Effective Navier-slip in non-Newtonian fluid flows over corrugated surfaces

Abstract

In this study, we show that complex local flow fields, particularly those near corrugated surfaces, can be accurately reproduced with effective Navier-slip boundary conditions over an imaginary smooth surface, in which the normalized slip length can be considered as a surface property even for non-Newtonian fluid flows. The expression for the normalized slip length was derived analytically using the effective viscosity and effective shear rate in a pressure-driven channel flow with a corrugated surface, based on the two-parameter model by separating geometrical and rheological factors with the effective viscosity concept. Our framework was established on the combination of the force balance approach for slip length characterization and the flow quantification method based on the energy dissipation rate. Effects of corrugated patterns with various aspect ratios were investigated. For verification, an example stick–slip–stick flow problem was tested and the results were compared with those of direct simulations. We report that the dimensionless normalized slip length appears to be almost constant and independent of the flow rate (or pressure drop). This implies that the normalized slip length is nearly independent of rheological properties. In addition, the dimensionless slip length of non-Newtonian fluids was found to be close to that of a Newtonian fluid, and it depends on the flow geometry itself.

Slip length of branched hydrocarbon oils confined between iron surfaces

“…Navier formulated the linear slip boundary condition s w ¼ ku s as a constitutive equation [1] relating the wall shear stress s w to the tangential slip velocity u s ¼ u À u w . The latter is the difference between the absolute velocity u of a fluid particle tangential to the wall and the lateral velocity u w of the wall.…”

“…(Note, that for high Reynolds number this is not true: for a turbulent Couette flow the shear rate is maximal at the wall and minimal in the symmetry plane of the channel.) [1][2][3][4].…”

Mixed Convection in a Lid‐Driven Cavity with Triangular Corrugations and Built‐in Triangular Block

“…The enormous popularity of such systems is due to their simple geometry and potential to explore vast significant fluid mechanics phenomena, such as corner eddies, flow bifurcation, flow transition, turbulence, longitudinal vortices, etc. [10][11][12]. Similarly, the convective heat transfer (CHT) within the rectangular enclosure is of prime interest owing to its implication in fields like slurry processing, thermal management in the electronic components, nuclear reactors, insulation to the high-rise buildings, lubrication, design of solar collectors, and many others [13].…”