It is important to understand what determines the flux in crossflow filtration to design an efficient system.Â Resistance in series model can be used for this discussion and following are the imaginary operating conditions of a tubular membrane system.

*J _{0}*Â Â Â = clean water flux at 100 kPa (1,000 LMH or 5.56×10

^{-4}m/s)

*P*Â Â = inlet pressure (550 kPa)

_{in}*P*Â = outlet pressure (50 kPa)

_{0utÂ }*J*Â = average flux during sludge filtration (100 LMH or 2.78×10

_{avgÂ }^{-5}m/s)

*Î¼*Â = viscosity of clean water (0.001 kg/m/s or 1 cP)

_{0 Â Â Â }*Î¼*Â Â Â Â = viscosity of liquid flowing through cake layer and membrane (0.001 kg/m/s or 7 cP)

Using the resistance in series model, following analysis can be performed.

In the channel entrance, *R _{m}*Â is calculated at 3.60×10

^{11}/m using the clean water flux,

*J*, assuming

_{0}*R*Â is zero. Subsequently

_{c}*R*Â is calculated at 1.98×10

_{c}^{13}/m by putting ,

*J*,

_{avg}*Î¼*Â and

*P*Â to the equation. As shown in Fig. 1, it is apparent that

_{in}*R*Â takes only 1.8% of the total resistance while

_{m}*R*Â takesÂ 98.2% of the total resistance. Â The identical calculation can be performed for the channel outlet. The calculated

_{c}*R*Â is 1.44×10

_{c}^{12}/m with an identical

*R*Â of 3.60×10

_{m}^{11}/m. In this case

*R _{m}* and

*R*Â are 20% and 80% of the total resistance, respectively. Therefore, it is obvious that

_{c}*R*Â is the flux determining parameter especially near the entrance of the membrane channel.

_{c}

a) At entranceÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â b) At exit

Fig. 1. Breakdown of filtration resistance near the entrance of tubular membrane (an example).

The extremely low influence of the *R _{m}*Â in the total resistance near the channel entrance indicates the filtration occurs in the mass transfer region in the figure here. On the other hand, the relatively lower dominance of the

*R*Â near the channel exit suggests that the filtration is performed closer to the transitional region, where flux may increase somewhat if TMP increases.

_{c}Two conclusions can be drawn.

- It is clear that flux can be only marginally increased by increasing TMP since the entire membrane surface areas are exposed to mass transfer controlled region with a possible exception of some downstream areas.

Flux can be increased only by increasing flow velocity to keep *R _{c}*Â low , but even this method is limited by increasing TMP in the entrance.

- Membrane resistance (or permeability) of membrane is not a determining factor of membrane performance. No matter how the membrane is permeable, flux is determined by the cake layer formed on membrane surface. This is a reason why there is little differentiation among commercial tubular membranes. Major differentiating factors of commercial membranes are mainly physical durability of membrane material, chemical and physical compatibility with feed water, connector design to minimize pressure loss,
*etc*.

Â© Seong Hoon Yoon