Analytical solution of one dimensional migration of suspended particles based on stochastic model

Based on the suspended particles (SPs) migration model considering the release effect, combined with the stochastic model, the analytical solution in the case of instantaneous injection was obtained. In the stochastic model, the probability density function (PDF) was characterized using the lognormal, bimodal lognormal and the joint lognormal distribution formulas. The single or double stochastic parameters were considered to study the migration characteristics of the SPs. When the single parameter deposition coefficient follows the lognormal distribution, the peak concentration of SPs increases with the standard deviation. As for the case of average pore velocity following the lognormal distribution, the peak concentration decreases and the corresponding time advances with the standard deviation increasing, and the breakthrough curves (BTCs) become more asymmetrical. When the deposition coefficient obeys the bimodal lognormal distribution, the peak concentration increases with increasing the proportion of low deposition coefficient. When the average pore water velocity follows the bimodal lognormal distribution, the peak concentration changes with the variation of the proportion of low pore water velocity, while the corresponding time is almost unchanged. When the double stochastic parameters follow the lognormal distribution, the peak concentration of SPs increases with the decrease of correlation coefficient and the BTCs become relatively symmetrical, with less trailing phenomenon. With the increase of migration distance, the peak concentration decreases and the time corresponding to the peak concentration of SPs increases.