Filtration of 2-particles suspension in a porous medium
During the construction of underground storage of hazardous waste, it is necessary to create waterproof walls in the ground. The grout is filtered in the rock, fills the pores and, when hardened, creates a reliable barrier to groundwater. A one-dimensional model of the flow of inhomogeneous particles in a porous medium is considered. The retained particles profiles formed during deep bed filtration are studied. It is shown that when filtering a 2-particle suspension, the deposit is distributed unevenly. The profile of large retained particles is always monotonous, and the profile of small retained particles is nonmonotonic. The monotonicity of the total deposit profile depends on the model parameters. The shape of non-monotonic profiles is time-dependent. At short times, the profile decreases monotonously. At some point, a maximum appears on the profile graph, which shifts from the inlet to the output with increasing time. When the maximum point reaches the outlet, the profile becomes monotonically increasing. With a further increase in time, the retention profiles remain monotonically increasing. Analytical solutions for a filtration model with particles of three or more different types are unknown. Analysis of the retention profiles of the polydisperse suspension requires further study.