FUNCTIONALLY GRADED ALL CERAMIC HIP JOINT - Advanced Biomaterials: Fundamentals, Processing, and Applications - page 328

predict the composition profi le in a one sided gradient as well as for semi-
symmetrically graded plate-shaped components [Put et al., 2003]. The prediction
of the concentration profi les are based on the description of the deposition yield
by means of the effective charge of the suspended powder particles, Q eff , the elec-
trophoretic mobility,

μ , and the specifi c conductivity of the solvent, σ liq . Although

this model predicts the yield during EPD well, the parameters Q eff , σ liq and μ are

fi tted parameters rather than real physical values.
If different powders i are present in the suspension, the deposition yield of
each powder on the deposition electrode can be described by [Biesheuvel and
Verweij, 1999 ]:

dy
dt

φ
φφ

i di

= ES f μ c (10.1)

i i i

−

di si

with dy
dt

i , the deposition rate of powder i on the electrode (g/s)

E , the electric fi eld strength (V/m)

μ i , the electrophoretic mobility of powder i (m 2 /V.s)

c i , the concentration i of powder i in suspension (g/cm 3 )
f i , factor for powder i which takes in account that not all powder brought to
the electrode is incorporated in the deposit
S , the surface area of the deposition electrode (m 2 )

φ di concentration (vol. %) of the powder in the deposit

φ si concentration (vol. %) of the powder in the suspension

The concentration c i , t of powder i at time t is a function of the powder mass in
the suspension and the suspension volume at ( t − 1) and the change in mass and

volume during Δ t :

t

MM dy
dt

∫

i

+ Δ − dt

it , − 1 i , Δ t

c =

t − 1

(10.2)

it ,

VV + Δ

t − 1 Δ t

1) (g) With M i , t − 1 the mass of powder i in suspension at time ( t −

Δ M i, Δ t the change in mass of powder i by adding or removing suspen-

sions between ( t 1) and t (g)

V t − 1 the total volume suspension at time ( t

−

− 1) (cm 3 )

Δ V Δ t change in suspension volume between ( t − 1) and t ( s )

The total amount of powder deposited ( Δ Y tot ) during Δ t is given by:

t

dy
dt

∑

∫

i

Δ Y = dt (10.3)

tot

i

t 1