Dust Control in Finite Air Volumes at Zero Gravity - Mean-Field Like Analysis

TL;DR

This paper models dust clogging in a filter under zero gravity using a mean-field approach, revealing how the number of clogged pores evolves over time with a non-universal exponent influenced by dust and filter properties.

Contribution

It introduces a simplified 1D model for dust clogging in zero gravity, analyzing how clog growth depends on dust size and filter stickiness, with a focus on non-universal scaling behavior.

Findings

Clog growth follows a power-law with a non-universal exponent.

The exponent depends on dust size distribution and filter stickiness.

The model provides insights into dust filtration in zero gravity environments.

Abstract

We study a simple 1D model of dust rods, with mean size \mu, passing through a parallel 1D alignment of pores as a problem of clogging of a filter by dust grains; \mu is kept less than the pore size, s. We assume that the filter is "sticky", characterized by some parameter 0 \le \lambda \le 1, which means that dust grains slightly smaller in size than s can get trapped in the pores. Our analyses suggest that the number of clogged pores, N_{cl}, grows in time as t_N^{clog} \propto N_{cl}^{\nu}, where \nu = \nu(\mu,\lambda) is a non-universal exponent that depends upon the dust size distribution and filter properties.