On numerical modelling and the blow-up behavior of contact lines with a 180∘ contact angle

We study numerically a reduced model proposed by Benilov and Vynnycky [J Fluid Mech 718:481–506, 2013], who examined the behavior of a contact line with a 180∘$$180^{\circ }$$ contact angle between liquid and a moving plate, in the context of a two-dimensional Couette flow. The model is given by a linear fourth-order advection–diffusion equation with an unknown velocity, which is to be determined dynamically from an additional boundary …