Sketch of a liquid film in contact with a surface structured by periodic array of gas-filled grooves. Dimensional Cartesian coordinates x* and y* are shown. The plot below the sketch illustrates the periodic function β*(x*) used to model slip length variation due to the presence of the grooves.
Perturbation growth rate plotted versus the wavenumber based on Floquet theory for , β = 0.3 (solid line). The solution for the substrate without grooves (β = 0) is also shown by the dashed line for comparison.
The maximum perturbation growth rate as a function of β for different geometric parameters of the structuring: δ = 0.5 (solid line), δ = 0.4 (dashed line), and δ = 0.3 (dotted-dashed line); for all three cases.
A dispersion curve with a discontinuity obtained for β = 0.3, δ = 0.5, (top); the maximum growth rate as a function of the scaled slip length for δ = 0.5, (bottom).
Comparison of the dispersion curves obtained from Floquet theory (solid line) and the discretized eigenvalue problem approach (filled squares) for β = 0.3, δ = 0.5, .
Article metrics loading...
Full text loading...