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Center for Nonlinear Studies |
The ability of a numerical method to accurately approximate a hydrodynamic problem in a domain containing moving contact-lines is critical for the description of a number of phenomena, ranging from curtain coating to dewetting of solid substrates covered by thin liquid films. It is often, that theoretical analysis of such problems, based on the standard or on the slip models uncovers singular behaviour of variables, such as pressure and stress tensor components, as the corner is approached, which requires special physical and numerical treatments. The near-field asymptotic behaviour in the moving contact-line problem described in the framework of the standard approach or on the basis of slip models has always solutions either with a pressure singularity at the contact line or with the flow kinematics qualitatively different from that observed in experiments. In the talk, I will discuss an 'alternative approach' and its implications for numerical algorithms. This 'alternative' model is based on the sharp interface formation theory, which leads to a singularity-free solution with the correct kinematics. The flow exhibits no spurious low-velocity region near the contact line which is unavoidable in the standard or in the slip models. The pressure at the contact line remains finite, and the dynamic contact angle, being part of the solution, depends on the flow field and not only on the contact-line speed. This last feature accounts for the effect of hydrodynamic assist of dynamic wetting reported in recent experiments and will form an example of numerical implementation of the sharp interface formation model. An important question in the physics of dynamic wetting is whether, for a given gas-liquid-solid system, the dynamic contact angle formed by an advancing free surface with a solid substrate is a mere function of the wetting speed, or its dependence on the wetting speed is just part of its dependence on the flow field near the moving contact line. In other words, is it possible to vary the contact angle at a given wetting speed by varying the flow conditions that would affect the flow field in the vicinity of the contact line? The answer to this question is the key to the effect of hydrodynamic assist of dynamic wetting. Since the influence of the flow field, obviously, cannot be accommodated in a finite or even countably infinite number of parameters, an answer to this question has also fundamental implications for the modelling of free surface flows where dynamic wetting plays a role. I will discuss numerical aspects of such a problem and show results of simulations.
Host: Mikhail Shashkov. shashkov@lanl.gov, 667-4400