# A Continuum Constitutive Model for Cohesionless Granular Flows

## Abstract

A constitutive model is developed to represent shear granular flows of cohesionless solids. The model is based on the postulate that the friction coefficient and the solids fraction in a moving granular material are exclusive functions of the inertial number, which represents the ratio of inertial to normal stress forces. The constitutive equation obtained has the same form as a multidimensional Bingham fluid model, albeit with apparent viscosity and yield stress that depend on the vertical normal stress. The model is applied to previously published experimental results dealing with shear flows of granular beds made up of cohesionless spherical particles. The first case analyzed corresponds to a granular bed moving on top of a rotating disk. The model captures the main trends of the velocity profiles with a single adjustable parameter. The second case is a conventional Couette flow, for which the model is capable of representing the velocity and solids fraction profiles measured experimentally.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 899802

- Report Number(s):
- PNNL-SA-51052

KP1302000; TRN: US200709%%131

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Chemical Engineering Science, 62(5):1343-1350

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; FLOW MODELS; SOLIDS FLOW; COUETTE FLOW; FRICTION; GRANULAR MATERIALS

### Citation Formats

```
Daniel, Richard C., Poloski, Adam P., and Saez, Avelino E.
```*A Continuum Constitutive Model for Cohesionless Granular Flows*. United States: N. p., 2007.
Web. doi:10.1016/j.ces.2006.11.035.

```
Daniel, Richard C., Poloski, Adam P., & Saez, Avelino E.
```*A Continuum Constitutive Model for Cohesionless Granular Flows*. United States. doi:10.1016/j.ces.2006.11.035.

```
Daniel, Richard C., Poloski, Adam P., and Saez, Avelino E. Thu .
"A Continuum Constitutive Model for Cohesionless Granular Flows". United States.
doi:10.1016/j.ces.2006.11.035.
```

```
@article{osti_899802,
```

title = {A Continuum Constitutive Model for Cohesionless Granular Flows},

author = {Daniel, Richard C. and Poloski, Adam P. and Saez, Avelino E.},

abstractNote = {A constitutive model is developed to represent shear granular flows of cohesionless solids. The model is based on the postulate that the friction coefficient and the solids fraction in a moving granular material are exclusive functions of the inertial number, which represents the ratio of inertial to normal stress forces. The constitutive equation obtained has the same form as a multidimensional Bingham fluid model, albeit with apparent viscosity and yield stress that depend on the vertical normal stress. The model is applied to previously published experimental results dealing with shear flows of granular beds made up of cohesionless spherical particles. The first case analyzed corresponds to a granular bed moving on top of a rotating disk. The model captures the main trends of the velocity profiles with a single adjustable parameter. The second case is a conventional Couette flow, for which the model is capable of representing the velocity and solids fraction profiles measured experimentally.},

doi = {10.1016/j.ces.2006.11.035},

journal = {Chemical Engineering Science, 62(5):1343-1350},

number = ,

volume = ,

place = {United States},

year = {Thu Mar 01 00:00:00 EST 2007},

month = {Thu Mar 01 00:00:00 EST 2007}

}