Analytical Models for Particle Diffusion and Flow in a Horizontal Cylinder with a Vertical Force

TL;DR

This paper develops a semi-analytical model for particle diffusion and flow in a cylindrical channel influenced by vertical forces, validated by simulations, offering a flexible and efficient tool for molecular communication analysis.

Contribution

It introduces a novel semi-analytical model incorporating boundary conditions and vertical forces, enhancing the understanding of particle dynamics in cylindrical channels.

Findings

Model matches particle-based simulations accurately

Provides low run-time algorithms for particle concentration prediction

Extends to various boundary conditions and parameters

Abstract

This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or magnetism. The dynamics of the diffusion process are modeled by multi-dimensional transfer functions in a spatio-temporal frequency domain. Realistic boundary conditions are incorporated by the design of a feedback loop. The result is a discrete-time semi-analytical model for the particle concentration in the channel. The model is validated by comparison to particle-based simulations. These numerical experiments reveal that the particle concentration of the proposed semi-analytical model and the particle-based model are in excellent agreement. The analytical form of the proposed solution provides several benefits over purely numerical models, e.g. high flexibility, existence of low run-time algorithms, extendability to several kinds of boundary conditions, and analytical connection to parameters from communication theory.