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Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh–Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler–Lagrange formalism are compared to Euler–Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.
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This content will become publicly available on January 10, 2026
Instability of a dusty shear flow
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence of any background flow. However, we demonstrate that the combined scenario – comprising a simple shear flow with a localized band of particles – can exhibit destabilization due to their two-way interaction. The instability originates solely from the momentum feedback from the particle phase to the fluid phase. Eulerian–Lagrangian simulations are employed to illustrate the existence of this instability. Furthermore, the results are compared with a linear stability analysis of the system using an Eulerian–Eulerian model. Our findings indicate that the instability has an inviscid origin and is characterized by a critical wavelength below which it is not persistent. We have observed that increasing particle inertia dampens the unstable modes, whereas the strength of the instability increases with the strength of the coupling between the fluid and particle phases.
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- Award ID(s):
- 2148710
- PAR ID:
- 10621285
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1002
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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