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For one-way coupled (1WC) flows, Tom & Bragg (J. Fluid Mech., vol. 871, 2019, pp. 244–270) advanced the analysis of Maxey (J. Fluid Mech., vol. 174, 1987, pp. 441–465), which applied to weakly inertial particles, to particles of arbitrary inertia, and the new theoretical result revealed the role that different scales play in the preferential sweeping mechanism that leads to enhanced particle settling in turbulent flows. Monchaux & Dejoan (Phys. Rev. Fluids, vol. 2, 2017, 104302) showed using direct numerical simulations that, while for low particle loading the effect of two-way coupling (2WC) on the global flow statistics is weak, 2WC enables the particles to drag the fluid in their vicinity down with them, significantly enhancing their settling, and they argued that 2WC suppresses the preferential sweeping mechanism. We explore this further by considering the impact of 2WC on the contribution made by eddies of different sizes on the particle settling. In agreement with Monchaux & Dejoan, we show that even for low loading, 2WC strongly enhances particle settling, and we show how 2WC modifies the contribution from different flow scales. However, contrary to their study, we show that preferential sweeping remains important in 2WC flows. In particular, for both 1WC and 2WC flows, the settling enhancement due to turbulence is dominated by contributions from particles in straining regions of the flow, but for the 2WC case, the particles in these regions also drag the fluid down with them, leading to an enhancement of their settling compared with the 1WC case.

In this work we aim to understand the interplay between deformation and energy of a fluid particle in a turbulent flow, focusing on the role of the pressure Hessian. A new decomposition of the Hessian is proposed, defining a conservative Hessian which contains the stabilizing effects of the full Hessian on energy and deformation of fluid elements. This conservative Hessian is then used to construct models for the velocity gradient which allow controlling alignments and singularities.

Experiments carried out using a lung model with a single horizontal bifurcation under different steady inhalation conditions explored the orientation of depositing carbon fibers, and particle deposition fractions. The orientations of deposited fibers were obtained from micrographs. Specifically, the effects of the sedimentation parameter ( γ ), fiber length, and flow rate on orientations were analyzed. Our results indicate that gravitational effect on deposition cannot be neglected for 0.0228 γ γ for values 0.0228 γ γ suggests these characteristics can be used to estimate fiber deposition in the lower airways. Computer simulations with sphere-equivalent diameter models for the fibers explored deposition efficiency vs. Stokes number. Using the volume-equivalent diameter model, our experimental data for the horizontal bifurcation were replicated. Results for particle deposition using a lung model with a vertical bifurcation indicate that body position also affects deposition.

In a seminal article, Maxey (J. Fluid Mech., vol. 174, 1987, pp. 441–465) presented a theoretical analysis showing that enhanced particle settling speeds in turbulence occur through the preferential sweeping mechanism, which depends on the preferential sampling of the fluid velocity gradient field by the inertial particles. However, recent direct numerical simulation (DNS) results in Ireland et al. (J. Fluid Mech., vol. 796, 2016b, pp. 659–711) show that even in a portion of the parameter space where this preferential sampling is absent, the particles nevertheless exhibit enhanced settling velocities. Further, there are several outstanding questions concerning the role of different turbulent flow scales on the enhanced settling, and the role of the Taylor Reynolds number $R_{\unicode[STIX]{x1D706}}$. The analysis of Maxey does not explain these issues, partly since it was restricted to particle Stokes numbers $St\ll 1$. To address these issues, we have developed a new theoretical result, valid for arbitrary $St$, that reveals the multiscale nature of the mechanism generating the enhanced settling speeds. In particular, it shows how the range of scales at which the preferential sweeping mechanism operates depends on $St$. This analysis is complemented by results from DNS where we examine the role of different flow scales on the particle settling speeds by coarse graining the underlying flow. The results show how the flow scales that contribute to the enhanced settling depend on $St$, and that contrary to previous claims, there can be no single turbulent velocity scale that characterizes the enhanced settling speed. The results explain the dependence of the particle settling speeds on $R_{\unicode[STIX]{x1D706}}$, and show how the saturation of this dependence at sufficiently large $R_{\unicode[STIX]{x1D706}}$ depends upon $St$. The results also show that as the Stokes settling velocity of the particles is increased, the flow scales of the turbulence responsible for enhancing the particle settling speed become larger. Finally, we explored the multiscale nature of the preferential sweeping mechanism by considering how particles preferentially sample the fluid velocity gradients coarse grained at various scales. The results show that while rapidly settling particles do not preferentially sample the fluid velocity gradients, they do preferentially sample the fluid velocity gradients coarse grained at scales outside of the dissipation range. This explains the findings of Ireland et al., and further illustrates the truly multiscale nature of the mechanism generating enhanced particle settling speeds in turbulence.