Symmetric drainage flow of a compressible fluid from a fracture: Analytical solution and slip-like flow rate. (July 2019)

• Record Type: Journal Article
• Authors: Shen, Di; Chen, Kang Ping
• Is Part Of: Mechanics research communications. Volume 99(2019)
• Page Start: 15
• Page End: 21
• Publication Date: 2019-07
• Subjects: Microchannel flow -- Compressible flow -- Navier-Stokes equations -- No-slip condition; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2019.06.002
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: An analytical solution is obtained for draining compressible fluid from a fracture. The drainage rate is slip-like. The drainage rate is proportional to the fluid's kinematic viscosity. 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.