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NJIT Applied Mathematics Colloquium

Friday, February 5th 2010, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Diffuse-interface simulations of moving contact lines

Pengtao Yue

Virginia Tech

The diffuse-interface method, also known as the phase-field method, may be used to compute moving contact lines because the Cahn-Hilliard diffusion regularizes the singularity at the contact line. In this talk, I will discuss some basic questions underlying this approach. The energy-based diffuse-interface method treats the fluid interface as a mixing layer with a finite thickness, which is always much larger than the physical interfacial thickness due to the current computing capability. This raises a fundamental question of the sharp interface limit. I will show that the diffuse-interface model does approach a sharp-interface limit as the interfacial thickness is reduced below a threshold while other parameters are chosen properly. In this limit, the diffuse interface exhibits a diffusion length that is equivalent to the slip length in the sharp-interface models. Another question arises as the current computational mesh can only resolve slip lengths that are much larger than the experimentally suggested ones. Through a simple analysis, I will show that a larger slip length can yield the same result if a finite-rate wall energy relaxation is allowed. This is confirmed by excellent agreements between our computational results and the experimental data in literature. In the end, I will present some recent results on dynamic wetting in viscoelastic fluids and point out some problems that we still need to work on.