In liquid-phase exfoliation for the production of 2D nanomaterials fluid forces are used to gently overcome adhesive interlayer forces, leading to single-or few-layer 2D nanomaterials. Predicting accurately the critical fluid shear rate for exfoliation is a crucial challenge. By combining notions of fluid mechanics and fracture mechanics, we analyse a mathematical model of exfoliation, focusing on the − regime in which bending forces are much smaller than the applied hydrodynamic forces. We find that in this regime the shear rate is approximately proportional to the adhesion energy, independent of the bending rigidity of the exfoliated sheet, and inversely proportional to the size of a (assumed pre-existing) material flaw. The model appears to give values comparable to those obtained in wet ball milling, but to overestimate the shear rate values reported for turbulent exfoliation (by rotor mixing or microfluidization). We suggest that for turbulent exfoliation a "cleavage model" may be more appropriate, as it gives a stronger dependence on and smaller critical shear rates. Figure 1: Optimising liquid-phase exfoliation processes (left, reproduced with permission from Ref. (Paton, 2014)) requires models to link large-scale flow variables to the micromechanics of exfoliation.Optimising liquid-exfoliation processes requires addressing a delicate balance: the mechanical stresses applied to the particles by the fluid must be sufficiently high to delaminate the particles, but not much higher. Excessive stresses can fragment the nanosheets, producing small area sheets of low intrinsic value, or damage the sheets (Johnson, 2015). Reaching the right stress level is thus paramount. However, particle-level stresses cannot be controlled directly. What can be controlled are large scale flow variables, such as the mixing power or, equivalently, the average shear rate the suspension is subject to. These are the macroscopic variables that can be controlled by the user in the production process. It would be highly valuable if analytical formulas relating these macroscopic variables to microscopic exfoliation thresholds and timescales were available. Developing these formulas requires an understanding of the flow physics and deformation mechanics at the particle level (Fig. 1).Quite surprisingly, despite the growing importance of liquid-phase processing in the production of graphene and other 2D nanomaterials, the development of theoretical models for liquidphase exfoliation is at its infancy. Two theoretical models have appeared recently which seem to be relevant. An exfoliation model based on a sliding deformation was proposed by Chen et al. (Chen, 2012), and later extended by Paton et al (Paton, 2014). In this model, the shear forces exerted by the fluid are assumed to balance the rate at which the total surface energy (including solid-solid, solid-liquid and liquid-liquid interaction energy) changes with respect to the sliding distance. The model was used to describe the dependence of the critical shear rate for exfoliation on ...