Large-Scale Marangoni Convection in a Liquid Layer with Insoluble Surfactant under Heat Flux Modulation (original) (raw)
Related papers
2010
The subject of this paper is the long-wave Marangoni convection in a horizontal liquid layer with insoluble surfactant absorbed on the free surface. The surfactant is convected by interfacial velocity field and diffuses over the interface but not into the bulk of the fluid. The layer is subjected to a transverse temperature gradient. The buoyancy effects are negligible as compared to the Marangoni forces. We consider both cases of flat nondeformable and deformable surface. The linear stability analysis of this system is performed. It is shown that in both cases of the upper surface monotonic and oscillatory modes exist. Convection thresholds are determined and the critical Marangoni numbers for monotonic as well as for oscillatory mode are obtained. It is shown that the monotonic long-wave instability is more dangerous than oscillatory one only for small elasticity numbers, if the Lewis number is small.
The subject of this paper is the long-wave Marangoni convection in a horizontal liquid layer with insoluble surfactant absorbed on the free surface. The surfactant is convected by interfacial velocity field and diffuses over the interface but not into the bulk of the fluid. The layer is subjected to a transverse temperature gradient. The buoyancy effects are negligible as compared to the Marangoni forces. We consider both cases of flat nondeformable and deformable surface. The linear stability analysis of this system is performed. It is shown that in both cases of the upper surface monotonic and oscillatory modes exist. Convection thresholds are determined and the critical Marangoni numbers for monotonic as well as for oscillatory mode are obtained. It is shown that the monotonic long-wave instability is more dangerous than oscillatory one only for small elasticity numbers, if the Lewis number is small.
We consider the long-wave Marangoni instability in a heated liquid layer covered by insoluble surfactant. The system of nonlinear equations derived in our previous work is regularized in the limit of strong surface tension. Recent research shows that, without the surfactant, a large-scale oscillatory instability mode exists in the interval of wave numbers k = O(Bi 1/2 ) (the Biot number Bi 1). Here we study the influence of the surfactant on the Marangoni oscillations. The bifurcation analysis for traveling waves and counterpropagating waves is performed. The types of bifurcation and selected pattern depend on the elasticity number and on the Biot number. Specifically, at small elasticity number, both types of waves are supercritical.
Marangoni instability of a liquid layer with insoluble surfactant under heat flux modulation
The European Physical Journal Special Topics, 2013
We investigate the parametric excitation of Marangoni convection by a periodic flux modulation in a liquid layer with insoluble surfactant absorbed on the nondeformable free surface. The stability analysis of the convective system is performed for arbitrary wave numbers of the disturbances. An interesting feature of the onset of convection is the existence of bifurcating neutral curves with double minima, one of which corresponds to a quasi-periodic solution, and the other one corresponds to a subharmonic solution. The evolution of the subharmonic instability region depending on the amplitude of the external heat flux modulation and the frequency of the modulation is studied. The quasi-periodic neutral curve is close to the oscillatory neutral curve of the nonmodulated problem.
Nonlinear large-scale Marangoni convection in a heated liquid layer with insoluble surfactant
The nonlinear development of monotonic and oscillatory long-wave Marangoni instabilities in a heated horizontal layer of a liquid, containing an insoluble surfactant on its surface, is investigated. By means of asymptotic expansions, weakly nonlinear amplitude equations, which govern the evolution of disturbances near the instability threshold, are derived. It turns out that both kinds of instabilities are subcritical; therefore, the asymptotic analysis does not allow us to find any stable supercritical regimes. In the case of sufficiently small concentration of the surfactant, where only monotonic instability is possible, the preferred kind of hexagons is predicted.
Thermal controller effect on Marangoni instability in a fluid layer with insoluble surfactant
2015
The Marangoni convective instability in a horizontal fluid layer with the insoluble surfactant and nondeformable free surface is investigated. The surface tension at the free surface is linearly dependent on the temperature and concentration gradients. At the bottom surface, the temperature conditions of uniform temperature and uniform heat flux are considered. By linear stability theory, the exact analytical solutions for the steady Marangoni convection are derived and the marginal curves are plotted. The effects of surfactant or elasticity number, Lewis number and Biot number on the marginal Marangoni instability are assessed. The surfactant concentration gradients and the heat transfer mechanism at the free surface have stabilizing effects while the Lewis number destabilizes fluid system. The fluid system with uniform temperature condition at the bottom boundary is more stable than the fluid layer that is subjected to uniform heat flux at the bottom boundary.
Large-scale Marangoni convection in a liquid layer with insoluble surfactant of low concentration
The European Physical Journal Special Topics, 2011
We derive a system of amplitude equations describing the evolution of a large-scale Marangoni patterns in a liquid layer with poorly conducting boundaries in the presence of a small amount of an insoluble surfactant on the free flat interface. The presence of quadratic nonlinear terms in the amplitude equation leads to the selection of hexagonal patterns. The type of hexagons bifurcating into the subcritical region, depends on the parameters of the system.
Microgravity Science and Technology, 2017
The paper presents the analysis of the impact of vertical periodic vibrations on the long-wavelength Marangoni instability in a liquid layer with poorly conducting boundaries in the presence of insoluble surfactant on the deformable gas-liquid interface. The layer is subject to a uniform transverse temperature gradient. Linear stability analysis is performed in order to find critical values of Marangoni numbers for both monotonic and oscillatory instability modes. Longwave asymptotic expansions are used. At the leading order, the critical values are independent on vibration parameters; at the next order of approximation we obtained the rise of stability thresholds due to vibration.
Marangoni Instability in a Fluid Layer with Insoluble Surfactant
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2011
The Marangoni convective instability in a horizontal fluid layer with the insoluble surfactant and nondeformable free surface is investigated. The surface tension at the free surface is linearly dependent on the temperature and concentration gradients. At the bottom surface, the temperature conditions of uniform temperature and uniform heat flux are considered. By linear stability theory, the exact analytical solutions for the steady Marangoni convection are derived and the marginal curves are plotted. The effects of surfactant or elasticity number, Lewis number and Biot number on the marginal Marangoni instability are assessed. The surfactant concentration gradients and the heat transfer mechanism at the free surface have stabilizing effects while the Lewis number destabilizes fluid system. The fluid system with uniform temperature condition at the bottom boundary is more stable than the fluid layer that is subjected to uniform heat flux at the bottom boundary.