Asymptotic analysis of evaporating droplets

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We consider the evaporation dynamics of a two-dimensional, partially-wetting sessile droplet of a volatile liquid in its pure vapour, which is supported on a smooth horizontal superheated substrate. Assuming that the liquid properties remain unchanged, we utilise a one-sided lubrication-type model for the evolution of the droplet thickness, which accounts for the effects of evaporation, capillarity, slip and the kinetic resistance to evaporation. We follow an asymptotic approach, which yields a set of coupled evolution equations for the droplet radius and area, estimating analytically the evaporation-modified apparent angle when evaporation effects are weak. The validity of our matching procedure is verified by numerical experiments, obtaining also an estimate for the evaporation time

Asymptotic theory for a Leidenfrost drop on a liquid pool

Droplets can be levitated by their own vapour when placed onto a superheated plate (the Leidenfrost effect). It is less known that the Leidenfrost effect can likewise be observed over a liquid pool (superheated with respect to the drop), which is the study case here. Emphasis is placed on an asymptotic analysis in the limit of small evaporation numbers, which proves to be a realistic one indeed for not so small drops. The global shapes are found to resemble "superhydrophobic drops" that follow from the equilibrium between capillarity and gravity. However, the morphology of the thin vapour layer between the drop and the pool is very different from that of classical Leidenfrost drops over a flat rigid substrate, and exhibits different scaling laws. We determine analytical expressions for the vapour thickness as a function of temperature and material properties, which are confirmed by numerical solutions. Surprisingly, we show that deformability of the pool suppresses the chimney instability of Leidenfrost drops

The relation of steady evaporating drops fed by an influx and freely evaporating drops

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning

The multiscale boiling investigation on-board the International Space Station: An overview

This publication lays the foundation for the description of the Multiscale Boiling Experiment, which was conducted within two measurement campaigns on the International Space Station between 2019 and 2021. The experiment addresses fundamental questions about two-phase heat transfer during boiling processes. For this purpose, single or few subsequential bubbles are selectively ignited on a heated substrate using a short laser pulse. A detailed investigation of the phenomena is possible, as the boiling process is temporally slowed down and spatially enlarged in microgravity. Within the Multiscale Boiling Project, the undisturbed growth of the bubbles, the influence of a shear flow, and the influence of an electric field are investigated within the same test facility using FC-72 as working fluid. Within the project, thirteen research groups from eight countries are collaborating. Over 3000 data sets have been generated over an 11-month measurement period. In the context of this publication, besides the motivation and necessity of such investigations, the basic structure of the experiment, the objectives of the investigations, and the organization are described. Finally, first results of the investigations are presented. Therefore, this publication has the primary aim to serve as a basis for many further planned publications and present the project as a whole

Influence of a nonlinear reference temperature profile on oscillatory Benard-Marangoni convection.

We analyze oscillatory instabilities in a fluid layer of infinite horizontal extent, heated from above or cooled from below, taking into account the nonlinearity of the reference temperature profile during the transient state of heat conduction. The linear stability analysis shows that a nonlinear reference temperature profile can have a strong effect on the system, either stabilizing or destabilizing, depending on the relative importance of buoyancy and surface tension forces. For the nonlinear analysis we use a Galerkin-Eckhaus method leading to a finite set of amplitude equations. In the two-dimensional (2D) case, we show the solution of these amplitude equations are standing waves

Experimental and numerical analysis of buoyancy-induced instability during CO2 absorption in NaHCO3–Na2CO3 aqueous solutions

This work deals with the experimental analysis and the mathematical modelling of the CO2 absorption in an initially quiescent aqueous solution of NaHCO3 and Na2CO3 inside a Hele-Shaw cell. This absorption, initially driven by the coupling between diffusion and chemical reactions, eventually leads to the apparition of a peculiar gravitational instability with non-monotonic dynamics, and liquid plumes generated at some distance from the gas-liquid interface (Wylock et al. 2014). Considering that this instability is triggered by a Rayleigh–Taylor like mechanism, a two-dimensional model, coupling diffusion, chemical reaction and convection, is proposed to simulate the onset and the dynamics of such an instability. It is observed that the simulated instability dynamics agree qualitatively with the experimental observations and that the order of magnitude of the onset time is well estimated. Thanks to the simulation, the interaction between the various phenomena after the instability onset is further investigated and a mechanism is proposed to explain the unusual dynamics of the studied system. It is notably shown that this dynamics is due to the particular non-monotonic liquid density variations with the depth, induced by the absorption. A criterion to obtain such type of density profile is presented. In addition, the simulation enables to assess the influence of the instability on the CO2 absorption rate and it is observed that the generated flow pattern does not lead to a significant enhancement of the gas–liquid absorption rate. This result is of significant importance for optimizing chemisorption (e.g. for CO2 capture or sequestration) processes.info:eu-repo/semantics/publishedSpecial issue GLS-1

Spheroidal approximation for finite-amplitude highly viscous axisymmetric drop/bubble free shape relaxation

A common simplification used in different physical contexts by both experimentalists and theoreticians when dealing with essentially non-spherical drops is treating them as ellipsoids or, in the axisymmetric case, spheroids. In the present theoretical study, we are concerned with such a spheroidal approximation for free viscous shape relaxation of strongly deformed axisymmetric drops towards a sphere. A general case of a drop in an immiscible fluid medium is considered, which includes the particular cases of high and low inside-to-outside viscosity ratios (e.g., liquid drops in air and bubbles in liquid, respectively). The analysis involves solving for the accompanying Stokes (creeping) flow inside and outside a spheroid of an evolving aspect ratio. Here this is accomplished by an analytical solution in the form of infinite series whose coefficients are evaluated numerically. The study aims at the aspect ratios up to about 3 at most in both the oblate and prolate domains. The inconsistency of the spheroidal approximation and the associated non-spheroidal tendencies are quantified from within the approach. The spheroidal approach turns out to work remarkably well for the relaxation of drops of relatively very low viscosity (e.g., bubbles). It is somewhat less accurate for drops in air. A semi-heuristic result encountered in the literature, according to which the difference of the squares of the two axes keeps following the near-spherical linear evolution law even for appreciable deformations, is put into context and verified against the present results