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When a mixture of viscous oil and non-colloidal particles displaces air between two parallel plates, the shear-induced migration of particles leads to the gradual accumulation of particles on the advancing oil–air interface. This particle accumulation results in the fingering of an otherwise stable fluid–fluid interface. While previous works have focused on the resultant instability, one unexplored yet striking feature of the experiments is the self-similarity in the concentration profile of the accumulating particles. In this paper, we rationalise this self-similar behaviour by deriving a depth-averaged particle transport equation based on the suspension balance model, following the theoretical framework of Ramachandran ( J. Fluid Mech. , vol. 734, 2013, pp. 219–252). The solutions to the particle transport equation are shown to be self-similar with slight deviations, and in excellent agreement with experimental observations. Our results demonstrate that the combination of the shear-induced migration, the advancing fluid–fluid interface and Taylor dispersion yield the self-similar and gradual accumulation of particles.
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This content will become publicly available on May 25, 2026
Confinement-induced spreading and fingering of suspensions
Viscous fingering, a classic hydrodynamic instability, is governed by the the competition between destabilising viscosity ratios and stabilising surface tension or thermal diffusion. We show that the channel confinement can induce ‘diffusion’-like stabilising effects on viscous fingering even in the absence of interfacial tension and thermal diffusion, when a clear oil invades the mixture of the same oil and non-colloidal particles. The key lies in the generation of long-range dipolar disturbance flows by highly confined particles that form a monolayer inside a Hele-Shaw cell. We develop a coarse-grained model whose results correctly predict universal fingering dynamics that is independent of particle concentrations. This new mechanism offers insights into manipulating and harnessing collective motion in non-equilibrium systems.
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- PAR ID:
- 10639472
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1011
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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