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Recent progress on the moving contact line problem

Monday 29th July 2013 - 15:00 to 16:30
INI Seminar Room 1
The moving contact line problem is a long-standing and fundamental challenge in the field of fluid dynamics, occurring when one fluid replaces another as it moves along a solid surface. Moving contact lines occur in a vast range of applications, where an apparent paradox of motion of a fluid-fluid interface, yet static fluid velocity at the solid satisfying the no-slip boundary condition arises. In this talk we will review recent progress on the problem made by our group.

The motion of a contact line is examined, and comparisons drawn, for a variety of proposed models in the literature. We first scrutinise a number of models in the classic test-bed system of spreading of a thin two-dimensional droplet on a planar substrate, showing that slip, precursor film and interface formation models effectively reduce to the same spreading behaviour. This latter model, developed by Shikhmurzaev a few years ago, is a complex and somewhat controversial one, differentiating itself by accounting for a variation in surface layer quantities and having finite-time surface tension relaxation. Extensions to consider substrate heterogeneities in this prototype system for slip models are also considered, such as for surface roughness and fluctuations in wetting properties through chemical variability.

Analysis of a solid-liquid-gas diffuse-interface model is then presented, with no-slip at the solid and where the fluid phase is specified by a continuous density field. We first obtain a wetting boundary condition on the solid that allows us to consider the motion without any additional physics, i.e. without density gradients at the wall away from the contact line associated with precursor films. Careful examination of the asymptotic behaviour as the contact line is approached is then shown to resolve the singularities associated with the moving contact line problem. Various features of the model are scrutinised alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall. But these are not necessary to resolve the moving contact line problem. Ongoing work to rigorously include non-local terms into models for contact line motion based on density functional theory will be discussed, with work analysing the contact line in equilibrium presented.

**Joint work with David Sibley, Andreas Nold & Nikos Savva

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons