  This work employs for the first time invariant solutions of the Navier-Stokes
equations to study the interaction between finite-size particles and near-wall
coherent structures. We consider horizontal plane Couette flow and focus on
Nagata's upper-branch equilibrium solution (Nagata, 1990) at low Reynolds
numbers where this solution is linearly stable. When adding a single heavy
particle with a diameter equivalent to 2.5 wall units, we observe that the
solution remains stable and is essentially unchanged away from the particle.
This result demonstrates that it is technically feasible to utilize exact
coherent structures in conjunction with particle-resolved DNS. While
translating in the streamwise direction, the particle migrates laterally under
the action of the quasi-streamwise vortices until it reaches the region
occupied by the low-speed streak, where it attains a periodic state of motion.
As a result of the ensuing preferential particle location, the time-average
streamwise particle velocity differs from the plane-average fluid-phase
velocity at the same wall-distance as the particle center, as previously
observed in experiments and in numerical data for fully turbulent wall-bounded
flows. Additional constrained simulations where the particle is maintained at a
fixed spanwise position while freely translating in the other two directions
reveal the existence of two equilibria located in the low-speed and in the
high-speed streak, respectively, the former being an unstable point. A
parametric study with different particle to fluid density ratios is conducted
which shows how inertia affects the spanwise fluctuations of the periodic
particle motion. Finally, we discuss a number of potential future
investigations of solid particle dynamics which can be conducted with the aid
of invariant solutions (exact coherent structures) of the Navier-Stokes
equations.
