1066 Journal of the American Ceramic Society--Bao and Nicholson Vol. 90. No. 4 Al2O3 2.5 E品 2 0 0 EPID Current(mA) Fig 8. Effect of the electrophoretic infiltration deposition(EPID) Fig. 6. Infiltration inside a I rent on the weight of deposited alumina after 60 m in the deposit. These voids cannot be eliminated by adjusting the (1 o=0 when y=0(bottom of the slit); EPD parameters, e.g., constant current or constant voltage (2)o =0 when y= a(top of the slit); modes. During EPD with conductive fiber bundles, pa (3)φ=φ。 when x=0( origin of the slit) first deposit on the outer fiber surfaces, thus clogging the bi (4)φ→0as This clogging effect is further enhanced by the electric field The solution of the two-dimensional Laplace equation gives shielding effect inside the conductive-fiber bundle as follows the potential as According to electrostatics, the electric potential distributio follows the Poisson equation (1) Thus, the electric field in the x direction at y= a/2 where o is the electric potential, E is the permittivity, and pe is the volume charge density. When pe=0. this reduces to the Laplace equation, i.e E=-2(9=S The electric field Ex declines drastically inside the slit(Fig. 12) In two-dimensional Cartesian coordinates this is The field penetration depth is only double the slit size(2a) eter of 10 um)forming a square array with a filament distance +ee 30 um, the fiber volume concentration is 8.5 vol %. As all fibers are grounded(they are the cathode), the outer square array (2 In two dimensions, the boundary conditions for an infinitely um away from the outside fibers) has a potential of 10 V(an long conductive slit with pore size, "a', are(Fig. 11) ode). Figure 13 shows a plot of the potential in this conductive fiber array via FEMLab 3. 0(COMSOL, Burlington, MA). Fig- 3.5 ire 14 shows the electric field distribution along the central line in the x direction. No electric field exists inside the fiber array 1200 0.90mA 2.5 1000 060mA 1.5 400 A 0.2mA 0.5 200 0.1m 600 250 750 1000 Fig. 7. Deposited alumina weight versus electrophoretic infiltration 9. Voltage change versus electrophoretic infiltration deposition e for different cell current valuesin the deposit. These voids cannot be eliminated by adjusting the EPD parameters, e.g., constant current or constant voltage modes. During EPD with conductive fiber bundles, particles first deposit on the outer fiber surfaces, thus clogging the bundle. This clogging effect is further enhanced by the electric field shielding effect inside the conductive-fiber bundle as follows: According to electrostatics, the electric potential distribution follows the Poisson equation: H2 f ¼ 1 e rE (1) where f is the electric potential, e is the permittivity, and rE is the volume charge density. When rE 5 0, this reduces to the Laplace equation, i.e.: H2 f ¼ 0 (2) In two-dimensional Cartesian coordinates, this is q2 f qx2 þ q2 f qy2 ¼ 0 (3) In two dimensions, the boundary conditions for an infinitely long conductive slit with pore size, ‘‘a’’, are (Fig. 11): (1) f 5 0 when y 5 0 (bottom of the slit); (2) f 5 0 when y 5 a (top of the slit); (3) f 5 fo when x 5 0 (origin of the slit); (4) f-0 as x-N. The solution of the two-dimensional Laplace equation gives the potential as27 fðx; yÞ ¼ 4fo p X1 m¼1;3;5... 1 m sin mpy a empx=a (4) Thus, the electric field in the x direction at y 5 a/2 is Ex ¼ qfðx; a 2Þ qx ¼ 4fo a X1 m¼1;3;5... sin mp 2 empx=a (5) The electric field Ex declines drastically inside the slit (Fig. 12). The field penetration depth is only double the slit size (2a). For a conductive fiber bundle (assuming fibers with a diam￾eter of 10 mm) forming a square array with a filament distance of 30 mm, the fiber volume concentration is 8.5 vol%. As all fibers are grounded (they are the cathode), the outer square array (20 mm away from the outside fibers) has a potential of 10 V (an￾ode). Figure 13 shows a plot of the potential in this conductive fiber array via FEMLab 3.0 (COMSOL, Burlington, MA). Fig￾ure 14 shows the electric field distribution along the central line in the x direction. No electric field exists inside the fiber array Al2O3 20µm PE Fig. 6. Infiltration inside a 10-mm pore. 0 0.5 1 1.5 2 2.5 3 3.5 0 200 400 600 800 Time (min.) Infiltrated Alumina Weight (g) Fig. 7. Deposited alumina weight versus electrophoretic infiltration deposition time. 0 0.5 1 1.5 2 2.5 3 0 0.5 1.5 EPID Current (mA) Deposited alumina (g) 1 Fig. 8. Effect of the electrophoretic infiltration deposition (EPID) cur￾rent on the weight of deposited alumina after 60 min. 0 200 400 600 800 1000 1200 0 250 500 750 1000 Time (min.) Voltage (V) 0.3mA 0.60mA 0.90mA 0.2mA 0.40mA 0.1mA Fig. 9. Voltage change versus electrophoretic infiltration deposition time for different cell current values. 1066 Journal of the American Ceramic Society—Bao and Nicholson Vol. 90, No. 4