Spreading Kinetics of Herschel-Bulkley Fluids Over Solid Substrates

Abstract

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 τ0 = 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.

Hep3Gel: A Shape-Shifting Extracellular Matrix-Based, Three-Dimensional Liver Model Adaptable to Different Culture Systems

“…Spreading ratios greater than one imply the flowing of the material from the center of the drop itself to its peripheral region. 77 According to Poiseuille’s law, the flow rate is inversely proportional to the viscosity η of the material, thus making η a crucial parameter to be considered when characterizing the spreading of a fluid. 78 Viscosity curves of Hep3Gel, GEL, and ALG at the examined time points are reported in Figure 5 b and highlight the shear thinning behavior of hydrogels.…”