טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentWeidenfeld Michael
SubjectMarangoni Instability of a Liquid Layer in an Unsteady
(Evolving) Temperature Field
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Itzchak Frankel
Full Thesis textFull thesis text - English Version


Abstract

Thin liquid layers appear in a variety of natural phenomena and engineering processes. Hydrodynamic instability may degrade the quality of these processes. The Marangoni-Bénard instability is such a mechanism which depends on surface-tension non-uniformities due to surface-temperature non-uniformities.

The problem of Marangoni-Bénard instability was extensively investigated throughout the literature; however, so far the focus was set to two main streams. The first main stream, postulate linear reference temperature profile which is consistent with the assumption of fast thermal relaxation processes compared with perturbations evolution. The second, considers quasi-steady non-linear reference temperature profiles, which is consistent with very slow thermal relaxation processes compared with perturbations evolution, so the reference temperature field is “frozen” throughout the instability analysis. Both main research streams lead to the formulation of an eigenvalue problem.

In many processes, the reference temperature field varies with time. Particularly at early times following the formation of the layer. In the present work we performed a linear, temporal, stability analysis of a thin liquid layer cooled from above assuming small perturbations. In contrast to the standard steady or quasi-steady approach which leads to an eigenvalue problem, we formulate and solve an initial value problem for the evolution of perturbations.

The results show that the dominant perturbations leading to instability have short-wavelengths compared with the depth of the fluid layer and that the convection is confined to a thermal boundary layer near the surface.

The effect of introducing perturbations during the relaxation process was studied and it was shown that the introduction time can significantly affect perturbations growth. A criterion to find the introduction time to give the most substantial growth was obtained.

The effect of Prandtl number was studied. It was found that increasing Prandtl number destabilizes the system due the velocity response time to temperature perturbations variation which is accelerated when Prandtl number is increased.