Hsien-Hung Wei | Searcharxiv

arXiv2026

Backflow-Induced Inertial Arrest of Velocity Fluctuations in Sedimenting Suspensions

A self-contained hydrodynamic theory is proposed to reconcile the discrepancy between divergent Stokesian velocity fluctuations and finite experimental measurements in sedimenting suspensions. We show that the compensating backflow induces non-negligible inertia, giving rise to an emergent screening length $ξ\sim aϕ^{-1/3}Re_p^{-1/3}$ far exceeding the mean interparticle spacing $aϕ^{-1/3}$ even at vanishingly small particle Reynolds numbers. This backflow inertial screening, together with finite-time viscous diffusion, arrests the indefinite spatiotemporal growth of large-scale velocity fluctuations. The resulting velocity fluctuations scale as $δu \sim ϕ^{1/3}V_sRe_p^{-1/6}$, together with the viscous correlation time $τ_c=ξ^2/ν$, reproducing the well-known hydrodynamic self-diffusivity scaling $D_H\sim V_s a$. The theory predicts the prefactors of these scaling laws without adjustable parameters, in good quantitative agreement with experimental measurements. It also successfully captures the experimentally observed crossover from the finite-correlation regime to the finite-system regime as the screening length becomes comparable to the system size.

physics.flu-dyn↗

arXiv2025

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

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 $θ_d$ 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 $θ_d \sim (h/h^*)^{(1-n)/3}$, with contact line motion being dissipated within $h^*$ extending beyond the local wedge height $h$ without requiring a cutoff. In drop spreading problems, $θ_d$ varies with the spreading radius $R$, leading to $θ_d \propto U^{3n/(2n+7)}$ 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 $θ_d \sim (h^*/h_m)^{(1-n)/3}$, 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 $θ_d \sim Ca_{eff}^{1/3}$ in terms of a capillary number $Ca_{eff} =η_f U/γ$ where $γ$ is the surface tension and $η_f \propto (U/ h_m)^{n-1}$ 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 $θ_d \propto U^{3n/(4-n)}$, making the spreading behavior highly sensitive to the contact line microstructure. Our predictions show good agreement with experimental results.

physics.flu-dyn↗