On dynamic excitation of Marangoni instability in a liquid layer with insoluble surfactant on the deformable surface (original) (raw)
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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.
Steady Marangoni Instability in a Fluid Layer with Insoluble Surfactant and Internal Heat Generation
The onset of Marangoni instability in a horizontal fluid layer on a rigid plate with a deformable free surface under the influences of insoluble surfactant and internal heat generation subject to a uniform heat flux is considered. The surface tension of the fluid is assumed to depend linearly on temperature and surfactant concentration. A closed form analytical solution for the steady marginal curves is obtained. The effects of various parameters namely the elasticity number, internal heating, Biot number and Crispation number are assessed. Internal heat generation and surface deformability have destabilizing effect while the heat transfer mechanism and surfactant distribution at the free surface show significant stabilizing effects.
On the flow-induced Marangoni instability due to the presence of surfactant
Journal of Fluid Mechanics, 2005
The flow-induced Marangoni instability due to the presence of surfactant is examined for long-wavelength perturbations. A unified view of the underlying mechanisms is provided through revisiting both falling film and two-fluid Couette flow systems. The analysis is performed by inspecting the corresponding coupled set of evolution equations for the interface and surfactant concentration perturbations. While both systems appear to have very similar sets of equations consisting of base flows and Marangoni effects, the origins of stability/instability are identified and illustrated from a viewpoint of vorticity. The base flow rearranges the surfactant distribution and the induced Marangoni flow tends to stimulate the interface's growth. But this destabilizing effect is reduced by effects combining the interface travelling motions and the Marangoni recoil. The competition between these opposing effects determines the system stability, and is elucidated using equations in concert with observations from initial value problems. Moreover, a criterion for the onset of instability can be established in line with the same rationale. The present work not only furnishes a lucid way to clarify the instability mechanisms, but also complements previous studies. Extension to the weakly nonlinear regime is also discussed.
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.
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.
Colloids and Interfaces
Marangoni patterns are created by instabilities caused by thermocapillary and solutocapillary stresses on the deformable free surface of a thin liquid layer. In the present paper, we consider the influence of the insoluble surfactant on the selection and modulational instability of stationary Marangoni patterns near their onset threshold. The basic governing parameters of the problem are the Biot number characterizing the heat-transfer resistances of and at the surface, the Galileo number indicating the role of gravity via viscous forces, and the elasticity number specifying the influence of insoluble surfactant on the interfacial dynamics of the liquid. The paper includes a review of the previous results obtained in that problem as well as new ones.
Physical Review E, 2001
Theoretical studies are performed to explain the mechanism of surface tension auto-oscillations recently found. The Marangoni instability in a system containing a surfactant droplet under the air-water interface is investigated numerically. The simulations, based on the equations of fluid mechanics, take into account convective diffusion and adsorption of the surfactant. The behavior of the system is determined by nonstationary concentration gradients that are nonuniform on the surface as well as in the normal to the surface direction. Initially a slow diffusion dissolution of the drop material takes place. The convective transfer of the surfactant is negligible, the surface tension remains nearly constant and the system parameters change rather slowly during the induction period. With the increase of the concentration gradients the system becomes unstable, resulting in a jump in the convection velocity, surface tension, and adsorption on the surface. The concentration and velocity distributions in the bulk and on the surface are obtained from the numerical solution of the problem. The contributions of different mechanisms of the mass transfer are compared in different stages of the process.