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

## Abstract

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$$Re_{p}<0.5$$are 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$$\dot{\unicode[STIX]{x1D6FE}_{c}}$$as a function of the particle and fluid properties.

- Authors:

- Publication Date:

- Research Org.:
- Clark Univ., Worcester, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1534388

- DOE Contract Number:
- SC0010274

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 808; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Mechanics; Physics

### Citation Formats

```
Kudrolli, Arshad, Scheff, David, and Allen, Benjamin.
```*Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow*. United States: N. p., 2016.
Web. doi:10.1017/jfm.2016.655.

```
Kudrolli, Arshad, Scheff, David, & Allen, Benjamin.
```*Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow*. United States. doi:10.1017/jfm.2016.655.

```
Kudrolli, Arshad, Scheff, David, and Allen, Benjamin. Wed .
"Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow". United States. doi:10.1017/jfm.2016.655.
```

```
@article{osti_1534388,
```

title = {Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow},

author = {Kudrolli, Arshad and Scheff, David and Allen, Benjamin},

abstractNote = {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$Re_{p}<0.5$are 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$\dot{\unicode[STIX]{x1D6FE}_{c}}$as a function of the particle and fluid properties.},

doi = {10.1017/jfm.2016.655},

journal = {Journal of Fluid Mechanics},

issn = {0022-1120},

number = ,

volume = 808,

place = {United States},

year = {2016},

month = {11}

}

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