English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Recognising that surfactants may impede the drag reduction resulting fromsuperhydrophobic surfaces (SHSs), and that surfactant concentrations canfluctuate in space and time, we examine the unsteady transport of solublesurfactant in a laminar pressure-driven channel flow bounded between two SHSs.The SHSs are periodic in the streamwise and spanwise directions. We assume thatthe channel length is much longer than the streamwise period, the streamwiseperiod is much longer than the channel height and spanwise period, and bulkdiffusion is sufficiently strong for cross-channel concentration gradients tobe small. By combining long-wave and homogenisation theories, we derive anunsteady advection-diffusion equation for surfactant flux transport over thelength of the channel, which is coupled to a quasi-steady advection-diffusionequation for surfactant transport over individual plastrons. As diffusion overthe length of the channel is typically small, the leading-order surfactant fluxis governed by a nonlinear advection equation that we solve using the method ofcharacteristics. We predict the propagation speed of a bolus of surfactant anddescribe its nonlinear evolution via interaction with the SHS. The propagationspeed can fall significantly below the average streamwise velocity as thesurfactant adsorbs and rigidifies the plastrons. Smaller concentrations ofsurfactant are therefore advected faster than larger ones, so thatwave-steepening effects can lead to shock formation in the surfactant-fluxdistribution. These findings reveal the spatio-temporal evolution of the slipvelocity and enable prediction of the dynamic drag reduction and effective sliplength in microchannel applications.

Unsteady evolution of slip and drag in surfactant-contaminated superhydrophobic channels