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 $Re_p$ 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 $Re_p < 0.5$ is in good agreement with analytical calculations of the drag and lift coefficients in the $Re_p \rightarrow 0$ limit. For higher $Re_p$, where analytical results are unavailable, the hydrodynamic coefficients are found to approach a constant for $Re_p > 1000$. 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.