caa a22 4500 606167099 CHVBK 20210128100701.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10665-014-9763-9 doi (NATIONALLICENCE)springer-10.1007/s10665-014-9763-9 On numerical modelling and the blow-up behavior of contact lines with a $$\mathbf{180}^{\varvec{\circ }}$$ 180 ∘ contact angle [Elektronische Daten] [Dmitry Pelinovsky, Chengzhu Xu] 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 $$180^{\circ }$$ 180 ∘ 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 condition at the contact line. The main claim of Benilov and Vynnycky is that for any physically relevant initial condition, there is a finite positive time at which the velocity of the contact line tends to negative infinity, whereas the profile of the fluid flow remains regular. Additionally, it is claimed that the velocity behaves as the logarithmic function of time near the blow-up time. Compared to the previous computations based on COMSOL built-in algorithms, we use MATLAB and develop a direct finite-difference method to study dynamics of the reduced model under different initial conditions. We confirm the first claim and also show that the blow-up behavior is better approximated by a power function, compared with the logarithmic function. This numerical result suggests a simple analytical explanation of the blow-up behavior of contact lines. Springer Science+Business Media Dordrecht, 2015 Advection-diffusion equation nationallicence Blow-up in a finite time nationallicence Numerical modelling nationallicence Pelinovsky Dmitry Department of Mathematics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut Xu Chengzhu Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, Canada aut Journal of Engineering Mathematics Springer Netherlands 92/1(2015-06-01), 31-44 0022-0833 92:1<31 2015 92 10665 https://doi.org/10.1007/s10665-014-9763-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9763-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pelinovsky Dmitry Department of Mathematics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut NATIONALLICENCE 700 1- Xu Chengzhu Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, Canada aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 92/1(2015-06-01), 31-44 0022-0833 92:1<31 2015 92 10665