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

Abstract

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>o</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>4</mml:mn> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">T</mml:mi> </mml:mrow> </mml:math> and elastic modulus E of the wall decreases), the flow rate also increases. We find that the flow rate scales as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mtext>flexible</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>α</mml:mi> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>p</mml:mi> <mml:mi>W</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>E</mml:mi> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>o</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:math> ; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mover> <mml:mi>m</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mtext>flexible</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mi>α</mml:mi> </mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>α</mml:mi> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>p</mml:mi> <mml:mi>W</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>E</mml:mi> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>o</mml:mi> </

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