What question did this study set out to answer?

To develop a mathematical model describing contaminant transfer in a filtration system involving hard water softening.

December 11, 2025Scientific ReportsOpen Access

Mathematical model of filtration of contaminated solution in a filter with hard water softening on experimental data at the boundary

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The mathematical model predicts contaminant dynamics in filtration systems, indicating adsorptive capacity influences efficiency.

To develop a mathematical model describing contaminant transfer in a filtration system involving hard water softening.
Constructed using a thermodynamic approach with experimental data
Formulated mass transfer equations reduced to dimensionless form
Applied integral transformations to solve initial-boundary value problem
Conducted numerical analysis to evaluate concentration profiles and steady states.
Demonstrated concentration increases until steady state at low convective velocities
Identified minimal influence of convective velocity on concentration at higher velocities
Showed steady state reaches earlier with more efficient filter performance
Estimated filter durability via maximum adsorptive capacity.

Chernukha et al. (2025) studied this question.

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