Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

Min Chan Kim; Do-Young Yoon; Eunsu Cho

Korean Journal of Chemical Engineering, Vol.26, No.6, 1461-1466, November, 2009

DOI10.1007/s11814-009-0284-6 Export Citation

Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

Min Chan Kim^†, Do-Young Yoon¹, and Eunsu Cho²

Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea
¹Department of Chemical Engineering, Kwangwoon University, Seoul 139-701, Korea
²Bead & Micro, Inc., Yongin-si, Gyeonggi-do 449-923, Korea

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The onset of Marangoni convection in an initially quiescent spherical droplet subjected to the impulsive change in boundary temperature is analyzed under the linear theory. For this system in which instabilities are driven by interface-tension gradients, a stability analysis on regular cell modes is conducted on the basis of the propagation theory we have developed. The present stability analysis predicts that τc decreases with increasing Ma. For the limiting case of τ →0, the present study approaches the planar limit as expected.

Keywords:Marangoni Convection;Spherical Droplet;Propagation Theory

[References]

Pearson JRA, J. Fluid Mech., 4, 489 (1958)
Scriven LE, Sternling CV, J. Fluid Mech., 19, 321 (1964)
Berg JC, Acrivos A, Adv. Chem. Eng., 6, 61 (1966)
Smith MK, Davis SH, J. Fluid Mech., 132, 119 (1983)
Pirotte O, Lebon G, Appl. Microgravity Tech., 1, 175 (1988)
Hoefsloot HC, Hoogstraten HW, Appl. Microgravity Tech., 106, 2 (1989)
Cloot A, Lebon G, Microgravity Sci. Tech., 3, 44 (1990)
Wilson SK, J. Eng. Math., 28, 427 (1994)
Vidal A, Acrivos A, I&EC Fund., 7, 53 (1968)
Kang KH, Choi CK, Phys. Fluids, 9, 7 (1998)
Kang KH, Choi CK, Hwang IG, AIChE J., 46(1), 15 (2000)
Gumerman RJ, Homsy GM, J. Fluid Mech., 68, 191 (1975)
Tan KK, Thorpe RB, Chem. Eng. Sci., 54(6), 775 (1999)
Tan KK, Int. J. Heat Mass Transf., 48(1), 135 (2005)
Ha VM, Lai CL, Proc. R. Soc. London A, 457, 885 (2001)
Patzer JF, Homsy GM, Phys. Fluids, 24, 567 (1981)
Ha VM, Lai CL, Int. J. Heat Mass Transf., 47(17-18), 3811 (2004)
Kim MC, Park JH, Choi CK, Chem. Eng. Sci., 60(19), 5363 (2005)
Choi CK, Park JH, Kim MC, Heat Mass Transfer., 41, 155 (2004)
Kim MC, Hong JS, Choi CK, AIChE J., 52(7), 2333 (2006)
Kim MC, Choi CK, Yeo JK, Phys. Fluids, 19, 084103 (2007)
Kim MC, Choi CK, Korean J. Chem. Eng., 26, 874 (2006)
Kim MC, Chung TJ, Choi CK, Theoret. Comp. Fluid Dynamics, 18, 105 (2004)
Kim MC, Choi CK, Chem. Eng. Sci., 60(3), 599 (2005)
Kim MC, Choi CK, Yoon DY, Chung TJ, Ind. Eng. Chem. Res., 46(17), 5775 (2007)
Carslaw HS, Jaeger JC, Conduction of heat in solids, 2nd ed., Oxford Univ. Press, UK (1959)
Crank J, The mathematics of diffusion, 2nd ed., Oxford Univ. Press, UK (1975)
Chen JC, Neitzel GP, Jankowski DF, Phys. Fluids, 28, 749 (1985)
Foster TD, Phys. Fluids, 12, 2482 (1969)

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[1] Pearson JRA, J. Fluid Mech., 4, 489 (1958)

[2] Scriven LE, Sternling CV, J. Fluid Mech., 19, 321 (1964)

[3] Berg JC, Acrivos A, Adv. Chem. Eng., 6, 61 (1966)

[4] Smith MK, Davis SH, J. Fluid Mech., 132, 119 (1983)

[5] Pirotte O, Lebon G, Appl. Microgravity Tech., 1, 175 (1988)

[6] Hoefsloot HC, Hoogstraten HW, Appl. Microgravity Tech., 106, 2 (1989)

[7] Cloot A, Lebon G, Microgravity Sci. Tech., 3, 44 (1990)

[8] Wilson SK, J. Eng. Math., 28, 427 (1994)

[9] Vidal A, Acrivos A, I&EC Fund., 7, 53 (1968)

[10] Kang KH, Choi CK, Phys. Fluids, 9, 7 (1998)

[11] Kang KH, Choi CK, Hwang IG, AIChE J., 46(1), 15 (2000)

[12] Gumerman RJ, Homsy GM, J. Fluid Mech., 68, 191 (1975)

[13] Tan KK, Thorpe RB, Chem. Eng. Sci., 54(6), 775 (1999)

[14] Tan KK, Int. J. Heat Mass Transf., 48(1), 135 (2005)

[15] Ha VM, Lai CL, Proc. R. Soc. London A, 457, 885 (2001)

[16] Patzer JF, Homsy GM, Phys. Fluids, 24, 567 (1981)

[17] Ha VM, Lai CL, Int. J. Heat Mass Transf., 47(17-18), 3811 (2004)

[18] Kim MC, Park JH, Choi CK, Chem. Eng. Sci., 60(19), 5363 (2005)

[19] Choi CK, Park JH, Kim MC, Heat Mass Transfer., 41, 155 (2004)

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[21] Kim MC, Choi CK, Yeo JK, Phys. Fluids, 19, 084103 (2007)

[22] Kim MC, Choi CK, Korean J. Chem. Eng., 26, 874 (2006)

[23] Kim MC, Chung TJ, Choi CK, Theoret. Comp. Fluid Dynamics, 18, 105 (2004)

[24] Kim MC, Choi CK, Chem. Eng. Sci., 60(3), 599 (2005)

[25] Kim MC, Choi CK, Yoon DY, Chung TJ, Ind. Eng. Chem. Res., 46(17), 5775 (2007)

[26] Carslaw HS, Jaeger JC, Conduction of heat in solids, 2nd ed., Oxford Univ. Press, UK (1959)

[27] Crank J, The mathematics of diffusion, 2nd ed., Oxford Univ. Press, UK (1975)

[28] Chen JC, Neitzel GP, Jankowski DF, Phys. Fluids, 28, 749 (1985)

[29] Foster TD, Phys. Fluids, 12, 2482 (1969)