## Abstract

We study capillary displacement in infinitely long right prisms filled with one wetting fluid and one nonwetting fluid, while restricting ourselves to zero gravity and totally wetting prism walls. At equilibrium, the intersection of the fluid-fluid interface with the cross section of the prism is composed of nonintersecting circular arcs with a uniform radius of curvature inversely proportional to the capillary pressure. We trace the circular arcs during capillary displacement using the so-called connected chordal axis (CCA) of the cross section. We identify the points on the CCA which are associated with the following events in the arcs' "lives": emergence, disappearance, end points (i.e., three phase contact points), getting pinned or unpinned, merging with another arc, or splitting into two arcs. The CCA comes with a decomposition of the cross section into triangular and trapezoidal regions marking the stages of the arcs' lives. We also characterize the (polygonal) cross-sectional shapes for which the fluid-fluid distribution responds continuously and reversibly to a change in capillary pressure, i.e., those cross-sectional shapes for which capillary displacement can be quasi-static. For these shapes the intersections of the nonwetting fluid with the cross section are precisely the morphological openings of the cross section, where the structuring elements are the disks whose radii coincide with those of the circular arcs. For any other (polygonal) shape, this correspondence does not hold, and, equivalently, capillary displacement cannot be quasi-static. We also formulate an assumption on the fluid-fluid distributions in such a cross section, which allows us to describe discontinuous capillary displacement.

Original language | English (US) |
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Pages (from-to) | 1765-1800 |

Number of pages | 36 |

Journal | Multiscale Modeling and Simulation |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2011 |

## Keywords

- Capillary displacement
- Chordal axis
- Opening
- Right prism
- Shape decomposition

## ASJC Scopus subject areas

- Chemistry(all)
- Modeling and Simulation
- Ecological Modeling
- Physics and Astronomy(all)
- Computer Science Applications