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Bead Formation near the Contact Line

Parthasakha Neogi, Chemical and Biological Engineering, Missouri University of Science and Technology, Rolla, MO 65409-1230

When a plate is moved out of a pool of liquid, the contact line is of the receding kind. Experiments have indicated that a bead is formed near the contact line, sometimes too small to be seen and sometimes transient in nature. This problem can be formulated under lubrication theory approximation. The formulation is similar to Landau-Levich problem and has been solved some years ago and does show that beads form. However, the solution comes with a number of unknown parameters. In the present work, an inner region has been defined near the dynamic contact line, an asymptotic solution has been constructed and matched to the main solution. In the inner region, the actual contact angle is taken to be its equilibrium value and a slip boundary condition is used. An outer region is also defined where gravity is important and the flow is not. It is also matched to the main solution. All unknowns are hence determined with the exception of the absolute height of the meniscus over the level of the bulk liquid. The solution is also confined to equilibrium contact angles close to ninety degrees, for simplicity. The nature of the solution will be discussed.