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On Marangoni effects in a heated thin fluid layer with a monolayer surfactant. I: Model development and stability analysis. (English) Zbl 1063.76033
Summary: We develop a model for surface tension driven flow induced by an insoluble surfactant monolayer on a heated thin fluid layer. The mathematical model is based on a perturbation analysis for a thin fluid layer. The resulting model involves coupling of flow and heat transfer to an additional transport equation for surfactant concentration on the surface. We develop the stability analysis of this coupled system. We characterize the stability behaviour and induced wave motion into four parametric regions based on linear stability analysis. A finite element formulation and numerical studies of the behaviour in various stability regimes are given in Part II [see the following entry].

MSC:
76E17 Interfacial stability and instability in hydrodynamic stability
76D45 Capillarity (surface tension) for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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