论文标题
如扩散界面模型所述，液膜的动力学
The dynamics of liquid films, as described by the diffuse-interface model
论文作者
论文摘要
研究了液体薄层的动力学，即在平坦的固体基材和无限厚的饱和蒸气层之间的动力学。液体和蒸气是相同流体的两个阶段，由弥漫性接口模型控制。底物保持在固定温度下，但是在大部分流体中，温度可以变化。假定液体/蒸气界面的坡度$ \ varepsilon $，其厚度与膜的厚度也很小。确定了三个渐近方案，具体取决于蒸气与液体密度比$ρ_{v}/ρ_{l} $。如果$ρ_{v}/ρ_{l} \ sim1 $（这意味着温度是可比较但不一定接近临界值的），则界面的演变由液体/蒸气相过渡引起的垂直流动，而水平流量可忽略不计。在限制中，$ρ_{v}/ρ_{l} \ rightarrow0 $，它是相反的方式，存在一个中间政权，$ρ_{v}/ρ_{l} \ sim \ sim \ sim \ sim \ varepsilon^{4/3} $，在两个效果的情况下是相同的效果。仅$ρ_{v}/ρ_{l} \ rightarrow0 $限制在数学上与不可压缩的（navier-stokes）液体相似，而对其他两个方案的渐近方程则是不同类型的。
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 $\varepsilon$ 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 $ρ_{v}/ρ_{l}$. If $ρ_{v}/ρ_{l}\sim1$ (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 $ρ_{v}/ρ_{l}\rightarrow0$, it is the other way around, and there exists an intermediate regime, $ρ_{v}/ρ_{l}\sim\varepsilon^{4/3}$, where the two effects are of the same order. Only the $ρ_{v}/ρ_{l}\rightarrow0$ 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.
