A comprehensive mathematical model for nanofibre formation in centrifugal spinning methods

Noroozi, S.; Arne, W.; Larson, R. G.; Taghavi, S. M.

doi:10.1017/jfm.2020.196

Motivated by our experimental observations of nanofibre formation via the centrifugal spinning process, we develop a string model to study the behaviours of a Newtonian, viscous curved jet, in a non-orthogonal curvilinear coordinate system including both air-drag effects and solvent evaporation for the first time. In centrifugal spinning a polymeric solution emerges from the nozzle of a spinneret rotating at high speeds around its axis of symmetry and thins as it moves away from the nozzle exit until it finally lands on the collector. Except for the Newtonian fluid assumption, our model includes the key parameters of the curved jet flow, e.g. viscous, inertial, rotational, surface tension, gravitational, mass diffusion within the jet, mass diffusion into air and aerodynamic effects, via Rossby ( $Rb$ ), Reynolds ( $Re$ ), Weber ( $We$ ), Froude ( $Fr$ ), Péclet ( $Pe$ ), air Reynolds ( $Re^{\ast }$ ) and air Péclet ( $Pe^{\ast }$ ) numbers, and the collector radial position ( ${\mathcal{R}}$ ). Our results, including comparison to experiments, reveal that the aerodynamic effects must be considered to enable a correct prediction of the jet trajectory and radius. Decreasing $Rb$ not only renders the jet thinning much faster, but also forces the jet to wrap tighter around the rotation axis. Increasing $Re$ , $Re^{\ast }$ and ${\mathcal{R}}$ leads to a longer jet. Decreasing $We$ causes the jet to wrap tighter around the spinneret but it shows trivial effects on the solvent evaporation. Changes in $Pe$ and $Pe^{\ast }$ do not significantly affect the jet trajectory. Finally, we propose simple relations to estimate the jet radius and the jet breakup length.

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