  In this paper we tackle the problem of surfactant spreading on a thin liquid
film in the framework of isogeometric analysis. We consider a mathematical
model that describes this phenomenon as an initial boundary value problem
(IBVP) that includes two coupled fourth order partial differential equations
(PDEs), one for the film height and one for the surfactant concentration. In
order to solve this problem numerically, it is customary to transform it into a
mixed problem that includes at most second order PDEs. However, the
higher-order continuity of the approximation functions in Isogeometric Analysis
(IGA) allows us to deal with the weak form of the fourth order PDEs directly,
without the need of resorting to mixed methods. We demonstrate numerically that
the IGA solution is able to reproduce results obtained before with mixed
approaches. Complex phenomena such as Marangoni-driven fingering instabilities
triggered by perturbations are easily captured.
