BROWNIAN MOTION OF SPHERICAL PARTICLES NEAR A DEFORMING INTERFACE

Yang SM

Korean Journal of Chemical Engineering, Vol.12, No.4, 421-427, September, 1995

In this paper Brownian diffusion of spherical particles near a deformable fluid interface was examined by considering interface deformations that were caused by impulsive motions of the Brownian particles. First, the velocity fields were constructed in terms of eigenfunctions on the bipolar coordinate system which facilitated the separation of variables. Then, the rate of interface deformation was determined to calculate the force acting on a Brownian sphere due to the interface relaxation back toward a flat configuration. In addition, the covariance function of velocity correlation was detemined by solving the Langevin equation which included the effects of the interface relaxation. Finally, the diffusion coefficient of spherical particles was evaluated by utilizing the Einstein-Smoluchowski relation in conjunction with the particle mobility calculated in the presence of a deforming interface.

Keywords:Brownian Motion;Brownian Diffusivity;Interface Deformation;Velocity Autocorrelation;Particle Mobility;Bipolar Coordinates

[References]

Berdan C, Leal LG, J. Colloid Interface Sci., 87, 62 (1982)
Brenner H, Leal LG, J. Colloid Interface Sci., 88, 136 (1982)
Buff FP, Lovett RA, Stilling FH, Phys. Rev. Lett., 15, 621 (1965)
Fuentes YO, Kim S, Jeffery DJ, Phys. Fluids, 31, 2445 (1988)
Geller AS, Lee SH, Leal LG, J. Fluid Mech., 169, 27 (1986)
Gotoh T, Kaneda Y, J. Chem. Phys., 76, 3193 (1982)
Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Martinus Nijhoff, Hague, Netherlands (1983)
Hauge EH, Martin-Lof A, J. Stat. Phys., 7, 259 (1973)
Lee SH, Leal Lg, J. Colloid Interface Sci., 87, 81 (1982)
O'Neill ME, Ranger KB, Phys. Fluids, 26, 2035 (1983)
Russel WB, Annu. Rev. Fluid Mech., 13, 425 (1981)
Stoos JA, Leal LG, AIChE J., 35(2), 196 (1989)
Teletzke GF, Scriven LE, Davis HT, J. Colloid Interface Sci., 87, 550 (1982)
Yang SM, Leal LG, J. Fluid Mech., 149, 275 (1984)
Yang SM, Korean J. Chem. Eng., 4(1), 15 (1987)
Yang SM, Leal LG, Int. J. Multiph. Flow, 16, 597 (1990)
Yang SM, Korean J. Chem. Eng., 12(3), 331 (1995)

[Referenced By]

[1] Berdan C, Leal LG, J. Colloid Interface Sci., 87, 62 (1982)

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

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

[4] Fuentes YO, Kim S, Jeffery DJ, Phys. Fluids, 31, 2445 (1988)

[5] Geller AS, Lee SH, Leal LG, J. Fluid Mech., 169, 27 (1986)

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

[7] Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Martinus Nijhoff, Hague, Netherlands (1983)

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

[9] Lee SH, Leal Lg, J. Colloid Interface Sci., 87, 81 (1982)

[10] O'Neill ME, Ranger KB, Phys. Fluids, 26, 2035 (1983)

[11] Russel WB, Annu. Rev. Fluid Mech., 13, 425 (1981)

[12] Stoos JA, Leal LG, AIChE J., 35(2), 196 (1989)

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

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

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

[16] Yang SM, Leal LG, Int. J. Multiph. Flow, 16, 597 (1990)

[17] Yang SM, Korean J. Chem. Eng., 12(3), 331 (1995)