Spreading Kinetics of Herschel-Bulkley Fluids Over Solid Substrates

The spreading kinetics of Herschel-Bulkley fluids on horizontal solid substrates were theoretically studied. The equations of film thickness were derived in both gravitational and capillary regimes. The dynamic contact angle for the capillary regime was also derived. Finally, a limiting result for the case of tau (0) = 0 was obtained, which was compared with the known solution for validation. The results show that the yield behavior of the fluids had a significant impact on the spreading kinetics in both cases. Only when stress was larger than the yield stress, would substantial flow occur. The spreading zone was divided into two parts by the yield surface: sheared zone and yield zone, which was completely different from common Newtonian fluids or power-law fluids. The thickness of the yield zone mainly depended on yield stress and pressure gradient along the z-direction. According to the final evolution, both the film thickness and dynamic contact angle were affected not only by the power-law index but also by the yield behavior.