Cellular thermocapillary convection under evaporation.

摘要

Both linear and nonlinear analyses are performed to investigate cellular thermocapillary convection induced by instability mechanisms in an evaporating liquid layer under a reduced or normal gravity condition. Before performing the analyses, experimental observations were conducted on evaporating organic liquid layers to get some knowledge concerning the behavior of the cellular convection. The transient thermal stratification in the system due to evaporative cooling is initiated from a quiescent and thermal equilibrium state. The analytical and experimental results are in qualitatively good agreement.; The linear analysis stresses the effect of surface expansion energy on the Marangoni instability. It is found that the effect can considerably destabilize the thermocapillary system when the dimensionless system parameter, called the surface expansion number, which couples the local interfacial energy with the surface motion due to thermocapillarity, exceeds 10{dollar}sp{lcub}-3{rcub}{dollar}. An important linear oscillatory convection phenomenon associated with the deformability of the thermocapillary interface, named the thermocapillary wave, is also disclosed by means of a singular perturbation technique.; In the nonlinear analysis, a systematic self-consistent approximation procedure for the evolution of the nonlinear truncated convection model, including evolution of the convection cell size, is developed based on the variational local potential theory. This procedure includes a finite difference scheme for solving the nonlinear partial differential evolution equation and an associated eigenvalue problem. A parametric study is performed to investigate transient properties, stabilities of the convection model, momentum and heart transport, preferred convection cell size (wave number), as well as interfacial deformation. The results include various effects such as thermocapillarity, buoyancy, fluid properties, surface expansibility, interfacial deformability and local evaporative cooling. The results are in accord with the existing analytical and experimental works.