Exploring Lagrangian Modelling Approach for Nanoparticle Transport in Microchannels

In this paper, we introduced a Lagrangian modelling approach to investigate the transport of particles at the nano/micro scale within a microchannel. The methodology of this work involves several stages. Initially, we used Langevin equation and then solved it numerically by finite difference approach to mimic particle transport. Subsequently, we explored various useful macroscopic quantities such as mean square displacement, particle trajectory, and identified numerous timescales of the Brownian motion involved. We considered two fundamental forces, specifically the Brownian force and the hydrodynamic force, with a particular emphasis on the Brownian force. The white noise term and random walk trajectories were solved numerically and simulated for various time step values. Moreover, we explored time scales greater than momentum relaxation time, where the suspended microparticles in a fluid flow exhibited distinctive diffusion behaviour. Furthermore, we observed the suspension of nanoparticles with a low Stokes number (St ≪ 1) transport in the fluid flow direction. Furthermore, we explored a one-way coupling approach between suspended alumina nanoparticles in a water-based fluid. Lastly, we conducted a detailed validation with previously published work in literature and found a good agreement.