Particle back-transport causes a stratification of cake layer with large particles in the bottom and small particles in the top. This phenomenon is more apparent in the constant pressure mode, where flux declines gradually over time. Under the declining flux condition, the large particles with high back-transport velocities can deposit mainly in the beginning of a filtration cycle since the convective flow velocity toward the membrane can exceed the back-transport velocity. But, the deposition of large particles becomes scarcer toward the end of the filtration cycle, where the slower water permeation at the low flux condition fails to exceed the back transport velocity.
The probability of particle deposition ( Pd ) can be calculated by dividing the effective particle deposition velocity (J – vT) by the convective flow caused by flux as expressed in Equation (1), where the higher the total back-transport velocity is the lower the probability of deposition is.
Pd¬† ¬† ¬† ¬† ¬† ¬† ¬† Probability of particle deposition (-)
J ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬†Flux (m/s or LMH)
vT ¬† ¬† ¬† ¬† ¬† ¬† ¬† Total back-transport velocity (m/s)
Figure 1¬†shows the size distributions of the particles that deposit on membrane surface as a function of flux. The areas underneath the curves represent the relative amount of particles that deposit. It is apparent that less amount of particles deposits at low fluxes. Simultaneously the average size of the particles depositing on membrane also declines as flux decreases. As a consequence of gradual change of the particle sizes among those deposit, cake layer becomes stratified in constant pressure mode as illustrated in Figure 2.¬†While the bottom part of the cake layer consists of large and small particles, the top consists of mainly small particles. On the contrary, particle size distribution does not change in constant flux mode, where the convective flow that brings particles down to membrane is maintained constant. However, as discussed in section 1.2.3, cake layer still appears stratified as a consequence of more severe cake layer compaction in the bottom of the cake layer especially when soft particles are filtered.
Conceptually cake layer resistance can be reduced by manipulating the TMP in the beginning of the filtration cycle. The deposition of large particles can be induced by allowing a high flux temporarily in the beginning and use the cake layer as a barrier for finer particle deposition under a lower flux. In addition, if the large particles in the bottom of the cake layer are less prone to the cake layer collapse than small particles, they can delay the cake layer compaction. This mechanism may explain the reasons why the quick initial cake layer formation delayed flux loss in the long run when anaerobically digested wastewater was filtered by tubular ceramic membranes (Imasaka et al. 1993).
Figure 1.¬†Size distribution of the particles deposit on membrane surface as a function of flux under the condition described in the caption of the figure here, where the area below the curve represent the amount of particles deposit.
Figure 2¬†Side view of the cake layer formed under constant pressure mode, where less large particles deposit as flux decreases toward the end of filtration cycle.
¬© Seong Hoon Yoon