A unified scaling law for wet powder strength under dynamic loading: Coupling capillary and inertial effects

The mechanical strength of wet powders under dynamic loading conditions plays a critical role in numerous industrial and natural processes involving rapid particle rearrangements, including high-shear wet granulation, powder mixing, chute flows and avalanche flows. Despite this importance, existing experimental methods are restricted to quasi-static conditions and fail to capture the rapid deformation regimes characteristic of these processes. This work extends Dynamic Ball Indentation (DBI) to wet granular systems, providing for the first time a method to quantify wet powder strength under the dynamic loading conditions (strain rates γ̇=25–265s−1) encountered in industrial processes. Experiments covered four granular materials (d50=5–247μm) with binders spanning two orders of magnitude in viscosity (η=1–349mPas), at preconsolidation stresses of 1–9 kPa and saturation levels of 5%–75%. Results demonstrate that dependence of dimensionless strength on the Capillary number alone is insufficient to describe wet powder behavior at high strain rates. Instead, a unified scaling law incorporating both viscous-capillary and inertial contributions accurately describes the experimental data: Str∗=210.53Ca0.16I0.79 (R2=0.96), where Str∗ is the dimensionless strength, Ca the Capillary number, and I the Inertial number. The dominant exponent (β=0.79) confirms that inertial effects control wet powder strength under dynamic loading, while viscous dissipation plays a secondary role (α=0.16) These findings establish DBI as an effective characterization tool for dynamic wet powder systems and provide a predictive framework for high-shear granulation process design.