Stability of Newtonian and viscoelastic dynamic contact lines

The stability of the moving contact line is examined for both Newtonian and viscoelastic fluids. Two methods for relieving the contact line singularity are chosen: matching the free surface profile to a precursor film of thickness b, and introducing slip at the solid substrate. The linear stability of the Newtonian capillary ridge with the precursor film model was first examined by Troian et al. [Europhys. Lett. 10, 25 (1989)]. Using energy analysis, we show that in this case the stability of the advancing capillary ridge is governed by rearrangement of fluid in the flow direction, whereby thicker regions develop that advance more rapidly under the influence of a body force. In addition, we solve the Newtonian linear stability problem for the slip model and obtain results very similar to those from the precursor film model. Interestingly, stability results for the two models compare quantitatively when the precursor film thickness b is numerically equal to the slip parameter α. With the slip model, it is ...

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