Abstract
Given any positive speed, we prove the existence of a travelling wave solution for a viscous incompressible thin dilatant liquid film coated with an insoluble surfactant. Relying on first principles of fluid mechanics, lubrication theory leads to a coupled system of second-order partial differential equations for the film's height and the surfactant's concentration where a second-order approximation of the viscosity function is used. The travelling wave solution is -regular and generates a heteroclinic orbit which connects two distinct equilibrium points of the associated plane dynamical system.
Acknowledgments
The first author would like to express his sincere thanks to Institut für Angewandte Mathematik, Leibniz Universität Hannover for the support from October 2018 to September 2019 as a joint PhD student.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 See the discussion following Lemma 3.1.
2 Here and in the following we use the notation and for the limits and respectively.