New correlation equations for the deep-bed filtration, including the term of diffusiophoresis, in addition to the Derjaguin and Landau, Verwey and Overbeek interactions, the Brownian diffusion and the interception, for predicting the initial collection efficiency under the favorable deposition condition and the filter coefficient ratio under the unfavorable deposition condition are derived by using the Brownian dynamics-simulation method. These new correlation equations for predicting the filter coefficient ratio are able to describe previous experimental results especially well for those submicron particles that are at high ionic strength.