In the process of crossflow microfiltration, a deposit of cake layer tends to form on the membrane, which usually controls the performance of filtration. There exists however the condition under which no deposit of cake layer is made. This condition is called the sub-critical flux condition, and the critical flux here means a flux below which a decline of flux with time due to the deposit of cake layer, does not occur. In this study, a concentration polarization model for the hollow fiber microfiltration was developed to study about the critical flux conditions. The model can predict the concentration distribution of particles in the membrane module under a certain operation condition which is subjected to the sub-critical flux condition.
The parameters which influence the critical flux condition include crossflow velocity, initial permeate flux, and particle size. The critical flux condition is found to be established at the condition of the higher crossflow velocity and the lower initial permeate flux. In addition, it is found that the larger the particle size is, the higher the value of the critical flux is. For modeling the effect of particle size on the critical flux condition, the concept of effective particle size is introduced. The effective particle size is a weighted average value of different sizes of particles. With those parameters, the model is formulated as follows :
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where u is the velocity in x-direction, v is the velocity in r-direction, $D_r$ is the diffusivity in r-direction, and c is concentration of particles.
This equation is solved by FDM(Finite Difference Method).
For the verification of the model, the experiments with $CaCO_3$(mean diameter 21.53㎛), Kaolin(4.11㎛), and, $Mg(OH)_2(6.03㎛)$ were carried out, respectively. The effective particle diameter of each particle is 3.46㎛(CaCO_3), 2.53㎛(Kaolin), and $2.85㎛(Mg(OH)_2)$. The simulated critical flux conditions with those effective particle diameters agreed reasonably well with the critical flux conditions measured by experiment.
The modeling and experiment results conclude as follows:
① The critical flux condition is determined by the ratio of initial permeate flux to crossflow velocity and the effective particle size.
② In the critical flux condition, the larger the effective particle size is, the higher the ratio of initial permeate flux to crossflow velocity is.
③ The critical flux condition is found in particles whose effective particle diameters are at least more than 3 ~ 4㎛.
④ The critical flux concept is most applicable to microfiltration, not ultrafiltration, nanofiltration, and reverse osmosis.
