### 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) |
---|---|

Pages (from-to) | 15-21 |

Number of pages | 7 |

Journal | Mechanics Research Communications |

Volume | 99 |

DOIs | |

State | Published - Jul 1 2019 |

### Fingerprint

### 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

### Cite this

**Symmetric drainage flow of a compressible fluid from a fracture : Analytical solution and slip-like flow rate.** / Shen, Di; Chen, Kangping.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Symmetric drainage flow of a compressible fluid from a fracture

T2 - Analytical solution and slip-like flow rate

AU - Shen, Di

AU - Chen, Kangping

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - Compressible flow

KW - Microchannel flow

KW - Navier-Stokes equations

KW - No-slip condition

UR - http://www.scopus.com/inward/record.url?scp=85067385566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067385566&partnerID=8YFLogxK

U2 - 10.1016/j.mechrescom.2019.06.002

DO - 10.1016/j.mechrescom.2019.06.002

M3 - Article

VL - 99

SP - 15

EP - 21

JO - Mechanics Research Communications

JF - Mechanics Research Communications

SN - 0093-6413

ER -