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In liquid-phase exfoliation for the production of 2D nanomaterials fluidforces are used to gently overcome adhesive interlayer forces, leading tosingle- or few-layer 2D nanomaterials. Predicting accurately the critical fluidshear rate for exfoliation is a crucial challenge. By combining notions offluid mechanics and fracture mechanics, we analyse a mathematical model ofexfoliation, focusing on the $\pi$-peel regime in which bending forces are muchsmaller than the applied hydrodynamic forces. We find that in this regime theshear rate is approximately proportional to the adhesion energy, independent ofthe bending rigidity of the exfoliated sheet, and inversely proportional to thesize $a$ of a (assumed pre-existing) material flaw. The model appears to givevalues comparable to those obtained in wet ball milling, but to overestimatethe shear rate values reported for turbulent exfoliation (by rotor mixing ormicrofluidization). We suggest that for turbulent exfoliation a "cleavagemodel" may be more appropriate, as it gives a stronger dependence on $a$ andsmaller critical shear rates.

Towards nanomechanical models of liquid-phase exfoliation of layered 2D nanomaterials: analysis of a $\pi$-peel model