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The transport of fluids in nanometer and Angstrom-sized pores has gotten much attention because of its potential uses in nanotechnology, energy storage, and healthcare sectors. Understanding the distinct material properties of fluids in such close confinement is critical for enhancing their performance in various applications. These properties dictate the fluid’s behavior and play a crucial role in determining flow dynamics, transport processes, and, ultimately, the performance of nanoscale devices. Remarkably, many researchers observed that the size of the geometry, such as the diameter of the confining nanotube, exerts a profound and intriguing influence on the material properties of nanoconfined fluids, including on the critical parameters such as density, viscosity, and slip length. Many researchers tried to model these material properties: viscosity η , density ρ , and slip λ using various models with many dependencies on the tube diameter. It is somewhat confusing and tough to decide which model is appropriate and needs to be incorporated in the numerical simulation. In this paper, we tried to propose a simple single equation for each nano confined material property such as for density $\rho {(D)/{\rho }_{o}=a+b/(D-c)}^{n}$ , viscosity $\eta {(D)/{\eta }_{o}=a+b/(D-c)}^{n}$ , and the slip length λ ( D ) = λ _1 D e ^− ^n ^D + λ _o (where a , b , c , n , λ _1 , λ _o are the free fitting parameters). We model a wealth of previous experimental and MD simulation data from the literature using our proposed model for each material property of nanoconfined fluids at the nanometer and Angstrom scales. Our single proposed equation effectively captures and models all the data, even though many different models have been employed in the existing literature to describe the same material property. Our proposed model exhibits exceptional agreement with multiple independent datasets from the experimental observations and molecular dynamics simulations. Additionally, the model possesses the advantageous properties of continuity and a continuous derivative, so the proposed model is well-suited for integration into numerical simulations. Further, the proposed models also obey the far boundary conditions, i.e., when tube diameter D ⟹ ∞, the material properties tend to the bulk properties of the fluid. Due to the models’ simplicity, smooth, and generic nature, this heuristic model holds promise to apply in simulations to design and optimize nanoscale devices.

Several researchers observed a significant increase in water flow through graphene-based nanocapillaries. As graphene sheets are flexible (Wang and Shi 2015 Energy Environ. Sci. 8 790–823), we represent nanocapillaries with a deformable channel-wall model by using the small displacement structural-mechanics and perturbation theory presented by Gervais et al (2006 Lab Chip 6 500–7), and Christov et al (2018 J. Fluid Mech. 841 267–86), respectively. We assume the lubrication assumption in the shallow nanochannels, and using the microstructure of confined water along with slip at the capillary boundaries and disjoining pressure (Neek-Amal et al 2018 Appl. Phys. Lett. 113 083101), we derive the model for deformable nanochannels. Our derived model also facilitates the flow dynamics of Newtonian fluids under different conditions as its limiting cases, which have been previously reported in literature (Neek-Amal et al 2018 Appl. Phys. Lett. 113 083101; Gervais et al 2006 Lab Chip 6 500–7; Christov et al 2018 J. Fluid Mech. 841 267–86 ; White 1990 Fluid Mechanics ; Keith Batchelor 1967 An Introduction to Fluid Dynamics ; Kirby 2010 Micro-and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices ). We compare the experimental observations by Radha et al (2016 Nature 538 222–5) and MD simulation results by Neek-Amal et al (2018 Appl. Phys. Lett. 113 083101) with our deformable-wall model. We find that for channel-height $H_o \lt 4$ Å, the flow-rate prediction by the deformable-wall model is 5%–7% more compared to Neek-Amal et al (2018 Appl. Phys. Lett. 113 083101) well-fitted rigid-wall model. These predictions are within the errorbar of the experimental data as shown by Radha et al (2016 Nature 538 222–5), which indicates that the derived deformable-wall model could be more accurate to model Radha et al (2016 Nature 538 222–5) experiments as compared to the rigid-wall model. Using the model, we study the effect of the flexibility of graphene sheets on the flow rate. As the flexibility α increases (or corresponding thickness $\mathcal{T}$ and elastic modulus E of the wall decreases), the flow rate also increases. We find that the flow rate scales as $\dot{m}_{\text{flexible}}\sim \alpha^0 $ for $(\alpha \Delta pW/EH_o) \ll 1$ ; $\dot{m}_{\text{flexible}}\sim \alpha $ for $(\alpha \Delta pW/EH_o ) \sim O(10^{-1})$ ; and $\dot{m}_{\text{flexible}}\sim \alpha^3 $ for $(\alpha \Delta pW/EH_o) \sim O(1)$ , respectively. We also find that, for a given thickness $\mathcal{T}$ , the percentage change in flow rate in the smaller height of the channel is more than the larger height of the channels. As the channel height decreases for the given reservoir pressure and thickness, the $\Delta \dot{m}/\dot{m}$ increases with $H_o^{-1}$ followed by $H_o^{-3}$ after a height-threshold. Further, we investigate how the applied pulsating pressure influences the flow rate. We find that due to the oscillatory pressure field, there is no change in the averaged mass flow rate in the rigid-wall channel, whereas the flow rate increases in the flexible channels with the increasing magnitude of the oscillatory pressure field. Also, in flexible channels, depending on the magnitude of the pressure field, either of the steady or oscillatory or both kinds of pressure field, the averaged mass flow rate dependence varies from $\Delta p$ to $\Delta p^4$ as the pressure field increases. The flow rate in the rigid-wall channel scales as $\dot{m}_{\text{rigid}}\sim \Delta p $ , whereas for the deformable-wall channel it scale as $\dot{m}_{\text{flexible}}\sim \Delta p $ for $ (\alpha \Delta pW/EH_o ) \approxeq 0$ , $\dot{m}_{\text{flexible}}\sim \Delta p^2 $ for $ (\alpha \Delta pW/EH_o ) \sim O(10^{-1})$ , and $\dot{m}_{\text{flexible}}\sim \Delta p^4 $ for $ (\alpha \Delta pW/EH_o ) \sim O(1)$ . We find that both the flexibility of the graphene sheet and the pulsating pressure fields to these flexible channels intensify the rapid flow rate through nano/Angstrom-size graphene capillaries.

We report the ferroelectric properties of pulsed laser deposited thin films of Nd and Ru co-doped bismuth titanate (Bi4−xNdxTi3−yRuyO12). Structural analysis of the as-grown films, using x-ray diffraction, showed a single-phase formation with a polycrystalline structure. In comparison to un-doped and Nd-doped films, ferroelectric measurements on co-doped films demonstrated improved properties with remnant polarization (Pr) ~ 12.5 µC cm−2 and an enhanced electrical fatigue life for Bi3.25Nd0.75Ti2.8Ru0.20O12 films. The enhancement in remanent polarization is attributed to microscopic changes, such as local structural distortion and the modification of the dynamical/effective charges on constituent ions due to chemical strain upon simultaneous Bi- (A) and Ti- (B) site doping with Nd and Ru, which has a far stronger effect than only A-site doping with Nd. Piezoresponse force microscopy further confirmed the polar structure and domain switching at nanoscale. The films exhibit small yet finite magnetization at 10 K resulting from strain. [ABSTRACT FROM AUTHOR]