Yielding and flow of highly concentrated, few-layer graphene suspensions

For a wide range of applications of graphene suspensions, a thorough understanding of their rheological properties is crucial. We probe the microstructure of dense suspensions of micron-sized, few-layer, defect-free graphene platelets by measuring their viscoelastic properties at various concentrations up to 39 mg ml(-1). We propose a model to relate the yield strain to the mesh size of the microstructure as a function of volume fraction phi. From the yield stress measurements we infer the typical bond energy (approximate to 20 k(B)T) and phi dependence of the bond number density. These results allow us to express the steady shear viscosity for Peclet number Pe < 10 in terms of the platelet dimensions, bond energy and phi using a relaxation ansatz.