Pulsatile pressure enhanced rapid water transport through flexible graphene nano/Angstrom-size channels: A continuum modelling approach using the micro-structure of nanoconfined water

Water transport through minuscule pores is widespread in the natural world and holds significant implications in various technological applications [1-4]. Radha et al. [5] has observed a significant increase in the water flow within graphene-based capillaries that are only a few nanometers or Angstrom-sized thick. By applying the Hagen-Poiseuille theory with confined water properties under continuum modelling, along with molecular dynamic simulations, Neek-Amal et al. [6] modelled these capillaries with rigid wall channels and attributed this enhancement to the high density and viscosity of water inside these nano capillaries. As Graphene sheets are flexible [7], we represent these graphene-based nanochannels with a deformable channel-wall model by using the small displacement structural mechanics and perturbation theory presented by Gervais et al. [8], and Christov et al. [9], 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. [6], we derive the model for deformable nanochannels. The newly derived model also facilitate the flow dynamics of Newtonian fluids under different conditions as its limiting cases, which has been previously reported in the literature [6,8-12]. Using the model, we study the effect of flexibility of graphene sheet on the flow rate. We also investigate how the applied pulsating pressure influences the behavior of the water flow rate within these flexible nano capillaries, as applying pulsating pressure fields or vibrations is a classical method for enhancing flow-rate of complex fluids through porous mediums such as channels and tube capillaries [13-15]. We compare the prediction of flow rate from both including the flexibility of the channel wall, and the application of pulsating pressure with the experimental observations by Radha et al. [5] and predictions from the molecular dynamic simulation by Neek-Amal et al. [6] which were well fitted by their rigid-wall model. 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.