The effect of the slip boundary condition on the flow of fluids in a channel

Abstract

Summary. The assumption that a liquid adheres to a solid boundary ("no-slip" boundary condition) is one of the central tenets of the Navier-Stokes theory. However, there are situations wherein this assumption does not hold. In this paper we investigate the consequences of slip at the wall on the flow of a linearly viscous fluid in a channel. Usually, the slip is assumed to depend on the shear stress at the wall. However, a number of experiments suggests that the slip velocity also depends on the normal stress. Thus, we investigate the flow of a linearly viscous fluid when the slip depends on both the shear stress and the normal stress. In regions where the slip velocity depends strongly on the normal stress, the flow field in a channel is not fully developed and rectilinear flow is not possible. Also, it is shown that, in general, traditional methods such as the Mooney method cannot be used for calculating the slip velocity.

Flows of granular material in two-dimensional channels

“…Within the preliminary work it is simply implemented, while in the two-dimensional finite element calculations it is prescribed as a natural boundary condition, which requires the addition of complementary zero-flux terms in the variational formulation. For other examples of slip boundary conditions and discussion see [28,31,32], while for a variational inequality possibility as applied to the Signorini boundary condition problem see [33]. In this instance we choose regularisation in line with our previous choice in the effective viscosity function µ(I).…”

On non-linear flows with slip boundary condition

“…Experimentalists [10][11][12][13] usually associate "spurt" with slip at the wall. More recently Rao and Rajagopal [14,15] discussed the flows of a JohnsonSegalman fluid explaining "spurt" and the effect of the slip condition on the flow of Newtonian fluids in a channel.…”

Homotopy Analysis for MHD Hiemenz Flow in a Porous Medium With Thermal Radiation, Velocity and Thermal Slips Effects

“…the polishing of artificial heart valves and internal cavities. So, in order to have a better understanding of the slips phenomena, many a researchers like Mooney (1931); Rao and Rajagopal (1999); Khaled and Vafai (2004);Wang (2002);Wang (2006) and Hayat et al (2007) examined the effects of slips boundary conditions on fluid flows through different geometries.…”