Numerical simulation of spin coating processes with carbon nanotubes suspensions

In this paper we address the problem of simulating the behaviour of Carbon nanotubes (CNTs) suspensions in spin coating processes. Spin coating is a procedure used to apply uniform thin films to flat substrates by means of a high rotating velocity and the subsequent centrifugal force. In this work we assume a suspension of chemically treated CNTs, such that they do not aggregate. In such a suspension, CNTs can be treated as rigid fibres whose orientation is dictated by the flow of the solvent. In order to treat the associated free-surface problem and to avoid the numerical problems associated to their FE solution, we have implemented a Natural Element strategy in an updated Lagrangian framework. The resulting model is thus composed by a description of the micro scale, related to the orientation of the carbon nanotubes and the assumption of a quadratic closure relation, together with the natural element approximation for the Navier-Stokes problem governing the macroscopic suspension kinematics.