Enhanced flow in deformable carbon nanotubes

Many researchers observed enhanced water flow through carbon nanotubes (CNTs) and attributed the reason to large slips. Even after taking significant slip effects into account, there remain unaddressed observations of significant improvements in flow rates. As CNTS are deformable, we represent nanotubes with a deformable-wall using a linear pressure–area relationship. We assume lubrication assumption, and using the properties of nanoconfined water, we derive the model for deformable-nanotubes. We validated our derived model in its limiting cases with the previously reported results in the literature. We compare the predictions by our deformable-wall and rigid-wall model with the experimental results and the MD-simulation predictions by multiple literature studies. Many studies were well-predicted by the rigid-wall model with slips. However, we find that there are many studies with high porosity and thin wall tubes, where elasticity or deformability of the tube is essential in modeling, which is well-predicted by our deformable-wall model with slips. In our study, we focus on investigating the impact of two key factors: the deformability, and the slip length on the flow rate. We find that the flow rate inside the tube increases as the deformability increases or the thickness T and elastic modulus E of the tube-wall decrease). We also find that the flow rate in deformable tubes scales as m˙deformable∼1/α0 for (Δp/αAo)≪1, m˙deformable∼1/α for (Δp/αAo)∼O(10−1) and m˙deformable∼α2 for (Δp/αAo)∼O(1). Further, for a given deformability, the percentage change in flow rate in the smaller diameter of the tube is much larger than the larger diameter. As the tube diameter decreases for the given pressure, Δm˙/m˙ increases. We find that for rigid-tube, the flow rate varies m˙rigid∼Δp, whereas for the deformable-tubes, the flow rate scales as m˙deformable∼Δp2 for (Δp/αAo)∼O(10−1), and finally to m˙deformable∼Δp3 for (Δp/αAo)∼O(1). We further find that slip also significantly increases flow rate, but, deformability has more substantial effect.