The problem of suspension filtration in a porous medium consisting of active and passive zones is posed and numerically solved in the case of a multistage kinetics of particle deposition. Some mathematical model of the process is proposed that is based on the general conservation laws and additional phenomenological assumptions. The influence of the multistage kinetics of particle deposition on the filtration characteristics is considered. We establish that, as the parameter characterizing the duration of the stage of formation of the irreversible deposition increases, a region with complete saturation of the passive zone capacity appears near the filter inlet. No further increase of the deposition concentration in the passive zone is observed, while the process of particles movement in suspension and deposition of them in the active zone continues.

A mathematical model of solute transport in porous media with two adsorption zones was developed, incorporating balance and kinetic equations, and initial and boundary conditions. The model was enhanced to account for multistage deposition kinetics in both adsorption zones, and numerical methods were employed to solve the problem. An algorithm using the finite difference method was presented as a solution. Computer experiments were conducted to ascertain the effect of different parameters of the model on solute transport, and the results of the study were analyzed. The primary focus of this study is to assess the impact of parameters within the kinetic equations on the transport process. These parameters are crucial in determining the intensity of adsorption during various stages of the process. The findings of this study demonstrate that multistage deposition kinetics significantly influences both the transport and adsorption processes. Furthermore, the presence of two distinct intensity areas in the concentration profile of the adsorbed substance is observed. This phenomenon is attributed to the effects of multistage kinetics.

A model for suspension filtration in a porous medium is developed with the formation of a consolidating sediment. A system of equations including the equation for determining the pressure and the equations for determining the saturation of the medium by different phases is derived based on various hypothetical considerations and assumptions regarding the mass exchange between phases and the consolidation of the sediment. The model is solved numerically, and the influence of sediment consolidation on the filtration characteristics of the suspension is estimated.

Polycystic Ovary Syndrome (PCOS) stands as a significant health concern affecting women globally, characterized by hormonal imbalances and reproductive irregula Polycystic Ovary Syndrome (PCOS) stands as a significant health concern affecting women globally, characterized by hormonal imbalances and reproductive irregula

This paper investigates the relaxation filtration of a suspension through a radial filter surface under conditions of constant flow velocity. A mathematical model for relaxation cake growth is formulated based on the liquid-phase continuity equation, Darcy’s relaxation law, and constitutive relations for both compressive and liquid pressures. The resulting governing equation is a nonlinear partial differential equation for the compressive pressure, complemented by a Stefan condition that characterizes the motion of the cake–slurry interface. The moving-boundary problem is solved numerically using a finite difference method employing a coordinate-based front-tracking technique combined with iterative procedures. The numerical results demonstrate the influence of relaxation effects on cake formation. Increasing the relaxation time slows the compaction process, thereby maintaining higher porosity and promoting accelerated growth of the cake layer thickness.