@article{d2816e4af6c842139216d2cc6685b33b,

title = "Nucleation on cylindrical plates: Sharp transitions and double barriers",

abstract = "We apply methods of density-functional theory in statistical mechanics to study the properties of droplets and bubbles formed on a single cylindrical plate or between two such disks immersed in a metastable fluid. Our approach allows us to analyze the properties of different types of aggregates and investigate the effect of disk size, disk separation, and solid-fluid interactions on the dynamics of a liquid-vapor phase transition. The finite size of disks induces nucleation phenomena that are not observed in the cases of either a planar wall or a slit pore. Heterogeneous nucleation on a single disk is characterized by the existence of two distinct types of critical nuclei that control the phase-transition dynamics at different supersaturations. Asymmetric droplets or bubbles formed on one side of the disk are the preferred nucleation path at high supersaturations. However, these types of aggregates become unstable close to the binodal, where they abruptly collapse into nuclei that engulf the cylindrical plates. Droplet or bubble nucleation in between two disks may occur through a free-energy barrier with one or two maxima depending on the value of the system parameters and the supersaturation. Metastable droplets or bubbles corresponding to local minima of the free energy are observed forming between two plates only after density fluctuations in the system achieve a critical size. These types of aggregates only exist for cylindrical plates larger than a minimum size given a fixed distance between the disks. The stability of these droplets and bubbles decreases when the plates are separated.",

author = "B. Husowitz and V. Talanquer",

note = "Funding Information: This work was supported by the National Science Foundation (Grant No. CHE 0241044). FIG. 1. Schematic representation of (a) a cylindrical single plate of radius R and (b) two parallel cylindrical plates separated by a distance L . FIG. 2. Density profiles ρ ( r , z ) for critical liquid nuclei on a single disk with R * = 3.0 , W * = 2.0 , and h * = 2.0 at T r = 0.5 . (a) Annular bump at S = 1.9794 ; (b) engulfing cluster at S = 1.5954 . r * = r ∕ b 1 ∕ 3 and z * = z ∕ b 1 ∕ 3 in this figure. FIG. 3. (a) Work of formation Δ Ω * of critical nuclei as a function of the supersaturation S for a single disk with R * = 3.0 , W * = 2.0 , and h * = 2.0 ( θ 0 = 74.9 ° ) at T r = 0.5 . S α indicates the supersaturation below which annular bumps are no longer stable; S β bounds the region where engulfing critical nuclei can be found. (b) Excess number of particles i e of the corresponding critical nuclei as a function of the supersaturation. FIG. 4. Work of formation Δ Ω * of critical nuclei as a function of the supersaturation S for a single disk with R * = 3.0 and W * = 2.0 at T r = 0.5 , and different values of the surface field: h * = 2.0 ( θ 0 = 74.9 ° ) ; h * = 2.5 ( θ 0 = 56.0 ° ) . FIG. 5. Density profiles ρ ( r , z ) for liquid bridges in between two disks with R * = 5.0 , W * = 3.0 , L * = 8.0 , and h * = 1.5 at T r = 0.5 . ( a ) Liquid bridge at S = 1.7450 ( i e = 264 ) ; (b) liquid bridge at S = 1.8131 ( i e = 686 ) . r * = r ∕ b 1 ∕ 3 and z * = z ∕ b 1 ∕ 3 in this figure. FIG. 6. (a) Work of formation Δ Ω * of liquid bridges as a function of the supersaturation S for two coaxial disks with R * = 5.0 , W * = 3.0 , L * = 8.0 , and h * = 1.5 ( θ 0 = 93.5 ) at T r = 0.5 . (b) Excess number of particles i e of the corresponding clusters as a function of the supersaturation. FIG. 7. Free-energy barrier Δ Ω for the formation of liquid bridges between two disks with R * = 5.0 , W * = 3.0 , L * = 8.0 , and h * = 1.5 at T r = 0.5 . Different curves depict the barrier to nucleation at those supersaturations highlighted in Fig. 6(a) . FIG. 8. Work of formation Δ Ω * of liquid bridges as a function of supersaturation S for two coaxial disks with R * = 5.0 , W * = 3.0 , and L * = 8.0 at T r = 0.5 , and different values of the surface field: h * = 1.0 ( θ 0 = 112.3 ° ) ; h * = 1.25 ( θ 0 = 102.6 ° ) ; h * = 1.5 ( θ 0 = 93.5 ° ) . FIG. 9. Work of formation Δ Ω * of liquid bridges as a function of supersaturation S for two coaxial disks with h * = 1.5 and W * = 3.0 at T r = 0.5 . (a) L * = 8 and different values of the radius R * ; (b) R * = 8 and different values of the disk separation L * . ",

year = "2005",

month = may,

day = "15",

doi = "10.1063/1.1899646",

language = "English (US)",

volume = "122",

journal = "Journal of Chemical Physics",

issn = "0021-9606",

publisher = "American Institute of Physics Publising LLC",

number = "19",

}