456 † To whom correspondence should be addressed. E-mail: tyughb@hhu.edu.cn Korean J. Chem. Eng., 30(2), 456-464 (2013) DOI: 10.1007/s11814-012-0141-x INVITED REVIEW PAPER Influence of particle distribution on filter coefficient in the initial stage of filtration Xing Min* ,† , Longcang Shu*, Wei Li**, and Emmanuel Kwame Appiah-Adjei* *State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China **Department of Hydrology and Water Resources, Nanjing Hydraulic Research Institute, Nanjing 210029, China (Received 19 May 2012 • accepted 22 August 2012) Abstract -Under the condition that the size of suspended particles is nonhomogeneous, we studied how filter grain and suspended particles affect filter coefficient in the early stage. A stochastic method was used to study the variation of the initial filter coefficient. Through physical experiment, the collected data include the initial inflow and outflow con- centration, the size distributions of particles in suspension and so on. By introducing the standard capture probability function P(d) and the characteristic length of filter bed L c , this separated the grains’ and particles’ influence on filter coefficient. An example showed that we could use P(d), L c to ascertain the result of effluent distribution, ratio of C out to C in in any depths and equivalent filter coefficient λ m . We also studied the filter coefficient λ l during the experiment and the first-order derivative of λ l . Key words: Variation of Filter Coefficient, Particle Size Distribution, The Characteristic Length of Filter Bed INTRODUCTION In water treatment systems, filtration is an important step in the solid-liquid separation process. A number of methods have been proposed in the literature [1-3] to calculate the removal of particles during the transient stage of deep bed filtration. Filter coefficient is an important parameter in the filtration study of those papers. It is a parameter reflecting the filtration efficiency of the filter bed that changes with time and space. During the filtration process, the filter coefficient varies due to the reducing of the filter’s porosity as well as the increasing of the interfacial velocity caused by the accumu- lation of suspended particles [4,5]. It indicates that the filter coeffi- cient is a function of time. Moreover, through the observation of initial stages of the filtration process, we found that the filter coeffi- cient also is affected by the filter bed depth even in the same suspen- sion and filter grain. This indicates that the filter coefficient is not only a function of time but also a function of space. Up to now, few studies have been carried out on that how the size distribution of suspended particles affects the filtration coeffi- cient during the filtering process. In general experimentsand theo- retical analysis, the impact of size distribution of suspended particles on the filtration process is usually ignored, because they generally Fig. 1. Variation of size distribution of suspended particles at different depth of filter bed.