PARTICLE MOTIONS INDUCED BY CAPILLARY FLUCTUATIONS OF A FLUID-FLUID INTERFACE

Yang SM

Korean Journal of Chemical Engineering, Vol.12, No.3, 331-339, July, 1995

The motion of a Brownian particle in the presence of a deformable interface is studied by considering the random distortions of interface shape due to spontaneous thermal impulses from the surrounding fluid. The fluctuation-dissipation theorem is derived for the spontaneous fluctuations of interface shape using the method of normal modes in conjunction with a Langevin type equation of motion for a Brownian particle, in which the fluctuating force arises from the continuum motions induced near the particle by the fluctuation of interface shape. The analysis results in the prediction of autocorrelation functions for the location of the dividing surface, for the random force acting on the particle, and for the particle velocity. The particle velocity correlation, in turn, yields the effective diffusion coefficient due to random fluctuations of the interface shape.

Keywords:Brownian Particle and Diffusion;Interface Fluctuations;Capillary Wave;Velocity Autocorrelation;Langevin Equation;Normal Mode Decomposition

[References]

Batchelor GK, "Developments in Microhydrodynamics," in "Theoretical and Applied Mechanics," ed. W. Koiter, Amsterdam, Netherlands (1976)
Brenner H, Leal LG, J. Colloid Interface Sci., 62, 238 (1977)
Brenner H, Leal LG, J. Colloid Interface Sci., 88, 136 (1982)
Buff FP, Lovett RA, Stillinger FH, Phys. Rev. Lett., 15, 621 (1965)
Chaplin JR, J. Fluid Mech., 147, 449 (1984)
Evans R, Mol. Phys., 42, 1169 (1981)
Gotoh T, Kaneda Y, J. Chem. Phys., 76, 3193 (1982)
Hauge EH, Martin-Lof A, J. Stat. Phys., 7, 259 (1973)
Hinch EJ, J. Fluid Mech., 72, 499 (1975)
Jhon MS, Desai RC, Dahler JS, J. Chem. Phys., 68, 5615 (1978)
Kreuzer HJ, "Nonequilibrium Thermodynamics and Its Statistical Foundations," Oxford University Press, Oxford (1984)
Lamb H, "Hydrodynamics," Dover, New York, N.Y. (1932)
Landau LD, Lifshitz EM, "Fluid Mechanics," Pergamon Press, New York, N.Y. (1959)
Lee SH, Chadwick RS, Leal LG, J. Fluid Mech., 93, 705 (1979)
Lee SH, Leal LG, J. Fluid Mech., 98, 193 (1980)
Squire HB, Proc. Roy Soc. London A, 142, 621 (1933)
Teletzke GF, Scriven LE, Davis HT, J. Colloid Interface Sci., 87, 550 (1982)
Whitham GB, "Linear and Nonlinear Waves," Wiley-Interscience, New York, N.Y. (1974)
Yang SM, Leal LG, J. Fluid Mech., 136, 393 (1983)
Yang SM, Leal LG, J. Fluid Mech., 149, 275 (1984)
Yang SM, Korean J. Chem. Eng., 4(1), 15 (1987)
Yang SM, Hong WH, Korean J. Chem. Eng., 4(2), 187 (1987)

[Referenced By]

[1] Batchelor GK, "Developments in Microhydrodynamics," in "Theoretical and Applied Mechanics," ed. W. Koiter, Amsterdam, Netherlands (1976)

[2] Brenner H, Leal LG, J. Colloid Interface Sci., 62, 238 (1977)

[3] Brenner H, Leal LG, J. Colloid Interface Sci., 88, 136 (1982)

[4] Buff FP, Lovett RA, Stillinger FH, Phys. Rev. Lett., 15, 621 (1965)

[5] Chaplin JR, J. Fluid Mech., 147, 449 (1984)

[6] Evans R, Mol. Phys., 42, 1169 (1981)

[7] Gotoh T, Kaneda Y, J. Chem. Phys., 76, 3193 (1982)

[8] Hauge EH, Martin-Lof A, J. Stat. Phys., 7, 259 (1973)

[9] Hinch EJ, J. Fluid Mech., 72, 499 (1975)

[10] Jhon MS, Desai RC, Dahler JS, J. Chem. Phys., 68, 5615 (1978)

[11] Kreuzer HJ, "Nonequilibrium Thermodynamics and Its Statistical Foundations," Oxford University Press, Oxford (1984)

[12] Lamb H, "Hydrodynamics," Dover, New York, N.Y. (1932)

[13] Landau LD, Lifshitz EM, "Fluid Mechanics," Pergamon Press, New York, N.Y. (1959)

[14] Lee SH, Chadwick RS, Leal LG, J. Fluid Mech., 93, 705 (1979)

[15] Lee SH, Leal LG, J. Fluid Mech., 98, 193 (1980)

[16] Squire HB, Proc. Roy Soc. London A, 142, 621 (1933)

[17] Teletzke GF, Scriven LE, Davis HT, J. Colloid Interface Sci., 87, 550 (1982)

[18] Whitham GB, "Linear and Nonlinear Waves," Wiley-Interscience, New York, N.Y. (1974)

[19] Yang SM, Leal LG, J. Fluid Mech., 136, 393 (1983)

[20] Yang SM, Leal LG, J. Fluid Mech., 149, 275 (1984)

[21] Yang SM, Korean J. Chem. Eng., 4(1), 15 (1987)

[22] Yang SM, Hong WH, Korean J. Chem. Eng., 4(2), 187 (1987)