instabilities of a thin viscous film flowing down a uniformly heated plane are investigated in this study. the heating generates a surface tension gradient that induces thermocapillary stresses on the free surface. thus, the film is not only influenced by gravity and mean surface tension but also the thermocapillary force is acting on the free surface. moreover, the heat transfer at the free su...

The spreading of surfactant coated thin liquid films is often accompanied by an instability producing significant film corrugation, fingering and branching. Marangoni stresses, responsible for the rapid and spontaneous spreading, are suspected as the main cause of unstable flow. Traditional eigenvalue analysis of a self-similar solution describing Marangoni driven spreading has predicted only s...

The effectiveness of a proportional feedback control to suppress the Marangoni instability in a variable-viscosity fluid layer with a deformable free upper surface is investigated. Viscosity variation and deformable free surface have destabilizing effects on the stability limit. The stability thresholds for the short-scale mode are strongly dependent on viscosity variation and controller gain w...

The Marangoni e#ect is a frequently observed phenomenon of enhancement of interphase mass transfer in liquid–liquid systems. Such an e#ect, originating from the hydrodynamic instability induced by surface tension sensitivity to surface concentration of transferred solute, is mathematically formulated and numerically simulated for slowly moving single spherical drops in an axisymmetric boundary-...

With the presence of a uniform vertical magnetic field and suspended particles, thermocapillary instability in a horizontal liquid layer is investigated. The resulting eigenvalue is solved by the Galerkin technique for various basic temperature gradients. It is found that the presence of magnetic field always has a stability effect of increasing the critical Marangoni number. Keywords—Marangoni...

The stability of Marangoni roll convection in a liquid-gas system with deformable interface is studied in the case when there is a nonlinear interaction between two modes of Marangoni instability: long-scale surface deformations and short-scale convection. Within the framework of a model derived in [1], it is shown that the nonlinear interaction between the two modes substantially changes the w...

The onset of Marangoni convection in a horizontal fluid layer with internal heat generation overlying a solid layer heated from below is studied. The upper free surface of a fluid is nondeformable and the bottom boundary are rigid and no-slip. The resulting eigenvalue problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and...

Instabilities of a thin viscous film flowing down a uniformly heated plane are investigated in this study. The heating generates a surface tension gradient that induces thermocapillary stresses on the free surface. Thus, the film is not only influenced by gravity and mean surface tension but also the thermocapillary force is acting on the free surface. Moreover, the heat transfer at the free su...