330
K. Xiao and C.-X. Wu
Fig. 8.2 Schematic representation of a microparticle of radius r suspended in a nematic liquid
crystal cell with surface-to-surface distance L and a normal anchoring and b planar anchoring in
the presence of an external electric field
where k
2
= (4π K )
−1
εE
2 , P(x) and C(x) denote the dipole and the quadrupole
moment densities respectively. When an electric field is applied along z axis, the
Euler-Lagrange equation are given by [42]
n μ − k
2 n μ = 4π [∂ μ P(x) − ∂ z ∂ μ C(x)].
(8.19)
When the external electric field is applied parallel to x axis, we have the EulerLagrange equations written as [42]
n μ + k
2
δ xμ n μ = 4π [∂ μ P(x) − ∂ z ∂ μ C(x)].
(8.20)
If the applied electric field is parallel to y axis, then the Euler-Lagrange equations
are [42]
n μ + k
2
δ yμ n μ = 4π [∂ μ P(x) − ∂ z ∂ μ C(x)].
(8.21)
K. Xiao and C.-X. Wu
Fig. 8.2 Schematic representation of a microparticle of radius r suspended in a nematic liquid
crystal cell with surface-to-surface distance L and a normal anchoring and b planar anchoring in
the presence of an external electric field
where k
2
= (4π K )
−1
εE
2 , P(x) and C(x) denote the dipole and the quadrupole
moment densities respectively. When an electric field is applied along z axis, the
Euler-Lagrange equation are given by [42]
n μ − k
2 n μ = 4π [∂ μ P(x) − ∂ z ∂ μ C(x)].
(8.19)
When the external electric field is applied parallel to x axis, we have the EulerLagrange equations written as [42]
n μ + k
2
δ xμ n μ = 4π [∂ μ P(x) − ∂ z ∂ μ C(x)].
(8.20)
If the applied electric field is parallel to y axis, then the Euler-Lagrange equations
are [42]
n μ + k
2
δ yμ n μ = 4π [∂ μ P(x) − ∂ z ∂ μ C(x)].
(8.21)