## Abstract

Symmetric drainage flow of a compressible fluid from a thin fracture modeled as a long narrow 2D channel is studied on the basis of linearized compressible Navier-Stokes equations with the no-slip condition. The Helmholtz decomposition theorem is used to decompose the velocity field into an irrotational part and a solenoidal part. The irrotational velocity is driven by the fluid's volumetric expansion; whilst the role of the solenoidal velocity is to enforce the no-slip condition for the overall velocity and it does not contribute to the mass flow rate. It is found that, at large times, this no-slip flow exhibits a time-dependent slip-like mass flow rate linearly proportional to the channel gap instead of the cubic power of the gap for the Poiseuille-type of flow. The drainage rate is also proportional to the kinematic viscosity, opposite to Poiseuille-type of flow, which produces a drainage rate proportional to the inverse of the kinematic viscosity. The same drainage rate formula also applies to drainage flow from a semi-sealed thin fracture.

Original language | English (US) |
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Pages (from-to) | 15-21 |

Number of pages | 7 |

Journal | Mechanics Research Communications |

Volume | 99 |

DOIs | |

State | Published - Jul 2019 |

## Keywords

- Compressible flow
- Microchannel flow
- Navier-Stokes equations
- No-slip condition

## ASJC Scopus subject areas

- Civil and Structural Engineering
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering