Analysis on creeping channel flows of compressible fluids subject to wall slip

Abstract

Creeping channel flows of compressible fluids subject to wall slip are widely encountered in industries. This paper analyzes such flows driven by pressure in planar as well as circular channels. The analysis elucidates unsteady flows of Newtonian fluids subject to the Navier slip condition, followed by steady flows of viscoplastic fluids, in particular, Herschel-Bulkley fluids and their simplifications including power law and Newtonian fluids, that slip at wall with a constant coefficient or a coefficient inversely proportional to pressure. Under the lubrication assumption, analytical solutions are derived, validated, and discussed over a wide range of parameters. Analysis based on the derived solutions indicates that unsteadiness alters crosssection velocity profiles. It is demonstrated that compressibility of the fluids gives rise to a concave pressure distribution in the longitudinal direction, whereas wall slip with a slip coefficient that is inversely proportional to pressure leads to a convex pressure distribution. Energy dissipation resulting from slippage can be a significant portion in the total dissipation of such a flow. A distinctive feature of the flow is that, in case of the pressure-dependent slip coefficient, the slip velocity increases rapidly in the flow direction and the flow can evolve into a pure plug flow at the exit.

Newtonian Poiseuille flows with pressure-dependent wall slip

“…Under the lubrication approximation, Tang (2012) also derived analytical time-dependent solutions of the same flows. As in Tang andKalyon (2008a, 2008b), he assumed that a à $ 1=p à and pointed out that such a dependence, also proposed for low-density compressible flow [Bird et al (2002)], is similar to that of Eq. (2).…”

“…He showed that, in general, the pressure gradient is not constant and depends on both the inlet and the outlet pressures. Tang andKalyon (2008a, 2008b) also developed a mathematical model describing the time-dependent pressure-driven flow of compressible polymeric liquids subject to pressure-dependent slip. They assumed that the slip coefficient a* is inversely proportional to the pressure.…”

Pressure dependent wall slip of wood flour filled polymer melts

“…A systematic experimental study at the capillary rheometer of pressure dependent slip of polyolefins, together with a very thorough mathematical model, is due to Hatzikiriakos and Dealy (1992), while a theoretical study of pressure dependent wall slip of Newtonian fluids without neglecting inertia is due to Rao and Rajagopal (1999). Tang and Kalyon (2008) and Tang (2012) have solved some pressure dependent slip flows of non-Newtonian compressible suspensions and compared them with experimental results obtained using polydimethylsiloxane as a test fluid. More recently, Kalogirou et al (2011), Damianou et al (2013) and Housiadas (2013) have solved theoretically and numerically some flows of incompressible Newtonian and non-Newtonian fluids with pressure dependent slip.…”

Analytical Solutions of Some Fully Developed Flows of Couple Stress Fluid between Concentric Cylinders with Slip Boundary Conditions

“…Although pressure driven flows are unidirectional and have been studied earlier for Newtonian and some non-Newtonian fluids, they still attract special attention in a number of emerging problems [16][17][18][19]. Ellahi [11] has examined the effect of the slip condition on flow of an Oldroyd 8-constant fluid in a channel.…”