Monte Carlo simulation of dead-end diafiltration of bidispersed particle suspensions

A two-dimensional Monte Carlo simulation of dead-end diafiltration of bidispersed particle suspensions was performed. The diafiltration process involves separation of components based on their size by using a permeable membrane. The continuous model was applied to study separation of mixture of disks with diameter d and D (D>d). It was assumed that the membrane at the bottom was permeable to the particles of the smaller diameter d, and impermeable to the particles of the larger diameter D. The process of vertical filtration was accompanied by the simultaneous Brownian motion of the particles and downward movement of the piston. The mixtures with different numerical concentrations of particles, diameter ratio, and initial size of the systems in the vertical direction L_{y} have been studied. The time dependencies of the rejection coefficient k and relative height of suspension h/L_{y} revealed the presence of complete and incomplete separation regimes. The presence of filtration and diffusion-driven stratification of the disks in the vertical direction was observed. The phenomenon of incomplete separation was explained by the formation of an impenetrable barrier from larger particles at the bottom of the deposit.