Non-Newtonian Drops Spreading on a Flat Surface

Abstract

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle θ of a droplet obeys a power law decay θ ∼ t −α except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent α of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.

Direct Compaction Drug Product Process Modeling

“…They proposed relations for the dynamics of drop spreading as well as the maximum spreading diameter as a function of the Weber and Reynolds numbers. Dechelette et al [211] developed a onedimensional theoretical model for droplet spreading and elucidated some differences in the process between non-Newtonian and Newtonian fluids.…”

Breakup Morphology and Mechanisms of Liquid Atomization

“…For evaluating the breakup of non-Newtonian fluid, the mean apparent viscosity of liquid during deformation and breakage is the key parameter. Three methods for determining the apparent viscosity of non-Newtonian fluid have been presented: (1) calculation of mean apparent viscosity according to the shear rate equal to γ ¼ u g =D [112], (2) increase the constant k determined by other test parameters, γ ¼ ku g =D [17,113], and (3) numerical analysis or analytical solution of energy and motion equations to determine dynamic shear rate [114][115][116][117].…”

Environmental Impact of Aviation and Sustainable Solutions

“…(1) calculation of mean apparent viscosity according to the shear rate equal to γ ¼ u g =D [112], (2) increase the constant k determined by other test parameters, γ ¼ ku g =D [17,113], and (3) numerical analysis or analytical solution of energy and motion equations to determine dynamic shear rate [114][115][116][117].…”