Reconcile apparent film-thickness decrease relative to the Nusselt solution in spinning-disc flows

Determine the cause of the apparent decrease in measured thin-film thickness relative to the classical Nusselt waveless film-thickness solution during flow over a spinning disc for the regime Q ν / ω^2 r^5 < 10^-7 (coinciding with wavy flow), and establish a reconciliation between theory and experimental measurements under these conditions.

Background

Prior experimental studies of thin films flowing over spinning discs reported film heights lower than predicted by the Nusselt waveless solution in regimes characterized by Q ν / ω2 r5 < 10-7, where interfacial waves are present. Hypotheses to explain this discrepancy included gas-phase effects driven by disc rotation and measurement error due to the extremely small film thickness.

In this paper, the authors used fully resolved DNS (including both liquid and gas phases) and found that azimuthally averaged film thickness agrees with the Nusselt prediction, suggesting that previously observed discrepancies likely arise from measurement bias and the nonuniform distribution of local interface heights (few tall peaks and large low-height baseline regions). The explicit historical framing as an open question is included in the text.

References

An open question over the last several decades has been the inability to reconcile previous experimental observations of an apparent decrease in film thickness relative to the Nusselt solution for Qν/ω2 r5 < 10{-7} shown in Fig. \ref{fig:6}, which coincides with the presence of wavy flow.

— Thin film flow over a spinning disc: Experiments and direct numerical simulations  (2412.12730 - Stafford et al., 2024) in Section 4.2 (Film thickness and wall shear rate distributions), near Figure 6