Marangoni Instability in a Fluid Layer with Insoluble Surfactant
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.
[1] H. Bénard, "Les tourbillons cellulaires dans une nappe liquid," Revue
Générale des Sciences Pures et Appliquées, vol. 11, pp. 1261−1271,
1900.
[2] 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.
[3] J.R.A. Pearson, "On convection cells induced by surface tension,"
Journal of Fluid Mechanics, vol. 4, 489−500, 1958.
[4] 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.
[5] 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.
[6] H. H. Bau, "Control of Marangoni-Bénard convection," International
Journal of Heat and Mass Transfer, vol. 42, pp. 1327−1341, 1999.
[7] 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.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[1] H. Bénard, "Les tourbillons cellulaires dans une nappe liquid," Revue
Générale des Sciences Pures et Appliquées, vol. 11, pp. 1261−1271,
1900.
[2] 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.
[3] J.R.A. Pearson, "On convection cells induced by surface tension,"
Journal of Fluid Mechanics, vol. 4, 489−500, 1958.
[4] 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.
[5] 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.
[6] H. H. Bau, "Control of Marangoni-Bénard convection," International
Journal of Heat and Mass Transfer, vol. 42, pp. 1327−1341, 1999.
[7] 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.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59900", author = "Ainon Syazana Ab. Hamid and Seripah Awang Kechil and Ahmad Sukri Abd. Aziz", title = "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.", keywords = "Analytical solutions, Marangoni Instability,
Nondeformable free surface, Surfactant.", volume = "5", number = "10", pages = "1629-5", }