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10.2 Control of Particulate Matter Emissions 283
2
where k is the permeability (m ), and it is often determined experimentally, DP is
the pressure drop across a porous media (a positive number), l is the air viscosity,
and Dx is the thickness of the porous media.
Consider a filter with a dust layer on the surface as shown in Fig. 10.3. The
pressure at the surface of the dust cake, between the cake and the filter, and after the
cake is P 1 , P 2 and P 3 , respectively. Applying Eq. (10.1) to the filter media leads to

P 2 P 3 k
U 0 ¼ : ð10:2Þ
l Dx
f
Similarly, applying Eq. (10.1) to the dust cake leads to

P 1 P 2 k
U 0 ¼ : ð10:3Þ
l Dx
ck
For the entire filter with cake, Eqs. (10.2) and (10.3) together give the total
pressure drop

" #

Dx Dx
DP ¼ P 1 P 3 ¼ lU 0 þ : ð10:4Þ
k k
ck f
Example 10.1: Dust Cake
2
A set of bag-house surface filters have an active area of 60 m . The pressure drop
through a freshly cleaned bag-house is 125 Pa and the bag-house is expected to be
cleaned to remove dust cake when the pressure drop reaches 500 Pa in 1 h. The gas
3
3
being cleaned has a flow rate of 300 m /min with a particle loading of 10 g/m .If
the average mass filtration efficiency is 99 %, and the dust cake has a solidity of 0.5.
3
Assume the real dust material is 2,000 kg/m . Estimate
a. the thickness of the cake when the filter is ready for cleaning
b. the permeability of the dust cake when it is due to be removed.

Solution
The mass of dust collected on the surface of the working filters in 1 h is

kg 300 m 3
m ¼ cQtg ¼ 0:01 60 min 0:99 ¼ 178:2kg
m 3 min

(a) The thickness of the cake collected in 1 h is
m 178:2kg
Dx ck ¼ ¼ ¼ 0:003 m or 3 mm
q Aa 2000 kg 3 60 m 0:5
2
ck
m