Linear stability analysis thin films

Pease, L.F., Russel, W.B. Electrostatically induced submicron patterning of thin perfect and leaky dielectric films A generalized linear stability analysis. J. Chem. Phys. 118(8), 3790-3803 (2003)... 

The condition of instability vis-a-vis stability of a thin film in terms <6 or II (or AG) as a function of h emerges from linear stability analysis (LSA) [33-38,65]. In order to facilitate the discussion of LSA, a brief summary of the kqr theoretical results on thin film instability is presented here. 

From linear stability analysis, two nondimensional numbers governing the instability of thin liquid film are... 

Theoretical analysis of sheeting in the drainage of thin liquid films has been conducted in [359]. Sheeting dynamics and hole formation (i.e. black spot formation) was described by non-linear hydrodynamic stability analysis based on the equilibrium oscillatory structural component of disjoining pressure. The effect of stepwise thinning, accompanied by formation of holes , was described qualitatively. It is rather arguable whether the term holes for a black spot is appropriate since in 1980 holes in NBF were described as lack of molecules. The use the same term for two different formations is at least confusing. Besides, to have a hole in a CBF is almost as to have a hole in the sea water . 

Also of significance is that initial instability of a thin film in accordance with the above mechanism does not inevitably lead to film rupture. The analysis, like all others in this chapter, is based on linear stability theory, and hence is valid only for small amplitude perturbations. It has been observed experimentally that at low surfactant concentrations instability of a film some tens of nanometers in thickness does produce rupture. But for many surfactants it is found that above a critical concentration, the instability leads to formation of black films which are only slightly thicker than the total length of two surfactant molecules (She-ludko, 1967). These black films can be very stable and are a major factor in foam stabihty. 

The authors review the theoretical analysis of the hydrodynamic stability of fluid interfaces under nonequilibrium conditions performed by themselves and their coworkers during the last ten years. They give the basic equations they use as well as the associate boundary conditions and the constraints considered. For a single interface (planar or spherical) these constraints are a Fickean diffusion of a surface-active solute on either side of the interface with a linear or an erfian profile of concentration, sorption processes at the interface, surface chemical reactions and electrical or electrochemical constraints for charged interfaces. General stability criteria are given for each case considered and the predictions obtained are compared with experimental data. The last section is devoted to the stability of thin liquid films (aqueous or lipidic films). 

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