Page 148 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 3 CHARACTERISTICS AND BEHAVIOR OF NANOPARTICLES AND ITS DISPERSION SYSTEMS
condensation surface [1, 9]. For water vapor in air
under the normal conditions, the following equation
in which the gradient of the partial pressure of water
vapor (dp/dx) is expressed in kPa/m and velocity v Dsf
in m/s was reported to agree well with the experi-
mental values [9].
dp
v Dsf 19 10 7 (3.2.24)
.
dx (a) (b)
Figure 3.2.3
References The electric double layer around the charged particles:
(a) stationary state; (b) during electrophoresis.
[1] L. Waldmann, K.H. Schmitt: Chapter 6 in Aerosol
Science, C.N. Davies (ed.), Academic Press, New York
(1966).
[2] D.E. Rosner, D.W. Mackowski, M. Tassopoulos, J. E E
Castillo and P. Garcia-Ybarra: Ind. Eng. Chem. Res.,
31, 760–769 (1992).
[3] J.R. Brock: J. Colloid Sci., 17, 768–780 (1962).
[4] L. Talbot, R.K. Cheng, R.W. Scheffer and D.R. Willis:
J. Fluid Mech., 101, 737–758 (1980).
> >
>>
[5] D.W. Mackowski: Int. J. Heat Mass Transf., 32, a 1/κ a 1/κ
843–854 (1989).
Figure 3.2.4
[6] P.J. Whitmore: J. Aerosol Sci., 12, 1–9 (1981).
The double layer thickness (1/ ) and the electric field lines
[7] S.P. Bakanov, V.I. Roldughin: Aerosol Sci. Technol., 7,
around the particles.
249–255 (1987).
[8] M.M.R. Williams, S.K. Loyalka: Chapter 7 in Aerosol
Science Theory and Practice, Pergamon (1991).
The -potential on a charged sphere is related to the
[9] P. Goldsmith, F.G. May: Chapter 7 in Aerosol Science, charge by the expression q/4 a; therefore, the
C.N. Davies (ed.), Academic Press, New York (1966). electrophoretic mobility is given by r 0
2
3.2.2.2 Electrokinetic effects in liquid u r 0 (3.2.27)
3
(1) Electrophoresis
Electrophoresis is the movement of an electrically As an actual colloidal particle is accompanied by the
charged particle toward an oppositely charged elec- double layer as shown in Fig. 3.2.3., the influence of
trode under the influence of an electric field. Suppose the double layer should be considered resting on its
the shape of a particle is spherical and the electrical thickness as shown in Fig. 3.2.4.
force acting on the double layer of the particle is
ignored. The forces acting on the particle are the (a) Hückel equation
direct electric force, f qE, and the viscous drag of When the double layer is very thick compared with
e
the liquid given by the Stokes equation, f 6 av. the particle radius, a 1/ , a charged particle may be
v
When the particle settles down to a constant velocity treated as a point charge in an unperturbed electric
v, these two forces are balanced: field. Therefore, equation (3.2.27) is applicable with-
out amendment.
qE 6 a (3.2.25)
where q is the net charge on the particle, E the elec- 2
0
r
tric field strength, the viscosity of the liquid and a u 3 (3.2.28)
the radius of the particle.
The electrophoretic mobility u is defined as fol-
lows: Hückel equation is not likely to be applicable to par-
ticle electrophoresis in aqueous media, however, it has
v q
u (3.2.26) possible applicability in non-aqueous media of low
E 6 a conductance.

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