Lifetime of a Nanodroplet: Kinetic Effects and Regime Transitions

Abstract

A transition from a d 2 to a d law is observed in molecular dynamics (MD) simulations when the diameter (d) of an evaporating droplet reduces to the order of the vapor's mean free path; this cannot be explained by classical theory. This Letter shows that the d law can be predicted within the Navier-Stokes-Fourier (NSF) paradigm if a temperature-jump boundary condition derived from kinetic theory is utilized. The results from this model agree with those from MD in terms of the total lifetime, droplet radius, and temperature, while the classical d 2 law underpredicts the lifetime of the droplet by a factor of 2. Theories beyond NSF are also employed in order to investigate vapor rarefaction effects within the Knudsen layer adjacent to the interface.

Efficient simulation of non-classical liquid–vapour phase-transition flows: a method of fundamental solutions

“…) these are obtained as Here, superscripts ‘’ and ‘’ denote the pressure-driven case ( and ) and temperature-driven case ( and ), respectively. The results of these two problems can be combined to evaluate the total evaporative mass and heat flux from the droplet (Rana et al 2019). Owing to the microscopic reversibility of the evaporation and condensation processes the Onsager reciprocity relations hold, which give (Chernyak & Margilevskiy 1989; Rana et al 2018 b ).…”

“…Extension of the current work to unsteady flows and coupling to liquid dynamics (Rana et al 2019;Chubynsky et al 2020) can be considered in the future, the liquid phase can be modelled as an incompressible fluid (Stokeset/Oseenlet and heatlet) and the vapour phase modelled via the CCR model. However, it will require solving the moving-boundary problem efficiently within the MFS framework (Jiang et al 2014).…”

“…The far-field conditions are given by T ∞ = 0, p ∞ = 0, that is, we consider the far-field conditions and the droplet radius (R 0 ) for non-dimensionalisation. Throughout this paper we do not consider dynamics within the droplets, surface tension, etc., see Rana et al (2019).…”

“…The classical phase-transition models, found in the literature, assume that the temperature and the velocity tangential to the interface are continuous across it. However, it is now well established, both experimentally and theoretically (McGaughey & Ward 2002; Bond & Struchtrup 2004; Rana, Lockerby & Sprittles 2019), that such assumptions are invalid at a nano-confined liquid–vapour interface. For such small length scales, the Knudsen number lies in the transition regime (or beyond) and a difference in velocity and temperature jump are observed across the interface, thus, it is important to employ models capable of describing strong non-equilibrium effects that occur at high Knudsen numbers.…”

“…For such small length scales, the Knudsen number lies in the transition regime (or beyond) and a difference in velocity and temperature jump are observed across the interface, thus, it is important to employ models capable of describing strong non-equilibrium effects that occur at high Knudsen numbers. In Rana et al (2019), the lifetime of an evaporating nanodroplet was studied. The study revealed that, when the drop size is large (larger than a micrometre), the square of its diameter decreases in proportion to time, this is known as the -law.…”