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

Fatih Dinc, Bayram Cevdet Akdeniz, Ali Emre Pusane, Tuna Tugcu

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.