2.9. Clogging model analysis
For purposes of modeling, pores in the filter are simplified to a collection of cylinders. While no filter has this simplified pore structure, we can expect to see differences in filtration behavior for the different clogging models that are representative of the processes. Considering that filtration occurs as the filtration solution passes through a collection of uniform cylindrical pores of some length and inner diameter, these models can be used to express the theoretical filter behavior due to changes in flow path resistance as a result of substances that cause clogging being retained in the filter based on shape. Equations expressing the relationship between filtration volume (throughput) and flow rate (flux) by constant pressure filtrations for the four clogging models (cake filtration, intermediate blocking, standard blocking and complete blocking) and the explanation of each model described in Sumiya[10] and Grace[11] are shown below.
2.9.1. Cake filtration model
In this clogging model, the substances causing clogging do not directly block the flow path through the pores but rather adhere to the pore surfaces, causing the formation of new flow paths that are different from those of the original filter material.