The Influence of Boundaries on Gravity Currents and Thin Films: Drainage, Confinement, Convergence, and Deformation Effects

Zhong Zheng, Howard A. Stone

Research output: Contribution to journalReview articlepeer-review

Abstract

Thin film flows, whether driven by gravity, surface tension, or the relaxation of elastic boundaries, occur in many natural and industrial processes. Applications span problems of oil and gas transport in channels to hydraulic fracture, subsurface propagation of pollutants, storage of supercritical CO2in porous formations, and flow in elastic Hele-Shaw configurations and their relatives. We review the influence of boundaries on the dynamics of thin film flows, with a focus on gravity currents, including the effects of drainage into the substrate, and the role of the boundaries to confine the flow, force its convergence to a focus, or deform, and thus feedback to alter the flow. In particular, we highlight reduced-order models. In many cases, self-similar solutions can be determined and describe the behaviors in canonical problems at different timescales and length scales, including self-similar solutions of both the first and second kind. Additionally, the time transitions between different solutions are summarized. Where possible, remarks about various applications are provided.

Original languageEnglish (US)
Pages (from-to)27-56
Number of pages30
JournalAnnual Review of Fluid Mechanics
Volume54
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Keywords

  • boundary influence
  • confinement
  • deformable boundaries
  • permeable boundaries
  • reduced-order models
  • self-similar solutions
  • viscous currents

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