Compressible Viscous-flow in Slits With Slip At the Wall
(1994) Journal of Rheology — Vol. 38, n° 3, p. 639-654 (1994)
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- Abstract
- We study the time-dependent compressible flow of a Newtonian fluid in slits using an arbitrary nonlinear slip law relating the shear stress to the velocity at the wall. This slip law exhibits a maximum and a minimum and so does the flow curve. According to one-dimensional stability analyses, the steady-state solutions are unstable if the slope of the flow curve is negative. The two-dimensional flow problem is solved using finite elements for the space discretization and a standard fully implicit scheme for the time discretization. When compressibility is taken into account and the volumetric flow rate at the inlet is in the unstable regime, we obtain self-sustained oscillations of the pressure drop and of the mass flow rate at the exit, similar to those observed with the stick-slip instability. The effects of compressibility and of the length of the slit on the amplitude and the frequency of the oscillations are also examined.
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Georgiou, GC., & Crochet, M. (1994). Compressible Viscous-flow in Slits With Slip At the Wall. Journal of Rheology, 38(3), 639-654. https://doi.org/10.1122/1.550479 (Original work published 1994)