A General Analytical Approximation to Impulse Response of 3-D Microfluidic Channels in Molecular Communication

TL;DR

This paper derives an analytical approximation for the impulse response of 3-D microfluidic channels with Poiseuille flow, providing a theoretical framework validated by Monte Carlo simulations for molecular communication systems.

Contribution

It introduces a general analytical approximation method for the impulse response in 3-D microfluidic channels considering radial flow variations, which is novel in the field.

Findings

Theoretical impulse response matches Monte Carlo simulations.

Radial distribution significantly affects axial molecular behavior.

Piecewise function effectively models molecule distribution in flow.

Abstract

In this paper, the impulse response for a 3-D microfluidic channel in the presence of Poiseuille flow is obtained by solving the diffusion equation in radial coordinates. Using the radial distribution, the axial distribution is then approximated accordingly. Since Poiseuille flow velocity changes with radial position, molecules have different axial properties for different radial distributions. We, therefore, present a piecewise function for the axial distribution of the molecules in the channel considering this radial distribution. Finally, we lay evidence for our theoretical derivations for impulse response of the microfluidic channel and radial distribution of molecules through comparing them using various Monte Carlo simulations.