Generation of nonlinear Marangoni waves in a two-layer film by heating modulation

Abstract

Longwave Marangoni convection in two-layer films under the action of heating modulation is considered. The analysis is carried out in the lubrication approximation. The capillary forces are assumed to be sufficiently strong, and they are taken into account. Periodic or symmetric boundary conditions are applied on the boundaries of the computational region. Numerical simulations are performed by means of a finite-difference method. Two regions of parametric instabilities have been found. In the first region, one observes the competition or coexistence of standing waves parallel to the boundaries of the computational region. The multistability of the flow regimes is revealed. In the second region, the regimes found in the case of periodic boundary conditions are more diverse than in the case of symmetric boundary conditions.

The influence of temporal heating modulation on non-isothermal floating droplet dynamics

“…2009). Specifically, in the case of an oscillatory Marangoni instability, the modulation of the substrate temperature can lead to the parametric excitation of Marangoni waves (Nepomnyashchy & Simanovskii 2015). In the supercritical parameter region, the action of heating modulation on the nonlinear Marangoni wave either creates a two-frequency quasiperiodic motion or leads to frequency locking (Nepomnyashchy & Simanovskii 2020).…”

“…The manifestations of the Marangoni instabilities in multilayer fluid systems are much more diverse (for a review, see Nepomnyashchy, Simanovskii & Legros (2012)). The instabilities can develop for heating both from below and from above, and it can be both monotonic and oscillatory (Nepomnyashchy & Simanovskii 2007).…”

“…In the case of Marangoni instability caused by heating, the temporal modulation of heating intensity can be a more efficient way for instability excitation and control (Gershuni, Nepomnyashchy & Velarde 1992;Or & Kelly 2002;Smorodin et al 2009). Specifically, in the case of an oscillatory Marangoni instability, the modulation of the substrate temperature can lead to the parametric excitation of Marangoni waves (Nepomnyashchy & Simanovskii 2015). In the supercritical parameter region, the action of heating modulation on the nonlinear Marangoni wave either creates a two-frequency quasiperiodic motion or leads to frequency locking (Nepomnyashchy & Simanovskii 2020).…”

Effect of charge modulation on the electroconvective flow of a low conducting liquid

“…Moreover, several nonlinear modes that differ in their properties, such as the intensity of heat and mass transfer, usually coexist. Convection in binary mixtures [15] and non-uniform magnetic fluids [16], in systems with interfacial surfaces [17,18], and electroconvection of nonisothermal liquid [6][7][8]19] are an incomplete list of problems that manifest such behaviour. Moreover, several nonlinear modes that differ in their properties, such as the intensity of heat and mass transfer, usually coexist.…”

Instability of nanometric fluid films on a thermally conductive substrate

“…Instabilities due to Marangoni effect have been studied extensively, and we will focus here exclusively on the settings that involve deformation of the free surface. The studies are often carried out using the long-wave approach; within this framework, a significant body of work has been established in the recent years, including extensive research on linear and weakly nonlinear instability mechanisms [4][5][6], as well as discussion of monotone and oscillatory type of Marangoni effect governed instabilities [3,[7][8][9] (only a subset of relevant works is listed here). While most of the works have focused on the regime where gravitational effects are relevant, there is also an increasing body of work considering the interplay between the instabilities caused by Marangoni effect and by liquid-solid interaction that becomes important for the films on nanoscale, see, e.g., [10][11][12][13].…”