Cusp at the three-fluid contact line in a cylindrical pore

    Research output: Contribution to journalArticle

    Abstract

    In a cylindrical pore of arbitrary wettability, we analyse the existence of a three-fluid contact line connecting the fluid-fluid interfaces between two bulk phases and the third phase contained in a cusp near the pore wall. This analysis is supported by the very similar, but simpler, analysis for a constriction between parallel plates. From the force balance at the contact line and the equations for the interface curvatures we derive expressions for the cusp height and for the capillary entry pressure related to piston-like displacement between the two bulk phases. The latter is independent of the existence of a cusp and its phase pressure. Based on some realistic assumptions, of which the most important is that a cusp grows continuously from the onset when its phase pressure is increased, we analyse under which conditions a cusp can exist, and, when it exists, what its behaviour is as a function of the cusp phase pressure. We find a simple criterion involving (two ratios of) the three interfacial tensions and two of the three contact angles, which determines whether the three-fluid contact line and, consequently, a cusp exists. The range of contact angles, as well as the size of the cusp increases, when the cusp phase is close to spreading. Not only cusps of the wetting phase can occur, but also of the intermediate-wetting phase. Numerical examples are presented to illustrate the range of behaviour of the cusps. © 2005 Elsevier Inc. All rights reserved.

    Original languageEnglish
    Pages (from-to)762-771
    Number of pages10
    JournalJournal of Colloid and Interface Science
    Volume297
    Issue number2
    DOIs
    Publication statusPublished - 15 May 2006

    Fingerprint

    cusps
    porosity
    fluids
    wetting
    wettability
    pistons
    parallel plates
    entry
    constrictions
    interfacial tension
    curvature

    Keywords

    • Capillary entry pressure
    • Constant total curvature
    • Contact angle
    • Cusp
    • Interfacial tension
    • Three-fluid contact line

    Cite this

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    abstract = "In a cylindrical pore of arbitrary wettability, we analyse the existence of a three-fluid contact line connecting the fluid-fluid interfaces between two bulk phases and the third phase contained in a cusp near the pore wall. This analysis is supported by the very similar, but simpler, analysis for a constriction between parallel plates. From the force balance at the contact line and the equations for the interface curvatures we derive expressions for the cusp height and for the capillary entry pressure related to piston-like displacement between the two bulk phases. The latter is independent of the existence of a cusp and its phase pressure. Based on some realistic assumptions, of which the most important is that a cusp grows continuously from the onset when its phase pressure is increased, we analyse under which conditions a cusp can exist, and, when it exists, what its behaviour is as a function of the cusp phase pressure. We find a simple criterion involving (two ratios of) the three interfacial tensions and two of the three contact angles, which determines whether the three-fluid contact line and, consequently, a cusp exists. The range of contact angles, as well as the size of the cusp increases, when the cusp phase is close to spreading. Not only cusps of the wetting phase can occur, but also of the intermediate-wetting phase. Numerical examples are presented to illustrate the range of behaviour of the cusps. {\circledC} 2005 Elsevier Inc. All rights reserved.",
    keywords = "Capillary entry pressure, Constant total curvature, Contact angle, Cusp, Interfacial tension, Three-fluid contact line",
    author = "{van Dijke}, {M. I J} and Sorbie, {K. S.}",
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    Cusp at the three-fluid contact line in a cylindrical pore. / van Dijke, M. I J; Sorbie, K. S.

    In: Journal of Colloid and Interface Science, Vol. 297, No. 2, 15.05.2006, p. 762-771.

    Research output: Contribution to journalArticle

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    N2 - In a cylindrical pore of arbitrary wettability, we analyse the existence of a three-fluid contact line connecting the fluid-fluid interfaces between two bulk phases and the third phase contained in a cusp near the pore wall. This analysis is supported by the very similar, but simpler, analysis for a constriction between parallel plates. From the force balance at the contact line and the equations for the interface curvatures we derive expressions for the cusp height and for the capillary entry pressure related to piston-like displacement between the two bulk phases. The latter is independent of the existence of a cusp and its phase pressure. Based on some realistic assumptions, of which the most important is that a cusp grows continuously from the onset when its phase pressure is increased, we analyse under which conditions a cusp can exist, and, when it exists, what its behaviour is as a function of the cusp phase pressure. We find a simple criterion involving (two ratios of) the three interfacial tensions and two of the three contact angles, which determines whether the three-fluid contact line and, consequently, a cusp exists. The range of contact angles, as well as the size of the cusp increases, when the cusp phase is close to spreading. Not only cusps of the wetting phase can occur, but also of the intermediate-wetting phase. Numerical examples are presented to illustrate the range of behaviour of the cusps. © 2005 Elsevier Inc. All rights reserved.

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