Research Papers: Multiphase Flows

Wall Effects on the Brownian Movement, Thermophoresis, and Deposition of Nanoparticles in Liquids

[+] Author and Article Information
Efstathios E. Michaelides

Department of Engineering,
Texas Christian University,
Fort Worth, TX 76132
e-mail: E.Michaelides@tcu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 8, 2015; final manuscript received November 11, 2015; published online January 8, 2016. Editor: Malcolm J. Andrews.

J. Fluids Eng 138(5), 051303 (Jan 08, 2016) (7 pages) Paper No: FE-15-1388; doi: 10.1115/1.4032030 History: Received June 08, 2015; Revised November 11, 2015

It is well known that the hydrodynamic drag on particles is significantly enhanced close to a plane or curved boundary. This enhancement impedes the movement of the particles in both the parallel and the normal directions with respect to the wall. In the presence of a temperature gradient, the Brownian movement of particles induces the phenomenon of thermophoresis, which results in the steady motion of the particles toward the colder domains of the flow field. This paper examines the effect of the enhanced wall drag on the thermophoretic movement of the nanoparticles in a Newtonian fluid, at short distances (0–10 radii) from a flat, horizontal wall. The effect of the flow shear lift on the thermophoretic motion of the particles close to a horizontal wall is also examined. It is observed that the movement of the particles toward the plane wall is significantly retarded because of the enhanced drag and that it, actually, causes particle accumulation close to the plane wall. It is also observed that the lift, which is induced by the relative Brownian movement, does not have an effect on the average motion of particles toward the wall and does not play an important role on the deposition of particles.

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Mabberley, D. J. , 1985, Jupiter Botanicus: Robert Brown of the British Museum, J. Cramer, Braunschweig.
Haw, M. , 2005, “ Einstein's Random Walk,” Phys. World, 18(1), pp. 19–22. [CrossRef]
Einstein, A. , 1905, “ Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys., 17, pp. 549–560. [CrossRef]
Li, A. , and Ahmadi, G. , 1992, “ Dispersion and Deposition of Spherical Particles From Point Sources in a Turbulent Channel Flow,” Aerosol Sci. Technol., 16(4), pp. 209–226. [CrossRef]
Michaelides, E. E. , 2014, Nanofluidics–Thermodynamic and Transport Properties, Springer, New York.
Michaelides, E. E. , 2015, “ Brownian Movement and Thermophoresis of Nanoparticles in Liquids,” Int. J. Heat Mass Transfer, 81, pp. 179–187. [CrossRef]
Epstein, P. , 1929, “ Zur theorie des radiometers,” Z. Phys., 54(7), pp. 537–563. [CrossRef]
Brock, J. R. , 1962, “ On the Theory of Thermal Forces Acting on Aerosol Particles,” J. Colloid Interface Sci., 17(8), pp. 768–780. [CrossRef]
Talbot, L. , Cheng, R. K. , Schefer, R. W. , and Willis, D. R. , 1980, “ Thermophoresis of Particles in a Heated Boundary Layer,” J. Fluid Mech., 101(4), pp. 737–758. [CrossRef]
McNab, G. S. , and Meisen, A. , 1973, “ Thermophoresis in Liquids,” J. Colloid Interface Sci., 44(2), pp. 339–346. [CrossRef]
Faxen, H. , 1922, “ Der Widerstand gegen die Bewegung einer starren Kugel in einer zum den Flussigkeit, die zwischen zwei parallelen Ebenen Winden eingeschlossen ist,” Ann. Phys., 68, pp. 89–119. [CrossRef]
Happel, J. , and Brenner, H. , 1986, Low Reynolds Number Hydrodynamics, 4th printing, Martinus Nijhoff, Dordrecht.
Saffman, P. G. , 1965, “ The Lift on a Small Sphere in a Slow Shear Flow,” J. Fluid Mech., 22(2), pp. 385–398. [CrossRef]
Mei, R. , 1992, “ An Approximate Expression of the Shear Lift on a Spherical Particle at Finite Reynolds Numbers,” Int. J. Multiphase Flow, 18(1), pp. 145–160. [CrossRef]
Berg, J. C. , 2010, An Introduction to Interfaces and Colloids—The Bridge to Nano-Science, World Scientific, Singapore.
Dandy, D. S. , and Dwyer, H. A. , 1990, “ A Sphere in Shear Flow at Finite Reynolds Number: Effect of Particle Lift, Drag and Heat Transfer,” J. Fluid Mech., 216, pp. 381–412. [CrossRef]
Feng, Z. G. , and Michaelides, E. E. , 2002, “ Inter-Particle Forces and Lift on a Particle Attached to a Solid Boundary in Suspension Flow,” Phys. Fluids, 14(1), pp. 49–60. [CrossRef]
Takemura, F. , 2004, “ Migration Velocities of Spherical Solid Particles Near a Vertical Wall for Reynolds Numbers From 0.1 to 5,” Phys. Fluids, 16(1), pp. 204–207. [CrossRef]
Russel, W. R. , Saville, D. A. , and Schowalter, W. R. , 1989, Colloidal Dispersions, Cambridge University Press, Cambridge.
Portela, L. M. , Cota, P. , and Oliemans, R. V. A. , 2002, “ Numerical Study of the Near-Wall Behaviour of Particles in Turbulent Pipe Flows,” Powder Technol., 125(2), pp. 149–157. [CrossRef]
Michaelides, E. E. , 2006, Particles, Bubbles and Drops—Their Motion, Heat and Mass Transfer, World Scientific Publishers, Singapore.
Michaelides, E. E. , 2003, “ Hydrodynamic Force and Heat/Mass Transfer From Particles, Bubbles and Drops: The Freeman Scholar Lecture,” ASME J. Fluids Eng., 125(2), pp. 209–238. [CrossRef]
Feng, Z.-G. , and Michaelides, E. E. , 2003, “ Equilibrium Position for a Particle in a Horizontal Shear Flow,” Int. J. Multiphase Flow, 29(6), pp. 943–957. [CrossRef]
Patankar, N. A. , Huang, P. Y. , Ko, T. , and Joseph, D. D. , 2001, “ Lift-Off of a Single Particle in Newtonian and Viscoelastic Fluids by Direct Numerical Simulation,” J. Fluid Mech., 438, pp. 67–100. [CrossRef]


Grahic Jump Location
Fig. 1

The time-average velocity of 1000, 30 nm particles subjected to the Brownian force. The ensemble average velocity is the thermophoretic velocity, Vth.

Grahic Jump Location
Fig. 2

The retardation coefficient, due to the plane wall

Grahic Jump Location
Fig. 3

The final relative position of the two ensembles of particles after 5000τp (4.93 × 10−6 s) and after 500,000τp (4.93 × 10−4 s). All particles were released at h/α = 5.5α.

Grahic Jump Location
Fig. 4

The higher fraction of particles of the second ensemble in the wall region

Grahic Jump Location
Fig. 5

The shear lift force on a sphere close to a wall with negative relative velocity



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