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 $\dot{\unicode[STIX]{x1D6FE}_{c}}$ 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 $\dot{\unicode[STIX]{x1D6FE}_{c}}$ 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 after including the torque component due to drag about the particle centre. The data 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 $\dot{\unicode[STIX]{x1D6FE}_{c}}$ as a function of the particle and fluid properties.