Investigating polydisperse suspensions involving fibres of very different aspect ratio: From direct numerical simulations to Folgar & Tucker modelling

Even though significant progress has been made in the modelling and simulation of short fibre suspensions involved in reinforced polymers, recent industrial practice mixes fibres of very different aspect ratio and no existing model has been validated in such circumstances when the concentration is large enough. In absence of fibre-fibre interactions, each fibre population associated to a particular aspect ratio can be modelled by means of the Jeffery equation at the microscopic scale or its macroscopic counterpart involving the moments of the orientation distribution function (e.g. the second-orientation tensor). Direct numerical simulations (DNS) showed that both descriptions are almost equivalent in unconfined flows. When fibre-fibre interactions are considered, we also showed in our former works that macroscopic approaches based on the Folgar & Tucker model offer a reasonable accuracy as well when compared with DNS predictions in unconfined flows. However, all these developments were carried out for mono-disperse suspensions, i.e. suspensions with a unique fibre aspect ratio. For a slight poly-dispersity about a given fibre aspect ratio, macroscopic predictions based on the Folgar & Tucker model remain reasonably accurate. In this work, we address a totally different scenario involving two populations with two very different aspect ratios, one of a few tens, thus approaching the configuration of rods, whereas the other is close to one, i.e. approaching the spherical shape. The validity of macroscopic models will be analyzed by means of appropriate direct numerical simulations.