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

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

Stability analysis of the evaporation of a binary liquid into an inert gas, considering solute/thermal and gravity/surface tension effects

peer reviewe

A comprehensive analysis of the evaporation of a liquid spherical drop

International audienc

Time-dependent Marangoni-Bénard instability of an evaporating binary-liquid layer including gas transients

info:eu-repo/semantics/publishe