Decomposition of a two-layer thin liquid film flowing under the action of Marangoni stresses

Abstract

The decomposition of a laterally heated two-layer film caused by intermolecular forces is considered. Long-wave nonlinear equations, which incorporate thermocapillary flows and the influence of the van der Waals forces, are derived. The main stages of the three-dimensional evolution of films are presented. The influence of the thermocapillary flow on the morphology and the evolution of unstable two-layer films is investigated. It is shown that the film instability leads typically to formation of droplets driven by the thermocapillary flow. Anisotropic coalescence of droplets and formation of rivulets are observed.

Nonlinear Marangoni waves in a two-layer film in the presence of gravity

“…Evolution equations (15) and (16) have been discretized by central differences for spatial derivatives and solved using an explicit scheme. Periodic boundary conditions have been applied on the boundaries of the computational region L × L. Initial conditions for h j , j = 1, 2 have been chosen in such a way that the mean value of h 1 (X, Y, 0) was equal to 1 and the mean value of h 2 (X, Y, 0) was equal to h, where h > 1.…”

“…14 and 15. The development of instabilities has been studied in the case of a temperature gradient directed along the interfaces 16 and across the layers, 9,17 as well as in the case where the temperature gradient is inclined with respect to the interfaces. 18,19 In the present paper, we consider the influence of the gravity on the instabilities of non-isothermal two-layer films under conditions, where the intermolecular forces are irrelevant.…”

The Influence of Gravity on the Dynamics of Non-Isothermic Ultra-Thin Two-Layer Films

“…The dynamics of ultra-thin films under the joint action of the Marangoni effect and the van der Waals forces has been studied in Merkt et al (2005), Pototsky et al (2005), Nepomnyashchy and Simanovskii (2006, 2007, 2008.…”

Controlling Nanoparticles Formation in Molten Metallic Bilayers by Pulsed-Laser Interference Heating

“…This applied modeling paper is motivated by the recent experiments on dewetting of non-reactive, immiscible metallic bilayers [16], and the need to better understand the physical mechanisms leading to spatial ordering of particles and the morphological pathways towards the final particle morphologies. The experimental [17][18][19][20][21][22][23][24] and theoretical [25][26][27][28][29][30][31][32][33][34] studies of the instabilities and dynamics of bilayer thin films so far have been largely limited to aqueous and polymer systems under isothermal conditions. Non-isothermal dewetting even in such more conventional systems has not been fully investigated theoretically.…”

“…[25,26] the equation set that accounts for the Marangoni effect is derived, but only the analysis and some computations in the isothermal case are performed; and in Refs. [32][33][34] either a special set of Hamaker coefficients is considered, such that dewetting exhibits autophobic behavior, or in addition a longitudinal temperature gradient is considered. Also, to our knowledge, even in the isothermal case no combined experimental/theoretical study has been published and thus the theory has not been quantitatively matched to an experiment.…”