Evaporation of a Sub-Micrometer Droplet

Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Flux and storage of energy in nonequilibrium stationary states

Systems kept out of equilibrium in stationary states by an external source of energy store an energy ΔU=U-U_{0}. U_{0} is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine ΔU for two model systems: ideal gas and a Lennard-Jones fluid. ΔU depends not only on the total energy flux, J_{U}, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where the energy flux per unit volume is (i) constant, (ii) proportional to the local temperature, and (iii) proportional to the local density. We show that ΔU/J_{U}=τ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. τ is the characteristic timescale of energy outflow from the system immediately after the shutdown of energy flux. We prove that τ is minimized in stable states of the Rayleigh-Benard cell.

Liquid phase stabilization versus bubble formation at a nanoscale curved interface

We investigate the nature of vapor bubble formation near a nanoscale-curved convex liquid-solid interface using two models: an equilibrium Gibbs model for homogenous nucleation, and a nonequilibrium dynamic van der Waals-diffuse-interface model for phase change in an initially cool liquid. Vapor bubble formation is shown to occur for sufficiently large radius of curvature and is suppressed for smaller radii. Solid-fluid interactions are accounted for and it is shown that liquid-vapor interfacial energy, and hence Laplace pressure, has limited influence over bubble formation. The dominant factor is the energetic cost of creating the solid-vapor interface from the existing solid-liquid interface, as demonstrated via both equilibrium and nonequilibrium arguments.

Phase-field lattice Boltzmann modeling of boiling using a sharp-interface energy solver

The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system. The mass flow generated at liquid-vapor phase interface is embedded in the pressure evolution equation. The sharp-interface treatment of internal energy equation helps to find the interfacial mass flow rate accurately where no free parameter is needed in the calculations. The proposed model is verified against available theoretical solutions of the two-phase Stefan problem and the two-phase sucking interface problem, with which our simulation results are in good agreement. The liquid droplet evaporation in a superheated vapor, the vapor bubble growth in a superheated liquid, and the vapor bubble rising in a superheated liquid are analyzed and underlying physical characteristics are discussed in detail. The model is successfully tested for the liquid-vapor phase change with large density ratio up to 1000.

Evaporation of nanodroplets on heated substrates: a molecular dynamics simulation study

Molecular dynamics simulations of Lennard-Jones particles have been performed to study the evaporation behavior of nanodroplets on heated substrates. The influence of the liquid-substrate interaction strength on the evaporation properties was addressed. Our results show that, during the temperature-raising evaporation, the gas is always hotter than the droplet. In contrast to the usual experimental conditions, the droplet sizes in our simulations are in the nanometer scale range and the substrates are ideally smooth and chemically homogeneous. As a result, no pinning was observed in our simulations for substrates denoted either hydrophilic (contact angle θ < 90°) or hydrophobic (contact angle θ > 90°). The evaporative mass flux is stronger with increasing hydrophilicity of the substrate because the heat transfer from the substrate to the droplet is more efficient for stronger attraction between the solid and the droplet. Evaporation and heat transfer to the gas phase occur preferentially in the vicinity of the three-phase contact line in the hydrophilic system. However, in the case of a hydrophobic substrate, there is no preferential location for mass and heat fluxes. During the whole evaporation process, no pure behavior according to either the constant-angle or the constant-radius model was found; both the contact angle and contact radius decrease for the droplets on hydrophilic and hydrophobic substrates alike.

Evaporation of freely suspended single droplets: experimental, theoretical and computational simulations

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) = -λΔT/(q(eff)ρ(L)), where λ is the thermal conductivity coefficient in the vapour at the interface, ΔT 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.

Large-scale molecular dynamics verification of the Rayleigh-Plesset approximation for collapse of nanobubbles

We report large-scale (10(7) atoms in an 85-nm-wide container) molecular dynamics simulations of collapse of nanoscopic (5-12 nm in diameter) voids in liquid argon. During the collapse the pressure on the liquid side decreases, and this decrease propagates into liquid at the speed of sound. Despite the nonuniform profile of pressure in the liquid the solutions of the Rayleigh-Plesset equation compares well to the measured evolution of the radius of the void and the velocity of the interface. Evaporation of liquid into the void does not affect the dynamics appreciably.

Challenges in thermodynamics: Irreversible processes, nonextensive entropies, and systems without equilibrium states

Recent works on evaporation and condensation demonstrate that even these simplest irreversible processes, studied for over 100 years, are not well understood. In the case of a liquid evaporating into its vapor, the liquid temperature is constant during evaporation and the evaporation flux is governed by the heat transfer from the hotter vapor into the colder liquid. Whether liquid evaporates into its own vapor or into the vacuum, the irreversible pathway in the process goes through a number of steps which quickly lead to the steady-state conditions with mechanical equilibrium in most parts of the system—the fact overlooked in all previous studies. Even less is known about general rules which govern systems far from equilibrium. Recently, it has been demonstrated that a work done in an irreversible process can be related to the free energy difference between equilibrium states joined by the process. Finally, a real challenge in thermodynamics is a description of living systems since they do not have equilibrium states, are nonextensive, (i.e., they cannot be divided into subsystems), and cannot be isolated. Thus, their proper description requires new paradigms in thermodynamics.

Evaporation into vacuum: Mass flux from momentum flux and the Hertz-Knudsen relation revisited

We performed molecular dynamics simulations of liquid film evaporation into vacuum for two cases: free evaporation without external supply of energy and evaporation at constant average liquid temperature. In both cases we found that the pressure inside a liquid film was constant, while temperature decreased and density increased as a function of distance from the middle of the film. The momentum flux in the vapor far from the liquid was equal to the liquid pressure in the evaporating film. Moreover the pseudopressure (stagnation pressure) was found to be constant in the evaporating vapor and equal to the liquid pressure. The momentum flux and its relation to the pressure determined the number of evaporating molecules per unit time and as a consequence the mass evaporation flux. We found a simple formula for the evaporation flux, which much better describes simulation results than the commonly used Hertz-Knudsen relation.

Kinetics of solvent extraction/evaporation process for PLGA microparticle fabrication

Organic solvent extraction/evaporation from an o/w-dispersion has been widely used for the fabrication of PLGA microparticles. The purpose of this work was to elucidate the kinetics of the solvent extraction/evaporation process. A mathematical diffusion model was developed and applied to predict the duration of the solvent extraction. As the diffusion coefficient, D(p), plays a major role in the modeled process, a new and experimentally simple method for estimating D(p) was developed. Both the experimental method and the mathematical model were validated through PLGA microparticle fabrication experiments. For microparticles of mode diameters of 2 and 20 microm, the solvent was extracted in approximately 10 s. Sufficient hardening of the microparticles required, however, the evaporation of solvent from the extraction phase. Residual solvent in extraction phase exerted a strong effect on the morphology of the final product as demonstrated by scanning electron microscopy. Only if most solvent was removed from the aqueous extraction phase, a powdery product of individual microparticles was obtained. At residual organic solvent concentration of above 0.2% in the extraction phase, the microparticles strongly aggregated during collection on a membrane filter and final drying. The presented methods may be useful for better controlling microparticle fabrication processes by solvent extraction/evaporation.

Heat transfer at the nanoscale: evaporation of nanodroplets

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 T(r,t)=T[r/R(t)], where R(t) 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.

On the protein crystal formation as an interface-controlled process with prototype ion-channeling effect

A superdiffusive random-walk action in the depletion zone around a growing protein crystal is considered. It stands for a dynamic boundary condition of the growth process and competes steadily with a quasistatic, curvature-involving (thermodynamic) free boundary condition, both of them contributing to interpret the (mainly late-stage) growth process in terms of a prototype ion-channeling effect. An overall diffusion function contains quantitative signatures of both boundary conditions mentioned and indicates whether the new phase grows as an orderly phase or a converse scenario occurs. This situation can be treated in a quite versatile way both numerically and analytically, within a generalized Smoluchowski framework. This study can help in (1) elucidating some dynamic puzzles of a complex crystal formation vs biomolecular aggregation, also those concerning ion-channel formation, and (2) seeing how ion-channel-type dynamics of non-Markovian nature may set properly the pace of model (dis)ordered protein aggregation.

Condensation of a vapor bubble in submicrometer container

Condensation of a spherically symmetric submicrometer size vapor bubble is studied using diffuse interface hydrodynamic model supplemented by the van der Waals equation of state with parameters characteristic for argon. The bubble, surrounded by liquid, is held in a container of constant volume with temperature of the wall kept fixed. The condensation is triggered by a sudden rise of the wall temperature. We find that in the same container and subjected to a similar increase of the wall temperature the condensation process is totally different from the opposite process of droplet evaporation. In particular, the rapid change of the wall temperature excites the wave, which hits the interface and compresses the bubble, leading to a considerable increase of the temperature inside. The condensation of the submicrometer size bubble takes tens of nanoseconds, whereas evaporation of the same size droplet lasts roughly 50 times longer. In contrast to evaporation the condensation process is hardly quasistationary.