Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary

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A charged oil droplet advancing into a charged capillary is considered, assuming the special case in which charges are opposite and equal. The droplet is surrounded by an aqueous phase that wets the capillary wall, such that a thin film adjacent to the wall is laid down as the droplet advances. Electro-osmotic conjoining pressures contrive to make the film even thinner than in an uncharged case. The pressure drop needed to drive the droplet along is examined. The pressure drop is dominated by capillarity but contains electro-osmotic and viscous corrections. The viscous correction is shown to be remarkably insensitive to the presence of electro-osmotic effects. The electro-osmotic pressure correction is negative, reflecting work done by the electro-osmotic conjoining pressure as film is laid down. The negative electro-osmotic correction to pressure drop can far exceed the positive viscous correction. As a result, in the presence of conjoining pressures, a droplet can be driven along a capillary channel with even less pressure drop than is seen for a static uncharged droplet.
Original languageEnglish
Article number20210801
Number of pages21
JournalProceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences
Issue number2258
Publication statusPublished - 9 Feb 2022


  • droplet
  • capillary
  • electroosmotic
  • thin film
  • pressure drop
  • waterflooding


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