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  • 1.
    Mancarella, Francesco
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden; Yale University, United States; University of Oxford, United Kingdom.
    Surface tension and a self-consistent theory of soft composite solids with elastic inclusions2017In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 13, no 5, p. 945-955Article in journal (Refereed)
    Abstract [en]

    The importance of surface tension effects is being recognized in the context of soft composite solids, where they are found to significantly affect the mechanical properties, such as the elastic response to an external stress. It has recently been discovered that Eshelby's inclusion theory breaks down when the inclusion size approaches the elastocapillary length L ≡ γ/E, where γ is the inclusion/host surface tension and E is the host Young's modulus. Extending our recent results for liquid inclusions, here we model the elastic behavior of a non-dilute distribution of isotropic elastic spherical inclusions in a soft isotropic elastic matrix, subject to a prescribed infinitesimal far-field loading. Within our framework, the composite stiffness is uniquely determined by the elastocapillary length L, the spherical inclusion radius R, and the stiffness contrast parameter C, which is the ratio of the inclusion to the matrix stiffness. We compare the results with those from the case of liquid inclusions, and we derive an analytical expression for elastic cloaking of the composite by the inclusions. Remarkably, we find that the composite stiffness is influenced significantly by surface tension even for inclusions two orders of magnitude more stiff than the host matrix. Finally, we show how to simultaneously determine the surface tension and the inclusion stiffness using two independent constraints provided by global and local measurements.

  • 2. Pramanik, S
    et al.
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Confinement effects in premelting dynamics2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 5, article id 052801Article in journal (Refereed)
    Abstract [en]

    We examine the effects of confinement on the dynamics of premelted films driven by thermomolecular pressure gradients. Our approach is to modify a well-studied setting in which the thermomolecular pressure gradient is driven by a temperature gradient parallel to an interfacially premelted elastic wall. The modification treats the increase in viscosity associated with the thinning of films, studied in a wide variety of materials, using a power law and we examine the consequent evolution of the confining elastic wall. We treat (1) a range of interactions that are known to underlie interfacial premelting and (2) a constant temperature gradient wherein the thermomolecular pressure gradient is a constant. The difference between the cases with and without the proximity effect arises in the volume flux of premelted liquid. The proximity effect increases the viscosity as the film thickness decreases thereby requiring the thermomolecular pressure driven flux to be accommodated at higher temperatures where the premelted film thickness is the largest. Implications for experiment and observations of frost heave are discussed.

  • 3.
    Toppaladoddi, S.
    et al.
    Univ Oxford, Oxford OX2 6GG, England.;Yale Univ, New Haven, CT 06520 USA..
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    The combined effects of shear and buoyancy on phase boundary stability2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 868, p. 648-665Article in journal (Refereed)
    Abstract [en]

    We study the effects of externally imposed shear and buoyancy driven flows on the stability of a solid-liquid interface. A linear stability analysis of shear and buoyancy-driven flow of a melt over its solid phase shows that buoyancy is the only destabilizing factor and that the regime of shear flow here, by inhibiting vertical motions and hence the upward heat flux, stabilizes the system. It is also shown that all perturbations to the solid-liquid interface decay at a very modest shear flow strength. However, at much larger shear-flow strength, where flow instabilities coupled with buoyancy might enhance vertical motions, a re-entrant instability may arise.

  • 4.
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Surface phase transitions in ice: From fundamental interactions to applications2019In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 377, no 2146, article id 20180261Article in journal (Refereed)
    Abstract [en]

    Interfaces divide all phases of matter and yet in most practical settings it is tempting to ignore their energies and the associated implications. There are many reasons for this, not the least of which is the introduction of a new pair of canonically conjugate variables-interfacial energy and its counterpart the surface area. A key set of questions surrounding the treatment of multiphase flows concerns how and when we must account for such effects. I begin this discussion with an abbreviated review of the basic theory of lower-dimensional phase transitions and describe a range of situations in which the bulk behaviour of a two-phase (and in some cases twocomponent) system is dominated by surface effects. Then I discuss a number of settings in which the bulk and surface behaviour can interact on equal footing. These can include the dynamic and thermodynamic behaviour of floating sea ice, the freezing and drying of colloidal suspensions (such as soil) and the mechanisms of protoplanetesimal formation by inter-particle collisions in accretion discs. This article is part of the theme issue 'The physics and chemistry of ice: Scaffolding across scales, from the viability of life to the formation of planets'. © 2019 Royal Society Publishing. All rights reserved.

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