Particle dynamics in a microfluidic T-junction vortex flow: the role of history force

Abstract

The motion of inertial particles suspended in a carrier fluid, together with the dynamics of the underlying vortical structures, is investigated in a square microfluidic T-junction. The coherent structures forming near the branching strongly affect the particle distribution and may promote particle trapping around the T-region. Single-phase numerical simulations of the unperturbed base flow are combined with integration of the particle force balance equation, which, unlike most previous studies, includes the Basset-Boussinesq (BB) history force. The flow topology is analysed for $Re=500$ and $570$, while particle properties are varied through the Stokes number $St$ and the particle-to-fluid density ratio $ρ$. At $Re=500$ the base flow exhibits a steady vortex pair, whereas at $Re=570$ a Hopf bifurcation gives rise to a helical oscillation of the primary vortex pair characterized by periodic breathing. The BB history force has a non-negligible impact over the whole range of $(ρ, St)$ pairs investigated. It acts as an additional viscous force which, together with the drag of the relative motion, opposes the pressure-gradient force, widening particle spiral trajectories radially and elongating them axially. Its inclusion reduces the basin of attraction, indicating that memory effects promote particle displacement away from the vortex core and weaken trapping. At $Re=570$, spectral proper orthogonal decomposition characterizes the breathing of the primary vortex pair. Particles injected at a given location interact with the vortical structure at different phases of the cycle depending on the injection time, producing substantially different trajectories. This phase dependence is reflected in the shape and extent of the basin of attraction, quantified through the trapping probability over the inlet section and the probability density functions of the force components.