2025/06/10 by David Halpern, Halpern, David, Hsien-Hung Wei +1
Engineering · Materials Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Pickering emulsions and particle stabilization #Surface Modification and Superhydrophobicity
paper · pdf · doi:10.48550/arxiv.2506.09224
openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Power-law fluids can strongly affect the degree of the contact line stress singularity and hence the nature of moving contact lines. We develop a framework beyond the classical paradigm for power-law fluids, providing a unified account for the distinct behaviors of the advancing contact lines. We show that the apparent dynamic contact angle θd can depend on the extent of the characteristic dissipation length h^* ∝ Un/(n-1), altering its dependence on the contact line speed U. For shear-thinning fluids, we find θd ∼ (h/h^*)(1-n)/3, with contact line motion being dissipated within h^* extending beyond the local wedge height h without requiring a cutoff. In drop spreading problems, θd varies with the spreading radius R, leading to θd ∝ U3n/(2n+7) consistent with the spreading law R ∝ tn/(3n+7) derived from a self-similar solution, where R is the spreading radius and t is time. For shear-thickening fluids, the apparent contact line motion is characterized by θd ∼ (h^*/hm)(1-n)/3, where dissipation is concentrated within h^* which is smaller than the microscopic liquid height hm near the contact line. In fact, the dynamic contact angle relationship in this case can be expressed as the Cox-Voinov law θd ∼ Caeff1/3 in terms of a capillary number Caeff =ηf U/γ where γ is the surface tension and ηf ∝ (U/ hm)n-1 is the viscosity based on the local shear rate U/hm across hm. We also show that a precursor film induced by molecular forces ahead of the wedge leads to hm ∝ U-n/(4-n) and hence θd ∝ U3n/(4-n), making the spreading behavior highly sensitive to the contact line microstructure. Our predictions show good agreement with experimental results.