Molecular dynamics (MD) study of equilibrium system of a single argon nanodroplet and its surrounding argon vapor is carried out to address a fundamental issue whether the thermodynamic description is applicable to the nanoscale inhomogeneous system. The numerical result is sufficiently reliable so that it can identify the smallest droplet standing stably over 200 ns. The validity of the Laplace equation for nanodroplet is proved by a purely mechanical argument on the basis of directly computed normal and tangential pressures in the transition layer. Furthermore, it is demonstrated that the chemical potentials of liquid and vapor phases are not equal when a droplet is so small that the number of molecules consisting the transition layer may be comparable to that in the droplet. The Kelvin equation does not hold in such a case.

In this study, we investigated nanodroplet spreading at the early stage after the impact using molecular dynamics simulations by changing the magnitude of the intermolecular force between the liquid and wall molecules. We showed that the droplet deformation after the impact greatly depends on the intermolecular force. The temporal evolution of the spreading diameters was measured by the cylindrical control volume for several molecular layers in the vicinity of the wall. At the early stage of the nanodroplet impact, the normalized spreading radius of the droplet is proportional to the square root of the normalized time,t. This result is understood by the geometrical consideration presented by Rioboo et al.["Time evolution of liquid drop impact onto solid, dry surfaces," Exp. Fluids 33, 112-124 (2002)]. In addition, we found that as the intermolecular force between the liquid and wall becomes stronger, the normalized spreading diameter of the first molecular layer on the wall remains less dependent on the impact velocity. Furthermore, the time evolution of the droplet spreading changes from √t to logt with time. C 2016 AIP Publishing LLC.

Two-dimensional Navier-Stokes equations are solved in an analytical way to clarify characteristics of low-Re flows in a microscopic channel consisting of two intersecting permeable walls, the intersection of which is supposed to be a sink or a source. Such flows are, therefore, considered to be an extension of the so-called Jeffery-Hamel flow to the permeable wall case. A set of nonlinear forth-order ordinary differential equations are obtained, and their solutions are sought for the small permeable velocity compared with the main flow one by a perturbation method. The solutions contain the solutions found in the past, such as the flow between two parallel permeable walls studied by Berman and the Jeffery-Hamel flow between the impermeable walls as special cases. Velocity distribution and friction loss in pressure along the main stream are represented in the explicit manner and compared with those of the Jeffery-Hamel flow. Numerical examples show that the wall permeability has a great influence on the friction loss. Furthermore, it is shown that the convergent main flow accompanied with the fluid addition through the walls is inversely directed away from the origin due to the balance of the main flow and the permeable one, while the flow accompanied with fluid suction is just directed toward the origin regardless of conditions.

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When droplets impact on a heated wall, they can levitate owing to the vapor stream generated by the droplet evaporation. This phenomenon is called the Leidenfrost effect, and the vapor layer prevents heat transfer between the droplet and heated wall. In this study, we investigated the influence of the intermolecular force between liquid and solid molecules on the levitating phenomenon, which is caused by heat transfer, for nanodroplets. We used a molecular dynamics (MD) simulation to evaluate the detailed behavior of droplet levitation and investigated the temperature field of the impacting droplet. We found that the droplet levitation was likely to occur at lower temperature when the intermolecular force was stronger. In addition, when the intermolecular force was strong enough, the liquid molecules stayed on the heated wall and an adsorption layer was formed. This adsorption layer exceeded the critical temperature of the liquid molecules, and the existence of the adsorption layer significantly affected the onset of the droplet levitation. IntroductionThe impact of droplets on a heated wall can be seen in spray cooling for heated steel, electronic devices, and other settings and applications [1,2]. The utilized droplets have become smaller (tens of a micrometer) and faster (tens of m/s) with the recent progression of technology [3]. When a droplet impacts