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nanofluidic transport with ultralow friction while effectively retaining larger molecules. Wang et al. also
demonstrated a strategy for stabilizing the Ti C T laminar architecture by alginate hydrogel pillars formed
3
2 x
[133]
between the adjacent nanosheets . After pillared by different alginate hydrogel pillars, the nanochannel
diameters are effectively fixed at ~ 7.4 Å, and the resulting membrane exhibited significantly enhanced the
ion-sieving property with distinct ions permeation cutoff depending on the multivalent cations cross-linked
with alginate molecules.

Regulating the length of nanochannels
Another physical factor influencing nanofluidic transport through 2D-material-based nanochannel
membranes is channel length, which largely depends on the membrane thickness and porosity. Nanoporous
2D materials of single- or few-atom thickness are the ultimate building blocks for constructing ultrathin
membranes with minimal resistance to maximize permeance.

As a straightforward way to shorten the channel length, many theoretical and experimental studies have
demonstrated the ultrafast permeation performance of ultrathin 2D-material membranes. For example,
Cohen-Tanugi et al. predicted that ultrathin nanoporous graphene membrane could have water
permeability several orders of magnitude higher than conventional membranes thanks to the chemical
functionalization, which may have a valuable role to play in water purification [Figure 7A] . Han et al.
[134]
fabricated ultrathin (~ 22-53 nm) graphene nanofiltration membranes on microporous substrates for
efficient water purification . Liu et al. prepared free-standing ultrathin rGO membranes with thickness
[103]
[104]
down to ~ 20 nm by HI vapor and water-assisted delamination . Yang et al. reported highly laminated
GO membranes of only several layers in thickness (~ 8 nm), exhibiting outstanding sieving properties
accompanied by ultrafast solvent permeation . Li et al. described a reproducible facile filtration method to
[135]
produce ultrathin GO membranes down to 1.8 nm in thickness, which exhibited superior gas separation
performance . Furthermore, single-layer 2D-material membranes for practical use have also been
[136]
attempted. For example, Heiranian et al. showed that a single-layer nanoporous MoS effectively allowed
2
water transport at a high rate associated with permeation coefficients, energy barriers, water density, and
velocity distributions in the pores [Figure 7B] .
[137]

Although the ultrathin 2D-material membranes exhibit exceptional permeation performances, the limited
mechanical strength of these membranes over large areas remains a hindrance to their widespread use. To
overcome this limitation, Yang et al. reported the production of an atomically thin nanoporous membrane
with a single-layer graphene nanomesh (GNM) supported by an interwoven network of single-walled
[138]
carbon nanotubes (SWNT) .The monolayer GNM featuring high-density subnanometer pores
[Figure 7C] allows efficient transport of water molecules with minimum resistance while effectively
blocking solute ions or molecules to enable size-selective separation. The mechanically strong,
interconnected SWNT network, acting as the microscopic framework, separates the GNM into microsized
islands, thus ensuring the structural integrity of the atomically thin GNM. The resulting large-area, ultrathin
GNM/SWNT hybrid membrane showed high water permeance and excellent size selectivity combined with
excellent anti-fouling characteristics, making it highly attractive for energy-efficient and robust water
treatment.

Regulating morphology of nanochannels
The morphology of the channel in ultrathin 2D-material membranes plays a crucial role in determining the
distance traveled by nanofluids. Inter-edge gaps [Figure 8A] and intrinsic pores [Figure 8B] are crucial
elements that influence this distance [135,136] . Ibrahim et al. proposed using nanofluidic pathways in laminar
GO membranes, where permeation occurs through pinholes within GO flakes and capillaries between
[139]
them . Utilizing small and porous nanosheets to assemble membranes can efficiently introduce more