Modeling Molecular Communications in Tubes With Poiseuille Flow and Robin Boundary Condition

Accurately modeling the molecular channel is crucial for the design and analysis of molecular communications. In this letter, we propose a Markovian-based channel model for molecular communications in tubes with Poiseuille flow and the Robin boundary condition. The cross section of the tube is divided into rings and the continuously varying flow velocity field is approximated by the mean of the flow velocity on each ring. The radial displacement of molecules versus time is modeled by a Markov chain, and then the probability density function of the axial displacement is modeled using this Markov chain and the approximated flow velocity field. The accuracy of the proposed model is verified through particle-based simulations.