Superhydrophobic surfaces with recirculating interfacial flow due to surfactants are 'effectively' immobilized

At high surface Peclet numbers, it is common to associate the presence of surfactants with surface immobilization, where a free surface becomes indistinguishable from a no-slip surface. A different mechanism has recently been proposed for longitudinal shear flow along a unidirectional trench (Baier & Hardt, J. Fluid Mech., vol. 949, 2022, A34) wherein, at high Marangoni numbers, the meniscus spanning the finite-length trench becomes a constant-shear-stress surface due to contamination by incompressible surfactant. That model predicts recirculating interfacial flows on the meniscus, a phenomenon that has been observed experimentally (Song et al., Phys. Rev. Fluids, vol. 3, issue 3, 2018, 033303). By finding an explicit solution to the constant-shear-stress model at all protrusion angles and calculating the effective slip length for a dilute mattress of such surfactant-laden trenches, we show that those effective slip lengths are almost indistinguishable from those for a surface whose menisci have the same deflection but have been completely immobilized (i.e. they are no-slip surfaces). This means that, despite the presence of non-trivial recirculating vortical flows on the menisci, the aggregate slip characteristics of such surfaces are that they have been effectively immobilized. This surprising result underscores the need for caution in comparing theory with experiments based on effective slip properties alone.

Automated summary

At high surface Peclet numbers, the presence of surfactants can lead to surface immobilization, but a different mechanism is proposed for longitudinal shear flow along a unidirectional trench at high Marangoni numbers, where the meniscus becomes a constant-shear-stress surface due to contamination by surfactant. Experimental observations support the presence of recirculating interfacial flows on the meniscus. By calculating slip lengths, it is shown that the effective immobilization of the surfaces with vortical flows on the meniscus highlights the caution needed when comparing theory and experiments based on effective slip properties alone.