Fig. 1. (a) Monolayer black phosphorus model, chiral angle θ is the intersection angle between the ripple direction of BP monolayer and z direction (the axial direction of the BPNT); (b) BPNT with a chiral angle of 23.4°; (c) model of the rotating BPNT filled with water molecules.

Fig. 2. For the angular velocity of the BPNT being 50 rad/ns, (a) the velocity in the axial direction of water molecules in BPNTs and (b) the resultant force in the axial direction of water molecules received from BPNTs with different chiral angles as a function of time.

Fig. 3. For the angular velocity of the BPNT being 50 rad/ns in different directions of rotation, (a) the velocity in the axial direction of water molecules in the BPNT and (b) the resultant force in the axial direction of water molecules received from the BPNT as a function of time when the chiral angle is 23.4°.

Fig. 4. The velocity in the axial direction of water molecules in the BPNT and the resultant force in the axial dire-ction of water molecules received from the BPNT as a function of the angular velocity of the BPNT when the chiral angle is 23.4°.

Fig. 5. Couette flow model diagram of water molecules flowing in BP nanochannel.

Fig. 6. Velocity distribution of water molecules along the width of the BP nanochannel.

Fig. 7. (a) The boundary slip velocity of water molecules and (b) the shear stress as a function of the shear strain rate.

Fig. 8. (a) Microstructure of the boundary of water molecules; (b) potential energy distribution cloud diagram of BP-water; (c) schematic diagram of the force of BP on water molecules.

Fig. 9. Model of water molecules filling between two BPNTs

Fig. 10. (a) The velocity in the axial direction of water molecules between BPNTs and (b) the resultant force in the axial direction of water molecules received from BPNTs as a function of the angular velocity of BPNTs in three cases.

Fig. 11. For different radius, (a) the velocity in the axial direction of water molecules in BPNTs and (b) the resultant force in the axial direction of water molecules received from BPNTs as a function of the angular velocity of BPNTs when the chiral angle is 23.4°.

Fig. 12. For different layers, (a) the velocity in the axial direction of water molecules in BPNTs and (b) the resultant force in the axial direction of water molecules received from BPNTs as a function of the angular velocity of BPNTs when the chiral angle is 23.4°.

Fig. 13. For the angular velocity of the BPNT being 50 rad/ns, the velocity in the axial direction of water molecules in the BPNT and the resultant force in the axial direction of water molecules received from the BPNT as a function of the temperature when the chiral angle is 23.4°.

Table 1. Parameter values of LJ potential function