Spreading of graphene oxide suspensions droplets on smooth surfaces

Understanding and predicting the spreading of droplets on solid surfaces is crucial in many applications such as inkjet printing, printed electronics and spray coating where the fluid is a suspension and in general non-Newtonian. However, many models that predict the maximum spreading diameter usually only apply to Newtonian fluids. Here we study experimentally and theoretically the maximum spreading diameter of graphene oxide suspension droplets impacting on a smooth surface for a wide range of concentrations and impact velocities of up to 6 g/l and 3 m/s, respectively. As the particle concentration increases the rheological behaviour changes from a viscous fluid to a shear-thinning yield stress fluid and the maximum spreading diameter decreases. The rheology for all concentrations is well described by a Herschel-Bulkley model that allows us to determine the characteristic viscosity during spreading. We use this viscosity to develop an energy balance model that takes into account the viscous dissipation and change in surface energies to find the maximum spread diameter for a given impact velocity. The model contains one non-dimensional parameter that encodes both the dynamic contact angle during spreading and the droplet shape at maximum spread. Our model is in good agreement with our data at all concentrations and agrees well with literature data on Newtonian fluids. Furthermore, the model gives the correct limits in the viscous and capillary regime and can be solved analytically for Newtonian fluids.