The analysis of the experimental data by Zeman is of particular interest. The log reduction values (LRV) obtained depended upon the particle loadings. Zeman refers to them as the number of pore volumes of removed particles (NPL). His analysis indicated that LRV levels decreased fourfold over the test’s duration. Plots of LRV against the number of pore volumes (NPV) removed by the filter, showed five different traces for five different latex-bead diameters (Figure 2). The LRVs showed a strong dependence on the particle loading.
In the usual situation where surfactant is absent, these five would not show a differentiation. This, in itself, is a benefit derived from working with dilute suspensions. According to Zeman, filter blockage occurred from the incipient cake formation when only 1% of the membrane pore volume (NPV, 0.01) was filled. With the larger particles, the greater build-up of filter cake caused the falling LRV to undergo an increase at higher NPVs.
The more numerous the particles and the larger their size, the more rapidly the filter’s porosity was blocked. The more rapid the blockage, the more restricted the throughput. From their work with latex beads, Emory et al., confirmed that “retention is strongly dependent on particle feed concentration.”
Zeman noted that the filters’ LRVs decreased some fourfold during the testing period. This translates to a fourfold increase in particle passage and was attributed to blockage of the smaller pores likely enhancing smaller particle flows to the larger pores with concomitant particle passage.
Zeman, in the context of surfactant being present, based his analysis of latex particle polydispersity upon the findings that when many larger particles were present, a reduction in the passage of smaller particles resulted. However, when the smaller particles were in greater numbers, more of the larger particles passed through the filter. Zeman reported that “the breakthrough of the smaller particles is retarded by the presence of larger particles,” and “the passage of larger particles occurs more rapidly when smaller particles are present in the stream.”
During filtration, fluid is simultaneously directed to both smaller and larger pores. According to the mean flow-pore concept, a small number of larger pores is seen to carry one-half the filter’s entire flow, while the remaining pores carry the other half. A far greater number of pores smaller than the mean flow pore are needed to balance the influence of the hydrodynamic preference for the larger pores. In line with the Hagen–Poiseuille equation, a greater proportion of smaller pores operating on the order of their radii to the fourth power serve to balance the greater flows of the larger pores.
With regard to particle retention, both larger and smaller particles would involve small pore blockage. The larger particles would similarly block larger pores. However, smaller particles could permeate larger pores. Blockage of the smaller pores will reduce their functional numbers, shifting the pore-size distribution in the direction of the larger pores. This will increase the likelihood of smaller particle penetrations in reverse proportion to the number of smaller pores still available.
In any case, to the extent that the proportion of larger particles dominates, their encounters with larger pores will exceed those of smaller particles. This will speed the closure of larger pores by larger particles. Nevertheless, until pore closure is complete, small particle passage can take place. This trend will continue until the larger pores are effectively blocked as judged by the rate of flow diminution.
In summation, the initial rate of particle passage will reflect the relative quantities of smaller and larger particles, and the numbers of smaller and larger pores, subject to mean flow-pore influences. As the smaller pores or interstices become increasingly blocked, whether by larger or smaller particles, the rate of smaller particle permeation in proportion to the number of larger pores will tend to increase, even as the number of larger pores is decreasing.
The rate of particle passage will progressively decrease as larger pores are successively blocked. The more numerous the larger particles, the faster the closure of pores through which the smaller particles can pass, and the less the overall number of filter penetrations. The earlier the termination of the filtration occurs, the lesser the amount of throughput.
Zeman’s second proposition, that “the passage of larger particles occurs more rapidly when smaller particles are present in the stream,” is also correct. Smaller particles block only the smaller pores of the filter. Due to the absence of adsorptive arrests, they have no effect on the progressive clogging of the larger pores leading eventually to their blocking. In effect, small particle competition with larger particles for occupying smaller pores, even if due only to their numbers, increases the frequency of larger particles coinciding with larger pores. To the extent that these larger particles are of shapes whose dimensions are suitably oriented within the flow stream to negotiate larger-pore passages, the presence of smaller particles enhances their filter penetrations.