Non-monotonic dependence of fluid dissipation on fluid density in fluid-coupled nanoresonators

Recent studies on fluid-coupled nanoresonators (represented by argon-filled carbon nanotubes or CNTs) have shown nonintuitive variation of the fluid dissipation (D_flu) with fluid density (⁠$ρ*$⁠) at high-frequency oscillations. In this letter, we propose a physical mechanism that can explain such a behavior. We identify that argon atoms are in the disordered (ordered) state within the CNTs at small (large) $ρ*$⁠. For low-frequency oscillations, i.e., for oscillations with large characteristic excitation time scales, the argon atoms, at both large and small $ρ*$⁠, have enough time to dissipate all the energy added from the imposed oscillations. But for high-frequency oscillations, i.e., for oscillations with small characteristic excitation time scales, while the argon atoms in the disordered state (low density) can dissipate all the energy in that small time, those in the ordered state (high density) cannot dissipate all the energy (and hence stores some energy) in that time. This explains the nonmonotonic density-dependence of D_flu in argon-filled CNTs at high frequency. We also explain this nonmonotonic density-dependence of D_flu from the corresponding Deborah number (De). De represents the ratio of the fluid relaxation to the excitation time scales. The relaxation time of CNT-confined argon increases with $ρ*$⁠. Therefore, for a large-frequency (or a small excitation time) oscillation, De becomes large and the fluid starts losing its fluidity and shows solidlike (“elastic”) characteristics. This viscoelastic behavior ensures a partial storage (without dissipation) of the imposed oscillation, which in turn explains the nonmonotonic variation of D_flu with $ρ*$ for large-frequency oscillations.