Marangoni instability in ultrathin two-layer films

Abstract

The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film on a heated or cooled substrate, is considered. The problem is solved by means of a linear stability theory and nonlinear simulations. Nontrivial change of the droplet shape in the presence of the Marangoni effect, which manifests itself as the deformation of a “plateau” into an “inkpot,” is observed. The appearance of the threshold oscillations predicted by the linear stability theory is confirmed by nonlinear simulations.

Linear instability analysis of thermocapillary convection in a bilayer system

“…The linear stability analysis revealed the existence of stationary and oscillatory unstable modes in this bilayer system. However, the complex coupling modes in the two-laye r flow system could not be studied by the long-wave theory [16][17][18]. Aside from that, to our knowledge, in previous works, oscillatory modes in multi-layer flow systems are all coupled with Rayleigh effects.…”

“…In [14,15], direct simulatio n preformed the nonlinear dynamics of system, and the finite-difference method was applied by considering a periodic boundary conditions in the lateral direction. Nepomnyashch y and Simanovskii [16] studied Marangoni instability in ultrathin twolayer films, and van der Waals forces were included in their model. Both linear and nonlinear analyses were employed to investigate the problem [16].…”

“…Nepomnyashch y and Simanovskii [16] studied Marangoni instability in ultrathin twolayer films, and van der Waals forces were included in their model. Both linear and nonlinear analyses were employed to investigate the problem [16]. Nepomnyashch y and Simanovskii [17] further investigated dynamics of the two-laye r films subjected to horizontal temperat ure gradient under the gravity effect.…”

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.…”