Rate-dependent viscosity in power-law fluids significantly affects contact line stress singularities and moving contact line behaviour. Contact line forces show more severe divergence for shear-thickening fluids (n 1) or remain finite for shear-thinning fluids (n 1). Complementing earlier self-similar derivations of spreading laws by Starov et al. (J. Colloid Interface Sci. vol. 257, 2003, pp. 284–290) for shear-thinning drops, we extend the classical Cox-Voinov theory to power-law fluids and obtain explicit dynamic contact angle relationships – results that are more fundamental than previously reported spreading laws. This development provides a unified yet fundamentally distinct description of advancing contact line behaviour across the full range of shear-thinning and shear-thickening rheologies. We show that the apparent dynamic contact angle ₃ depends critically on the characteristic dissipation length h^* U^n/ (n-1), fundamentally altering its dependence on contact line speed U. For shear-thinning fluids (n 1) that exhibit more strongly diverging contact line stresses, by contrast, the contact line motion is dissipated within a much narrow region h^* that is much smaller than the required microscopic cutoff h m. A complete precursor theory is also developed, showing h₌ U^-n/ (4-n). This leads to ₃ U^n/ (4-n), making the global spreading behaviour highly sensitive to the contact line microstructure. Importantly, regardless of the microscopic mechanisms, the apparent dynamic contact angle relationship can always be expressed in the analogous Cox–Voinov form ₃ Ca₄₅₅^1/3 in terms of the effective capillary number
Halpern et al. (Thu,) studied this question.