A nonlocal multiscale model for Brownian particles: Application to hindered deposition in microfluidic systems

Separation of neutrally buoyant sub-micron particles from a fluid flow in a microfluidic device under the action of an external field (e.g. electric, magnetic, gravitational, concentration) is an important challenge in the engineering sciences. In such processes, the hydrodynamic force resisting the motion of the particles towards a target wall becomes distinctively nonlocal, being influenced by particle velocities in past locations via the history force. The nonlocality of the hydrodynamic force implies that the Brownian force exhibits similar correlations in time, owing to the fluctuation–dissipation relation. The problem of identifying the optimal design parameters for the microfluidic system then traditionally necessitates the application of computationally expensive simulation models. In this work, we develop a novel computationally efficient nonlocal multiscale model for Brownian particles in confined geometries. The model accounts for nonlocality and hindrance effects by employing multiphase Direct Numerical Simulation (DNS) data to determine the memory kernels associated with the particles in the system. The memory kernels are then used in a Lagrangian Particle Tracking (LPT) routine to evolve particle trajectories without the need for analytical models to describe the forces involved and their modulation due to hindrance. We show that the focusing of particles on a target wall during hindered deposition in microfluidic systems can be controlled via two parameters (the magnitude of the attracting force and the size of the geometry) that interact in non-trivial ways. For the parameter space investigated in the current work, the focusing, as quantified via the normalized impact radius, can be reduced by up to 80% by optimally designing the microfluidic device. The implications of using the new model for further development of microfluidic particulate systems are discussed. • Low cost method presented to simulate Brownian motion including nonlocal effects. • Short Direct Numerical Simulations generate memory kernel map of domain. • Kernels produce accurate hydrodynamic and Brownian forces sans analytical models. • Particle focusing facilitated by increased hindrance and reduced residence time. • Hindrance is controlled via device design, residence time via attraction force.