TY - JOUR

T1 - The dynamics of liquid films, as described by the diffuse-interface model

AU - Benilov, E. S.

N1 - Publisher Copyright:
© 2020 Author(s).

PY - 2020/11/1

Y1 - 2020/11/1

N2 - The dynamics of a thin layer of liquid between a flat solid substrate and an infinitely thick layer of saturated vapor is examined. The liquid and vapor are two phases of the same fluid governed by the diffuse-interface model. The substrate is maintained at a fixed temperature, but in the bulk of the fluid, the temperature is allowed to vary. The slope ϵ of the liquid/vapor interface is assumed to be small, as is the ratio of its thickness to that of the film. Three asymptotic regimes are identified, depending on the vapor-to-liquid density ratio ρv/ρl. If ρv/ρl ∼1 (which implies that the temperature is comparable, but not necessarily close, to the critical value), the evolution of the interface is driven by the vertical flow due to liquid/vapor phase transition, with the horizontal flow being negligible. In the limit ρv/ρl → 0, it is the other way around, and there exists an intermediate regime, ρv/ρl ∼ϵ4/3, where the two effects are of the same order. Only the ρv/ρl → 0 limit is mathematically similar to the case of incompressible (Navier-Stokes) liquids, whereas the asymptotic equations governing the other two regimes are of different types.

AB - The dynamics of a thin layer of liquid between a flat solid substrate and an infinitely thick layer of saturated vapor is examined. The liquid and vapor are two phases of the same fluid governed by the diffuse-interface model. The substrate is maintained at a fixed temperature, but in the bulk of the fluid, the temperature is allowed to vary. The slope ϵ of the liquid/vapor interface is assumed to be small, as is the ratio of its thickness to that of the film. Three asymptotic regimes are identified, depending on the vapor-to-liquid density ratio ρv/ρl. If ρv/ρl ∼1 (which implies that the temperature is comparable, but not necessarily close, to the critical value), the evolution of the interface is driven by the vertical flow due to liquid/vapor phase transition, with the horizontal flow being negligible. In the limit ρv/ρl → 0, it is the other way around, and there exists an intermediate regime, ρv/ρl ∼ϵ4/3, where the two effects are of the same order. Only the ρv/ρl → 0 limit is mathematically similar to the case of incompressible (Navier-Stokes) liquids, whereas the asymptotic equations governing the other two regimes are of different types.

UR - http://www.scopus.com/inward/record.url?scp=85095866483&partnerID=8YFLogxK

U2 - 10.1063/5.0027152

DO - 10.1063/5.0027152

M3 - Article

AN - SCOPUS:85095866483

SN - 1070-6631

VL - 32

JO - Physics of Fluids

JF - Physics of Fluids

IS - 11

M1 - 112103

ER -