Line-tension-induced scenario of heterogeneous nucleation on a spherical substrate and in a spherical cavity

Abstract

Line-tension-induced scenario of heterogeneous nucleation is studied for a lens-shaped nucleus with a finite contact angle nucleated on a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension on the free energy of a critical nucleus can be separated from the usual volume term. By comparing the free energy of a lens-shaped critical nucleus of a finite contact angle with that of a spherical nucleus, we find that a spherical nucleus may have a lower free energy than a lens-shaped nucleus when the line tension is positive and large, which is similar to the drying transition predicted by Widom [B. Widom, J. Phys. Chem. 99 2803(1995]. Then, the homogeneous nucleation rather than the heterogeneous nucleation will be favorable. Similarly, the free energy of a lens-shaped nucleus becomes negative when the line tension is negative and large. Then, the barrier-less nucleation with no thermal activation called athermal nucleation will be realized.

Line tension and morphology of a sessile droplet on a spherical substrate

“…Since the droplet volume is conserved, the radius r of the droplet changes as the contact angle θ on the spherical substrate is altered. For a given spherical substrate with radius R, the droplet volume characterized by ρ 180 , and the size parameter ρ (θ) as a function of the contact angle θ, are determined from the implicit equation We also show the contact angle θ = cos −1 (1/ρ 180 ) for the fixed radius ρ 180 (dashed curve), which is characteristic of the nucleation problem [12,22]. The contact line can cross the equator as the size parameter ρ (θ) changes as a function of θ (see Fig.…”

Size-dependent contact angle and the wetting and drying transition of a droplet adsorbed onto a spherical substrate: Line-tension effect

“…where ρ c is the radius of the droplet when the contact angle is θ c . In this case, the equilibrium contact angle is given simply by the Young's contact angle θ Y , and the contact line coincides with the equator of the spherical substrate [23]. In other words, the equilibrium contact angle is simply given by the Young's contact angle (θ e = θ Y ) and it is not affected by the presence of the line tension when the contact line coincides with the equator (θ e = θ c ).…”

“…We previously considered the line-tension effects on the morphology of a volatile [22,23] and a non-volatile [24,25] liquid droplet placed on a convex spherical substrates and a concave spherical cavity. Here, we extend our previous work [25] and focus on the evolution of the droplet morphology with respect to the liquid volume.…”

“…Unfortunately, there are few previous studies of the line-tension effect, and those that exist are mainly on flat substrates [9,[15][16][17], or on convex spherical substrates [18][19][20][21]. We have previously derived an analytical formula for the Gibbs free energy [22,23] and the Helmholtz free energy [24,25] of a droplet placed on a spherical substrate and on the inner wall of a spherical cavity. In this paper, we will consider the morphological phase transition induced by the volume change of a spherical droplet due to the presence of line tension, as shown in Fig.…”

Effect of line tension on axisymmetric nanoscale capillary bridges at the liquid-vapor equilibrium

“…Most of those theoretical studies rely on the atomic simulations [15,32], the mesoscopic disjoining pressure, and the density functional theory using various model surface potentials [12,13,29,30]. However, the classical capillary theory using the macroscopic concepts such as the surface tension [17,33] and the line tension [33,34] is still useful [29,35,36]. In particular, the analytical or semi-analytical results obtained from the classical capillary theory have been useful to understand the physics of capillary phenomena and to analyze experimental results directly [16,24].…”