Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow

We advance a quantitative description of the critical shear rate $\dot{{\gamma }_c}$ needed to dislodge a spherical particle resting on a surface with a model asperity in laminar and turbulent fluid flows. We have built a cone-plane experimental apparatus which enables measurement of $\dot{{\gamma }_c}$ over a wide range of particle Reynolds number $R{e}_p$ from ${10}^{-3}$ to $1.5 \times 10^3$. The condition to dislodge the particle is found to be consistent with the torque balance condition, which { yields a lower $\dot{{\gamma }_c}$ compared with} force balance because of the torque component due to drag about the particle center. The data for $R{e}_p<0.5$ is in good agreement with analytical calculations of the drag and lift coefficients in the $Re_p \rightarrow 0$limit\mathrm{.}Forhigher$Re_p$, where analytical results are unavailable, the hydrodynamic coefficients are found to approach a constant for $R{e}_p>1000$. We show that a linear combination of the hydrodynamic coefficients found in the viscous and inertial limits can describe the observed $\dot{{\gamma }_c}$ as a function of the particle and fluid properties.