A Statistical Model of Pressure Drop Increase with Deposition in   Granular Filters
  As deposits accumulate in a granular filter, pressure drop across the filter bed required to maintain a constant fluid flow rate may increase. Two pressure drop increase patterns had been observed. In slow sand filters pressure drop remains unchanged for a certain period of time then increases exponentially with the volume of filtrate; in granular aerosol filters pressure drop increases linearly with the amount of deposits from the beginning of the filtration process. New concepts of homogeneous and heterogeneous depositions were introduced in this paper. A statistical model based on these new concepts was developed. This non-linear model was able to reproduce both observed pressure drop increase patterns, including the linear one. Excellent agreements between the present model and experimental measurements were obtained. It was concluded that the two pressure drop increase patterns were indeed caused by different deposit distributions rather than different pressure drop increase mechanisms. 
Zhaohui Qin, Richard H. Pletcher
cond-mat.soft physics.flu-dyn