The analysis of the rotation of a ferromagnetic ellipsoid suspended in a Newtonian fluid and subjected to a uniform magnetic field is extended to include a long, slender cylindrical fiber which is magnetically saturated. Experimental observations of rotating nickel cylinders with aspect ratios
L/D ranging from 5 to 40 agree with the theoretical predictions that: (1) the proper magnetoviscous time constant for the motion is
MV =
s/
µ
0
M
s
2
, (2) larger fiber aspect ratios result in considerably longer orientation times; and (3) the strength of the applied external field has only a slight effect on the overall fiber rotation, and has no effect on the maximum angular velocity achieved. Quantitative agreement of theory and experiments is obtained for fibers with
L/D 20; for the shorter fibers, the theory tends to overpredict the fiber rotation rate by as much as 30%.
D
diameter of the cylinder
-
D
P
(
r)
position-dependent demagnetization tensor, implicitly defined in eq. (2.5)
-
D
xx,
D
yy,
D
zz
volume-averaged demagnetizing factors for an ellipsoid equivalent to a uniformly magnetized cylinder, defined in eq. (2.6)
-
H
i
;
H
i
magnetic field inside a ferromagnetic body; magnitude of
H
i
-
H
0;
H
0
magnetic field applied by external sources; magnitude of
H
0
-
k
geometric parameter in the hydrodynamic resistance of a body rotating in a Newtonian fluid, eq. (2.2)
-
L
length of the cylinder
-
L
(h);
L
z
(h)
hydrodynamic torque exerted on a rotating body; the
z-component of
L
(h) on the cylinder
-
L
(m);
L
z
(m)
magnetic torque exerted on a magnetic body in a magnetic field, eq. (2.4); the
z-component of
L
(m) on the cylinder
-
M
the magnetization of a magnetic material
-
M
s
the saturation magnitude of
M, approached by all ferromagnetic materials as
H
i becomes large
-
r
position vector of a point within a ferromagnetic body
-
V
volume of a magnetic particle
-
x, y, z
rectangular coordinate axes fixed in the cylinder according to figure 1
-
angle of inclination of the axis of the cylinder with respect to
H
0
-
shear rate
-
small parameter of slender body theory,
=1/ln (2
L/D)
-
s
constant viscosity of the suspending fluid
-
µ
0
the magnetic permeability of free space,
µ
0=4
· 10
–7 H/m
-
MV
the magnetoviscous time constant, a characteristic time for a process involving a competition of viscous and magnetic stresses
-
1
the first normal-stress coefficient
-
;
z
angular velocity of a rotating body; angular velocity of a cylinder about the
z-axis,
z =
– d/dt 相似文献