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Symmetric drainage flow of a compressible fluid from a fracture modeled as along narrow channel is studied on the basis of linearized compressibleNavier-Stokes equations with no-slip condition. The Helmholtz decompositiontheorem is used to decompose the velocity field into an irrotational part and asolenoidal part. The irrotational velocity is driven by the fluid's volumetricexpansion whilst the role of the solenoidal velocity is to enforce the no-slipcondition for the overall velocity and it does not contribute to the mass flowrate. It is found that at large times this no-slip flow exhibits atime-dependent slip-like mass flow rate linearly proportional to the channelgap instead of the cubic power of the gap from the Poiseuille-type of flow. Thedrainage rate is also proportional to the kinematic viscosity, opposite toPoiseuille-type of flow which has a drainage rate proportional to the inverseof the kinematic viscosity. The same drainage rate formula also applies todrainage flow from a semi-sealed microchannel.

Symmetric drainage flow of a compressible fluid from a fracture: analytical solution and slip-like flow rate