Mathematical Modeling of Sediments in the Filter and Improvement of the Filter Construction

TL;DR

This paper develops a mathematical model to analyze sediment formation on filter walls, considering flow dynamics and sedimentation effects, with numerical results highlighting the importance of preliminary filter design calculations.

Contribution

It introduces a new mathematical model for sedimentation growth on filter walls, including analytical and numerical analysis of sediment effects on filter performance.

Findings

Flow speed and filtration time significantly affect sediment buildup.

Preliminary filter design calculations are crucial for effective filtration.

Sediment formation can be modeled analytically and numerically for different filter geometries.

Abstract

The filters work in many areas of technology. There constructions are different and substances under filtration are different. It is necessary in some cases to take into account forming of sediments on the walls of the filter since they can change properties of the filter or blind the filtering apertures at all. I construct a mathematical model of sedimentation growth on the walls of the porous filter in this article. Analytical investigation is present in the article and numeric results too. There are formulas for dependencies of concentration near the walls on inner concentration in liquid in the article. Flow speed, calculated time of work, purification efficiency and other parameters proved to be important factors. Differing of radiuses of apertures from membrane to membrane can make contamination equal along the filter. Numerical results show importance of preliminary calculation of the filter for the purpose it will serve. Forming of calcic sediment is an investigated example of chemical reaction.