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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We discuss the creeping motion of plugs of negligible viscosity in roughcapillary tubes filled with carrier fluids. This extends Bretherton's researchwork on the infinite-length bubble motion in a cylindrical or smooth tube forsmall capillary numbers Ca. We first derive the asymptotic dependence of theplug speed on the finite length in the smooth tube case. This dependence onlength is exponentially small, with a decay length much shorter than the tuberadius R. Then we discuss the effect of azimuthal roughness of the tube on theplug speed. The tube roughness leads to an unbalanced capillary pressure and acarrier fluid flux in the azimuthal plane. This flux controls the relaxation ofthe plug shape to its infinite-length limit. For long-wavelength roughness, wefind that the above decay length is much longer in the rough tube, and evenbecomes comparable to the tube radius R in some cases. This implies amuch-enhanced dependence of the plug speed on the plug length. This mechanismmay explain the catch-up effect seen experimentally.

Plugs in rough capillary tubes: enhanced dependence of motion on plug length