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  • 1.
    Cortat, Frédéric
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Digital Media.
    Miklavcic, Stan
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    Application of the variational calculus to wetting phenomena in chemical engineering2004Report (Other academic)
  • 2.
    Cortat, Frédéric
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Digital Media.
    Miklavcic, Stan
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    How closely can a solid approach an air-water surface without becoming wet?2003In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 68, no 5Article in journal (Refereed)
    Abstract [en]

    Through a study of the van der Waals interaction between a solid and an air-water interface, we investigate the practical and fundamental problem of the limiting height at which an object can approach a free surface. A numerical study of the interface shape reveals dependencies governed by two disparate length scales associated with the relative strengths of the van der Waals and bouyancy forces, to surface tension. A study of the limits of solvability of the governing equation has led to the principal result: a closed-form expression for the absolute limiting height to which an object can be lowered to the air-water interface. The formula depends explicitly and only on the Hamaker constant of the van der Waals force and the geometry of the solid.

  • 3.
    Cortat, Frédéric
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Digital Media.
    Miklavcic, Stan
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    Using stable and unstable profiles to deduce deformation limits of the air-water interface2004In: Langmuir, ISSN 0743-7463, E-ISSN 1520-5827, Vol. 20, no 8, p. 3208-3220Article in journal (Refereed)
    Abstract [en]

    The shape of the air-water interface deformed by a van der Waals stress induced by a paraboloid shaped solid body is addressed and discussed. Emphasis is placed on the existence limit of solutions to the governing Euler-Lagrange equation for the equilibrium shape. Two legitimate solutions, one stable and one unstable, are found to converge at the existence limit, giving a numerical criterion for establishing critical physical conditions guaranteeing absolute stability. Insight is aided by a study of an analogous mechanical problem that exhibits very similar properties. Among numerical data produced are critical lower height limits of the paraboloid to the air-water surface and associated peak deformation heights and their dependencies on physical parameters. Of further interest to experimentalists in the surface force field are the variations in peak deformation height and total surface force on the solid as a function of position of the paraboloid, paraboloid geometry, and strength of the van der Waals stress.

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