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Marangoni Instability in a Fluid Layer with Insoluble Surfactant
Abstract: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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076032Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1571
 H. Bénard, "Les tourbillons cellulaires dans une nappe liquid," Revue Générale des Sciences Pures et Appliquées, vol. 11, pp. 1261−1271, 1900.
 L. Rayleigh, "On convection currents in a horizontal layer of fluid with the higher temperature is on the other side," Philosophical Magazine, vol. 32, 529−543, 1916.
 J.R.A. Pearson, "On convection cells induced by surface tension," Journal of Fluid Mechanics, vol. 4, 489−500, 1958.
 M. Takashima, "Surface tension driven instability in a horizontal liquid layer with a deformable surface, I. Stationary convection," Journal of the Physical Society of Japan, vol. 50, pp. 2745−2750, 1981.
 M. Takashima, "Surface tension driven instability in a horizontal liquid layer with a deformable surface, II. Overstability," Journal of the Physical Society of Japan, vol. 50, pp. 2751−2756, 1981.
 H. H. Bau, "Control of Marangoni-Bénard convection," International Journal of Heat and Mass Transfer, vol. 42, pp. 1327−1341, 1999.
 S. Awang Kecil, and I. Hashim, "Control of Marangoni instability in a layer of variable-viscosity fluid," International Communications in Heat and Mass Transfer, vol. 35, pp. 1368−1374, 2008.
 M. I. Char, and K. T. Chiang, "Stability analysis of Bénard-Marangoni convection in fluids with internal heat generation," Journal of Physics D: Applied Physics, vol. 27, pp. 748−755, 1994.
 Zh. Kozhoukharova, and C. Rozé, "Influence of the surface deformability and variable viscosity on buoyant-thermocapillary instability in a liquid layer," The European Physical Journal B, vol. 8, pp. 125−135, 1999.
 N. Rudraiah, and V. Prasad, "Effect of Brinkman boundary layer on the onset of Marangoni convection in a fluid-saturated porous layer," Acta Mechanica, vol. 127, pp. 235−246, 1998.
 A. B. Mikishev, and A. A. Nepomnyashchy, "Long-wavelength Marangoni convection in a liquid layer with insoluble surfactant: linear theory," Microgravity Science Technology, vol. 22, pp. 415−423, 2010.