XIX Sympozjum Srodowiskowe PTZE - materialy.pdf

XIX Sympozjum PTZE, Worliny 2009
and electric field strength is calculated as E = −∇V. Boundary conditions on the
computational problem boundary are Neuman’s or Dirichlet’s type. On the bottom and top
insulating substrate current cannot flow into this boundary, so Neuman’s conditions here
apply. Periodic boundary conditions are present on the left and right sides A-B and C-D of the
model boundary to simulate the presence of neighboring electrodes. It is assumed that all
computational cells are of the same type. Using typical fabrication procedures, the thickness
of the deposited metal that forms the interdigitated electrodes is in most cases less than 1µm.
Simulation results
The finite element calculations was done for following geometrical dimensions: A-B = 60
µm, A-C = 160 µm, a = 40 µm, b = 40 µm, h = 4 µm. Spherical dielectric particle has radius r
= 5 µm and relative permittivity ε2 = 80. The fluid, where particle moves has permittivity ε1 =
4. Simulation was carried out for frequency ω = 50 kHz.
A
∂ ϕ
= 0
∂n
B
particle
∂ ϕ
= 0
∂n
ε2
substrate
F DEP
100
substrate
fluid with known ε 1
electrodes with known voltages
a a
h ϕ = U z
ϕ = 0
b
0.5a
C
∂ ϕ
= 0
∂n
Fig. 1. Cross section of the electrode arrangement with one pair of electrodes
and moving biological particle is depicted.
Fig. 2. Equipotential lines in computational domain (left) and electric displacement D
in vector form (right).
The total force acting on particle computed from (10) has the value
( x y)[
]
FDEP = 21.09a −50.65a
pN/m (12)
D