Pore size and pore size distribution

It has been postulated that the particles that closely fit to membrane pores efficiently block the pores and reduces flux most (Imasaka, 1989; Chang, 1994). It has been also assumed that smaller particles than pore size can easily penetrate into the tortuous networks of pores and cause pore blockings. Although these theories are immaculate, a thorough survey of the relation between pore size and particle size failed to show a general trend in real world (Le-Clech, 2006). The obscure effect of pore and particle sizes was attributed to the complex and changing nature of the feed water composition especially when it comes to the biological suspension presents in MBR system. Therefore, pore size and its distribution effect can be considered as one of the potential factors that can affect membrane performance.

Pore size distribution can play a role in accelerated membrane fouling under certain circumstances. According to Hagen-Poiseuille equation shown below, flow rate is proportional to the fourth power of pore radius, if all other conditions are identical. Thus, 5 times and 16 times higher liquid flow rates are expected when pore size increases by by 50% and 100%, respectively.

1         ————————— (1)

Q     =   flow rate (m3/s)
r      =   pore radius (m)
ΔPT =   trans-membrane pressure (Pa or kg/m/s2)
μ      =   viscosity of liquid in pore (cP or kg/m/s)
L      =   length of pore (m)

In addition, the pores are distributed randomly on membrane surface, thereby some local areas can have more bigger pores than other local areas. The inhomogeneous surface porosity caused by manufacturing defects also plays a role. As a result, as can be seen in Fig. 1, some local areas exist with substantially higher permeability than other areas. In the figure, zone 2 has higher flux than zone 1 due to a few big pores while TMP is universally identical across the membrane surface. Under this circumstance, zone 2 is fouled quicker than zone 1. Then flux in zone 1 increases while the local fluxes redistribute to maintain a constant apparent flux, which in turn causes accelerated membrane fouling in zone 1. Eventually the local membrane fouling triggered by pore size and porosity distributions spreads across the membrane surface. In conclusion, producing membranes with  uniform porosity across the membrane surface is as important as producing membranes with narrow pore size distributions in reducing membrane fouling.












Fig. 1. Local flux variation caused by porosity and pore size variation.

The potential issue of localized high flux issue has been fundamentally solved by recently developed patterned membranes based on the lithographic technology originally developed for microelectronics manufacturing. Fig. 2 shows two examples of patterned membranes with different pore shapes at different sizes (Fluxxion, 2007). These membranes are currently produced as flat sheet membranes attached on both sides of discs that are stacked up in a cylindrical pressure vessels. The most apparent application of this membrane is for sterilization of juice, milk, etc. due to the very tight pore size distributions that do not allow any bacterium passing the membrane. The commercial unit is operated with very frequent backwashing to prevent cake layer formation on it. However, no rigorous performance comparison with conventional MF/UF is available in public domain in terms of flux and pathogen removal efficiencies yet.


PoreSi3      PoreSi4

Fig. 2. Examples of patterned membranes with evenly distributed pores with identical shape and size (Fluxxion, 2007)


Using a similar lithographic technique, artificial pattern can be imbedded on membrane surface. By casting membranes on a template made by lithographic technique, membranes with pyramid or prism pattern can be made (Won, 2012). Method of making patterned membrane is briefed in the slide here.

Fig. 3a shows a pyramid-patterned membrane made of PVDF and Fig. 3b shows a typical membrane without pattern. Due to the larger effective surface area, water flux of pyramid patterned membrane was ~20% higher than its counterpart. In addition, when those two membranes were fabricated as immersed membrane module, pyramid patterned membrane experienced much slower TMP rise, which indicated less membrane fouling, as shown in Fig. 4.

In other literature (Lee, 2013), modelling study was performed for prism patterned membranes (Fig. 5). The result shows that shear stress is the highest near the top of the prison while the lowest in the bottom in the valley. Overall shear stress on membrane surface was much higher with prism-patterned membrane as shown in Fig. 6. Though solids in feed water tend to deposit in the bottom of the valley, they hardly deposit on the top of the valley. Overall flux can be higher relative to the membranes without pattern due to the much higher shear stress in the top of the prisms.










a) Pyramid patterned membrane (0.89 micron)                  b) Flat sheet membrane without pattern (0.85 micron)
Fig. 3. Pyramid-patterned PVDF membrane in comparison with regular flat sheet PVDF membrane ((Won, 2012)














Fig. 4. TMP profiles of flat and pyramid-patterned membranes in the continuous submerged MBR for wastewater treatment (Won, 2012).











Fig. 5. Prism patterned membrane (Won, 2012)















Fig. 6. Contour of shear stress in plate and frame module with rectangular slit channel, where flow velocity in the center of the channel (umax) is 0.1m/s  (Lee, 2013)

© Seong Hoon Yoon