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.

Figure 1

Schematic of coordinates for system showing inner surface at $r$, vapor bubble between $r$ and $R$, and the bulklike liquid. Note that $d$ is chosen to be large enough that any pressure waves reflected from the outer boundary, where the pressure is held constant, do not have sufficient time to return to the bubble region during the course of simulation.

Figure 2

The Gibbs free energy change, Eq. (1), at $T=0.85T_c$ for argon on a goldlike nanosphere for $\widetilde{\delta r}=1$ nm, for hydrophilic ($\theta =1.26$ rad) and hydrophobic ($\theta =1.57$ rad) surfaces with different strengths of solid-fluid interaction, as determined by ${\gamma }_{\mathrm{SL}}/{\gamma }_{\mathrm{LV}}$. (Inset) The critical radius estimates for the same angles as a function of ${\gamma }_{\mathrm{SL}}/{\gamma }_{\mathrm{LV}}$.

Figure 3

Heat flux into hot boundary for varying inner radius $r_{np}$. The calculation uses a fixed kinematic viscosity $1.67\times {10}^{-6}{\mathrm{m}}^2/\mathrm{s}$, with $\alpha =0.208$, $\beta =47.192$, $\delta ={10}^{-3}$, and $\chi =-{10}^{-3}$.

Figure 4

Density profile at $t=3500$ vs $x$, the radial distance from the particle surface see also (1) for several different inner radii $r$ showing liquid phase stabilization at small radius and bubble formation and expansion at large radius, converging to the planar case as $r\to \infty$. The viscosity is $\nu =1.67\times {10}^{-6}{\mathrm{m}}^2/\mathrm{s}$ and $\alpha =0.208$, $\beta =47.192$, $\delta ={10}^{-3}$, and $\chi =-{10}^{-3}$, a weakly hydrophilic surface.

Figure 5

Several snapshots of the temperature profiles for ${\beta }_o=47.192$ and $0.25{\beta }_o$, and $\chi =-{10}^{-3}$. Inset shows a comparison of the density profiles near the interface for $t=1000$. Calculations for a range of $\delta ={10}^{-9}–{10}^{-1}$ show essentially the same behavior.

Figure 6

Heat flux (top) and interfacial density profiles (bottom) for strongly hydrophilic, $\chi =10$, strongly hydrophobic, $\chi =-10$, and neutral, $\chi =0$, interfaces. Inset shows a comparison of the density profiles near the interface for $t=1000$. Calculations are shown for $\delta ={10}^{-2}$. The surface interaction enters in the capillary terms and is much weaker for small $\delta$.