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This work employs for the first time invariant solutions of the Navier-Stokesequations to study the interaction between finite-size particles and near-wallcoherent structures. We consider horizontal plane Couette flow and focus onNagata's upper-branch equilibrium solution (Nagata, 1990) at low Reynoldsnumbers where this solution is linearly stable. When adding a single heavyparticle with a diameter equivalent to 2.5 wall units, we observe that thesolution remains stable and is essentially unchanged away from the particle.This result demonstrates that it is technically feasible to utilize exactcoherent structures in conjunction with particle-resolved DNS. Whiletranslating in the streamwise direction, the particle migrates laterally underthe action of the quasi-streamwise vortices until it reaches the regionoccupied by the low-speed streak, where it attains a periodic state of motion.As a result of the ensuing preferential particle location, the time-averagestreamwise particle velocity differs from the plane-average fluid-phasevelocity at the same wall-distance as the particle center, as previouslyobserved in experiments and in numerical data for fully turbulent wall-boundedflows. Additional constrained simulations where the particle is maintained at afixed spanwise position while freely translating in the other two directionsreveal the existence of two equilibria located in the low-speed and in thehigh-speed streak, respectively, the former being an unstable point. Aparametric study with different particle to fluid density ratios is conductedwhich shows how inertia affects the spanwise fluctuations of the periodicparticle motion. Finally, we discuss a number of potential futureinvestigations of solid particle dynamics which can be conducted with the aidof invariant solutions (exact coherent structures) of the Navier-Stokesequations.

Can preferential concentration of finite-size particles in plane Couette turbulence be reproduced with the aid of equilibrium solutions?