is supported by scaling arguments. Finally, a phase diagram for drop bouncing, deposition and splashing as a function of substrate temperature and impact velocity is provided

Triple condensate halo from water droplets impacting on cold surfaces

Understanding the dynamics in the deposition of water droplets onto solid surfaces is of importance from both fundamental and practical viewpoints. While the deposition of a water droplet onto a heated surface is extensively studied, the characteristics of depositing a droplet onto a cold surface and the phenomena leading to such behavior remain elusive. Here we report the formation of a triple condensate halo observed during the deposition of a water droplet onto a cold surface, due to the interplay between droplet impact dynamics and vapor diffusion. Two subsequent condensation stages occur during the droplet spreading and cooling processes, engendering this unique condensate halo with three distinctive bands. We further proposed a scaling model to interpret the size of each band, and the model is validated by the experiments of droplets with different impact velocity and varying substrate temperature. Our experimental and theoretical investigation of the droplet impact dynamics and the associated condensation unravels the mass and heat transfer among droplet, vapor and substrate, offer a new sight for designing of heat exchange devices

Nonlinear enthalpy transformation for transient convective phase change in Smoothed Particle Hydrodynamics (SPH)

A three-dimensional model is presented for the prediction of solidification behavior using a nonlinear transformation of the enthalpy equation in a Smoothed Particle Hydrodynamics (SPH) discretization. The effect of phase change in the form of release and absorption of latent heat is implemented implicitly as variable source terms in the enthalpy calculation. The developed model is validated against various experimental, analytical, and numerical results from the literature. Results confirm accuracy and robustness of the new procedure. Finally, the SPH model is applied to a study of suspension plasma spraying (SPS) by predicting the impact and solidification behavior of molten ceramic droplets on a substrate

Wetting and energetics in nanoparticle etching of graphene

Molten metallic nanoparticles have recently been used to construct graphene nanostructures with crystallographic edges. The mechanism by which this happens, however, remains unclear. Here, we present a simple model that explains how a droplet can etch graphene. Two factors possibly contribute to this process: a difference between the equilibrium wettability of graphene and the substrate that supports it, or the large surface energy associated with the graphene edge. We calculate the etching velocities due to either of these factors and make testable predictions for evaluating the significance of each in graphene etching. This model is general and can be applied to other materials systems as well. As an example, we show how our model can be used to extend a current theory of droplet motion on binary semiconductor surfaces

Transient surface cooling by non-contacting droplet impingement

Following a large loss of coolant accident in a PWR, cooling is performed by superheated vapour with entrained droplets, which bounce from the hot metal without wetting it. This thesis describes experimental and modelling studies aimed at the evaluation of the direct cooling by these droplets. Droplet diameters are less than 2 mm, they spend ~15 ms near the surface, extract ~1/5 J, cooling the metal by ~50 oC with heat fluxes of the order of MW/m2. An interface-tracking CFD code was used to model the droplet approach, the generation of vapour from its underside and its rebound or break-up, and to compute the transient cooling of the hot metal below the droplet. Validation of this model requires measurements of the heat transfer. A novel method to measure the transient surface temperature beneath the droplet is reported, using transient high resolution infra-red spectroscopy. Spatial and temporal resolutions of ~100.μm and ~4ms respectively are achieved, observing an opaque metallic layer from beneath through an infrared-transparent substrate. Post-processing via transient finite elements permits all thermal quantities (heat flux, energy, etc) to be determined. Associated simultaneous high speed optical recording of the droplet motion and deformation provided data for validation of the hydrodynamic aspect of the prediction. It is estimated that these methods allow the heat extracted by (for example) a 1.5 mm droplet during the 10 ms it spends in the vicinity of the hot surface to be obtained with an uncertainty of 15%. This heat extracted is approximately 0.19 J, associated with a transient temperature reduction of ~47 oC, and is removed by a heat flux peaking at 3.5 MW/m2. Encouraging agreement was obtained between these measurements and the computational simulations. For this same case, the CFD analyses predict 0.12 J and a peak heat flux of 5 MW/m2