Evaporative cooling of microscopic water droplets in vacuo: Molecular dynamics simulations and kinetic gas theory (original) (raw)
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A molecular dynamics simulation of droplet evaporation
International Journal of Heat and Mass Transfer, 2003
A molecular dynamics (MD) simulation method is developed to study the evaporation of submicron droplets in a gaseous surrounding. A new methodology is proposed to specify initial conditions for the droplet and the ambient fluid, and to identify droplet shape during the vaporization process. The vaporization of xenon droplets in nitrogen ambient under subcritical and supercritical conditions is examined. Both spherical and non-spherical droplets are considered. The MD simulations are shown to be independent of the droplet and system sizes considered, although the observed vaporization behavior exhibits some scatter, as expected. The MD results are used to examine the effects of ambient and droplet properties on the vaporization characteristics of submicron droplets. For subcritical conditions, it is shown that a spherical droplet maintains its sphericity, while an initially non-spherical droplet attains the spherical shape very early in its lifetime, i.e., within 10% of the lifetime. For both spherical and non-spherical droplets, the subcritical vaporization, which is characterized by the migration of xenon particles that constitute the droplet to the ambient, exhibits characteristics that are analogous to those reported for ''continuum-size'' droplets. The vaporization process consists of an initial liquid-heating stage during which the vaporization rate is relatively low, followed by nearly constant liquidtemperature evaporation at a ''pseudo wet-bulb temperature''. The rate of vaporization increases as the ambient temperature and/or the initial droplet temperature are increased. For the supercritical case, the droplet does not return to the spherical configuration, i.e., its sphericity deteriorates sharply, and its temperature increases continuously during the ''vaporization'' process.
Heat Transfer at the Nanoscale: Evaporation of Nanodroplets
Physical Review Letters, 2008
We demonstrate using molecular dynamics simulations of the Lennard-Jones fluid that the evaporation process of nanodroplets at the nanoscale is limited by the heat transfer. The temperature is continuous at the liquid-vapor interface if the liquid/vapor density ratio is small (of the order of 10) and discontinuous otherwise. The temperature in the vapor has a scaling form Tr; t Tr=Rt, where Rt is the radius of an evaporating droplet at time t and r is the distance from its center. Mechanical equilibrium establishes very quickly, and the pressure difference obeys the Laplace law during evaporation.
Reports on Progress in Physics, 2013
Evaporation is ubiquitous in nature. This process influences the climate, the formation of clouds, transpiration in plants, the survival of arctic organisms, the efficiency of car engines, the structure of dried materials and many other phenomena. Recent experiments discovered two novel mechanisms accompanying evaporation: temperature discontinuity at the liquid-vapour interface during evaporation and equilibration of pressures in the whole system during evaporation. None of these effects has been predicted previously by existing theories despite the fact that after 130 years of investigation the theory of evaporation was believed to be mature. These two effects call for reanalysis of existing experimental data and such is the goal of this review. In this article we analyse the experimental and the computational simulation data on the droplet evaporation of several different systems: water into its own vapour, water into the air, diethylene glycol into nitrogen and argon into its own vapour. We show that the temperature discontinuity at the liquid-vapour interface discovered by Fang and Ward (1999 Phys. Rev. E 59 417-28) is a rule rather than an exception. We show in computer simulations for a single-component system (argon) that this discontinuity is due to the constraint of momentum/pressure equilibrium during evaporation. For high vapour pressure the temperature is continuous across the liquid-vapour interface, while for small vapour pressures the temperature is discontinuous. The temperature jump at the interface is inversely proportional to the vapour density close to the interface. We have also found that all analysed data are described by the following equation: da/dt = P 1 /(a + P 2), where a is the radius of the evaporating droplet, t is time and P 1 and P 2 are two parameters. P 1 = −λ T /(q eff ρ L), where λ is the thermal conductivity coefficient in the vapour at the interface, T is the temperature difference between the liquid droplet and the vapour far from the interface, q eff is the enthalpy of evaporation per unit mass and ρ L is the liquid density. The P 2 parameter is the kinetic correction proportional to the evaporation coefficient. P 2 = 0 only in the absence of temperature discontinuity at the interface. We discuss various models and problems in the determination of the evaporation coefficient and discuss evaporation scenarios in the case of single-and multi-component systems.
Journal of Physics: Condensed Matter, 2013
For a one-component fluid on a solid substrate, a thermal singularity may occur at the contact line where the liquid-vapor interface intersects the solid surface. Physically, the liquid-vapor interface is almost isothermal at the liquid-vapor coexistence temperature in one-component fluids while the solid surface is almost isothermal for solids of high thermal conductivity. Therefore, a temperature discontinuity is formed if the two isothermal interfaces are of different temperatures and intersect at the contact line. This leads to the so-called thermal singularity. The localized hydrodynamics involving evaporation/condensation near the contact line leads to a contact angle depending on the underlying substrate temperature. This dependence has been shown to lead to the motion of liquid droplets on solid substrates with thermal gradients (Xu and Qian 2012 Phys. Rev. E 85 061603). In the present work, we carry out molecular dynamics (MD) simulations as numerical experiments to further confirm the predictions made from our previous continuum hydrodynamic modeling and simulations, which are actually semi-quantitatively accurate down to the small length scales in the problem. Using MD simulations, we investigate the motion of evaporative droplets in one-component Lennard-Jones fluids confined in nanochannels with thermal gradients. The droplet is found to migrate in the direction of decreasing temperature of solid walls, with a migration velocity linearly proportional to the temperature gradient. This agrees with the prediction of our continuum model. We then measure the effect of droplet size on the droplet motion. It is found that the droplet mobility is inversely proportional to a dimensionless coefficient associated with the total rate of dissipation due to droplet movement. Our results show that this coefficient is of order unity and increases with the droplet size for the small droplets (∼10 nm) simulated in the present work. These findings are in semi-quantitative agreement with the predictions of our continuum model. Finally, we measure the effect of liquid-vapor coexistence temperature on the droplet motion. Through a theoretical analysis on the size of the thermal singularity, it can be shown that the droplet mobility decreases with decreasing coexistence temperature. This is observed in our MD simulations.
AIP Conference Proceedings
Molecular dynamics simulations of vapor-liquid equilibrium states and those of evaporation from liquid phase into a virtual vacuum are performed for water. In spite of the formation of molecular clusters in the vapor phase and the presence of the preferential orientation of molecules at the interface due to uneven sharing of the bonding electron pair, essentially the same results as in our previous study for argon are obtained. That is, when the bulk liquid temperature is relatively low, the distribution function of evaporation can be expressed as the product of the equilibrium distribution of saturated vapor at the temperature in the bulk liquid phase and a well-defined evaporation coefficient, which is determined as a decreasing function of the liquid temperature, and is found to approach unity with the decrease of the temperature. α e = J evap J out eq , (3) where the brackets denote the ensemble average (see Fig. 2).
The evaporation rate () of n-alkanes C 8 –C 27 from molecular clusters and nanodroplets is analysed using the quantum chemical solvation model (SMD) and the kinetic gas theory, assuming that the system is in a state of thermodynamic equilibrium (i.e. evaporation and condensation rates are equal). The droplet size, liquid density, evaporation enthalpy and Gibbs free energy of evaporation are calculated over a broad temperature range of 300–640 K. The quantum chemical calculations (SMD/HF or SMD/B3LYP methods with the 631G(d,p) basis set) are used to estimate changes in the Gibbs free energy during the transfer of a molecule from a liquid medium (modelled by clusters or nanodroplets) into the gas phase. The kinetic gas theory is used to estimate the collision rate of molecules with clusters/nanodroplets in the gas phase. This rate depends on partial pressures of components, temperature, sizes and masses of molecules and clusters/nanodroplets. An increase in the molecular size of evaporated alkanes from octane to heptacosane results in a strong decrease in the values.
Modelling of multi-component droplet evaporation under cryogenic conditions
Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles
The vaporization of drops of highly vaporizable liquids falling inside a cryogenic environment is far from being a trivial matter as it assumes harnessing specialized thermodynamics and physical equations. In this paper, a multi-component falling droplet evaporation model was developed for simulating the spray cooling process. The falling speed of the sprayed droplets was calculated with the momentum equations considering three forces (gravity, buoyancy and drag) applied to a droplet. To evaluate the mass and heat transfer between the sprayed droplet and the surrounding gas phase, a gaseous boundary film of sufficient thinness was assumed to envelope the droplet, while the Peng-Robinson equation of state was used for estimating the phase equilibrium properties on the droplet’s surface. Based on the relevant conservation equations of mass and energy, the key properties (such as temperature, pressure and composition) of the liquid and gas phases in the tank during the spray process co...
Evaporation and condensational growth of tiny droplets
Journal of Aerosol Science, 1980
The one-speed transport equation normally used in neutron transport and radiative transfer studies is applied to the process of vapour (mass) transport in a gaseous media to a spherical droplet. The rate of mass transfer has been obtained in the quasi-stationary approximation. The treatment is quite general and valid for any "accommodation coefficient" and any "saturated vapour pressure". A method for incorporating these concepts in the transport equation is outlined. It is shown that the use of Kelvin's equation in this theory leads to results quite different from those given by conventional diffusion theory.