deposition method (see table 3.1) is marked in the gray zone of figure 3.8. The broken line shows the limit of closest spherical packing (ǫ = 26%) for comparison. 1 10 100 1000 20 40 60 80 100 Porosity (%) C a k e c a p il la ry d ia me te r (n m) C lo se st sp h e ri ca l p a cki n g Direct deposition
Figure 3.8 The reachable capillary size for cake deposits calculated from equation 3.29 for 8 nm particles. The range reachable with the direct deposition method is marked with as gray. The closest spherical packing is marked as the broken line at ǫ = 26%.
If ballistic deposition is possible (ǫc ≈ 85%), then the capillary-size may
be as low as 30 nm. However, it is not possible to reach O(1) nm capillary diameter with the direct deposition method. In fact, the porosity should be decreased to 65% if a capillary diameter < 10 nm is required. To do so, restructuring is required. One way of restructuring the cake, is by simulta- neous sintering and deposition, when the characteristic time for sintering is much smaller than the time between particle arrival to the substrate [50, 64]. This methods requires very high temperatures (> 1000◦
C) as well as a low aerosol concentration. Due to the high temperature, any thermal expansion mismatch can lead to peeling, cracking and lift-off of the deposited cake [23] (discussed later in section 4.2.6).
3.3
Experimental
3.3.1 Particle deposition
Alumina nanoparticles, produced in a premixed flame using the settings of table 2.4 and characterized in section 2.4, were deposited on a porous ceramic tube (α-alumina). Figure 3.9 shows a schematic of the deposition cell. The ceramic substrate was sealed using o-rings. By applying a low pressure on the outside of the tube, the aerosol was forced through the substrate. This caused particles to be filtered off on the inner substrate surface, and a porous
3.3 Experimental 36
ceramic film was formed [15, 24, 22, 5, 23]. A back-pressure regulator (BPR) adjusted the pressure for constant pressure-filtration and a mass-flow meter (MFM) measured the flow rate through the substrate. A PC equipped with Labview was used for the control of the BPR and the collection of data from the MFM. Aerosol from flame To pump Outlet Porous ceramic substrate Flange(s) O-ring
Figure 3.9 Schematic showing the deposition cell. Aerosol laden gas from the flame enters at the inlet. A pump applies a low pressure on the outside and a back-pressure regulator controls the pressure-drop across the substrate. The flow is measured by a mass-flow meter and the data is collected via Labview on a PC.
3.3.2 Substrate properties
The substrates were porous α-alumina ceramic tubes with the dimensions given in table 3.2.
Table 3.2 α-alumina substrate dimensions
Inner radius (Ri) Outer radius (RO) Length (L)
mm mm mm
3.25 4.75 23.5 / 58
The porosity of the substrates was measured by first weighing the dry mass of the tubes, dipping them into water then weighing the wet mass, then weighing them again. Once the mass of water contained in the substrate capillaries was known, the capillary volume could be calculated. From the total volume of the substrate, the porosity could be determined from:
ǫs,1 = mwater ρwater π R2 O− R2i L (3.31)
where mwater and ρwater is the mass and density of water respectively. An-
other method is to weigh the dry support, then calculate the expected mass from the solid density (ρalumina = 3900 kg/m3) and the volume of the sup-
port:
ǫs,2 = 1 −
msubstrate
ρsubstrate
3.3 Experimental 37
By the first method (equation 3.31), the entire volume accessible is deter- mined, which includes dead-end capillaries. In the latter method (equation 3.32), the entire capillary volume is considered, which includes ”closed-in” capillaries. Typical results of the permeability and porosity measurements are shown in table 3.3.
Table 3.3 α-alumina substrate properties. The average capillary radius was measured using the permeability of section 3.2.4. The porosity was calculated using equation 3.31.
Average capillary diameter∗
(dcs) ǫ∗∗s,1 ǫ∗∗s,2
µm % %
4.0 ± 1.8 31.3 ± 1.12 30.6 ± 1.31
∗: Average of 15 samples ∗∗: Average of 12 samples
The maximum porosity (ǫs,2) is somewhat smaller than the accessible
porosity (ǫs,1), however the difference is well within the experimental error
as indicated in table 3.3. In fact, it can be concluded that the substrates does not contain any closed-in capillary volume.
3.3.3 Deposition conditions
Deposition conditions are shown in table 3.4. The deposition cell tempera- ture, Tcell, was kept constant at approximately 200◦C throughout deposition.
To investigate the influence of fluid velocity on the morphology, two differ- ent pressure-drops was used. The maximum pressure-drop, which gives the maximum flow-rate through the substrate, is 0.5 bar. As it is the Pe number which determines the morphology (cf. section 3.2.2), the average Pe num- ber experienced by most particles for flow in the substrate capillaries is also shown. This is calculated from the measured average mobility diameter of the agglomerates (27.9 nm), shown in section 2.4. The diffusion coefficient of the agglomerate is estimated using the equations of section 2.2.4. By assuming a low (< 2) fractal dimension, the number of primary particles in an agglomerate of 27.9 nm was estimated from eq. 2.6 to be 19, when the primary particle diameter is assumed to be 8 nm. This gives a diffu- sion coefficient of the agglomerate of approximately 61 % of that of a dense sphere with the same mobility diameter. With this diffusion coefficient and the given pressure drop (∆P ), two sets of Pe numbers can be calculated: 0.3 and 0.5. The Pe numbers are given for the initial deposition which oc- curs at the substrate capillaries. This shows, that deposition takes place far from the ballistic limit that is at Pe > 10 (cf. section 3.2.2), and that the morphology is expected to be dominated by the diffusional deposition.
Once plugging has finished and cake growth has begun, the fluid velocity will decrease as filtration takes place on the entire filter surface. Therefore,