Moving contact lines of power-law fluids: How nonlinear fluid rheology drastically alters stress singularity and dynamic wetting behavior

TL;DR

This paper develops a unified framework to understand how power-law fluid rheology influences moving contact lines, revealing significant effects on stress singularity, dynamic contact angle, and spreading behavior, with predictions aligning well with experiments.

Contribution

It introduces a novel theoretical approach for power-law fluids that captures their impact on contact line dynamics and wetting behavior beyond classical models.

Findings

Dynamic contact angle depends on dissipation length scale and contact line speed.

Spreading law for shear-thinning fluids: R ∝ t^{n/(3n+7)}.

Contact angle sensitivity to microstructure and velocity.

Abstract

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 $\theta_d$ can depend on the extent of the characteristic dissipation length $h^* \propto U_n/(n-1)$, altering its dependence on the contact line speed $U$. For shear-thinning fluids, we find $\theta_d \sim (h/h^*)^{(1-n)/3}$, with contact line motion being dissipated within $h^*$ extending beyond the local wedge height $h$ without requiring a cutoff. In drop spreading problems, $\theta_d$ varies with the spreading radius $R$, leading to $\theta_d \propto U^{3n/(2n+7)}$ consistent with the spreading law $R \propto t^{n/(3n+7)}$ 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 $\theta_d \sim (h^*/h_m)^{(1-n)/3}$, where dissipation is concentrated within $h^*$ which is smaller than the microscopic liquid height $h_m$ near the contact line. In fact, the dynamic contact angle relationship in this case can be expressed as the Cox-Voinov law $\theta_d \sim Ca_{eff}^{1/3}$ in terms of a capillary number $Ca_{eff} =\eta_f U/\gamma$ where $\gamma$ is the surface tension and $\eta_f \propto (U/ h_m)^{n-1}$ is the viscosity based on the local shear rate $U/h_m$ across $h_m$. We also show that a precursor film induced by molecular forces ahead of the wedge leads to $h_m \propto U^{-n/(4-n)}$ and hence $\theta_d \propto U^{3n/(4-n)}$, making the spreading behavior highly sensitive to the contact line microstructure. Our predictions show good agreement with experimental results.