Torsional parallel plate flow of Herschel-Bulkley fluids with wall slip
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916170930585600 |
|---|---|
| author | Gryparis, Evgenios Georgiou, Georgios C. |
| author_facet | Gryparis, Evgenios Georgiou, Georgios C. |
| contents | The effect of wall slip on the apparent flow curves of viscoplastic materials obtained using torsional parallel plate rheometers is analysed by considering Herschel-Bulkley fluids and assuming that slip occurs above a critical wall shear stress, the slip yield stress τ_c, taken to be lower than the yield stress, τ_0. Thus, different flow regimes are encountered as the angular velocity of the experiment is increased. When the rim shear stress τ_R is below the slip yield stress, the exerted torque is not sufficient to rotate the disk and the material remains still. When τ_c<τ_R<τ_0 the material is still unyielded but exhibits wall slip and rotates as a solid at half the angular velocity of the rotating disk. Finally, when τ_R>τ_0, the material exhibits slip everywhere and yields only in the annulus r_0<r<R, where r_0 is the critical radius at which the shear stress is equal to the yield stress and R is the radius of the disks. In the general case, the slip velocity, which varies with the radial distance, can be calculated numerically and then all quantities of interest, such as the true shear rate, and the two branches of the apparent flow curve can be computed by means of closed form expressions. Analytical solutions have also been obtained for certain values of the power-law exponent. In order to illustrate the effect of wall slip on the apparent flow curve and on the torque, results have been obtained for different gap sizes between the disks choosing the values of the rheological and slip parameters to be similar to reported values for certain colloidal suspensions. The computed apparent flow curves reproduce the patterns observed in the experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Torsional parallel plate flow of Herschel-Bulkley fluids with wall slip Gryparis, Evgenios Georgiou, Georgios C. Fluid Dynamics Soft Condensed Matter The effect of wall slip on the apparent flow curves of viscoplastic materials obtained using torsional parallel plate rheometers is analysed by considering Herschel-Bulkley fluids and assuming that slip occurs above a critical wall shear stress, the slip yield stress τ_c, taken to be lower than the yield stress, τ_0. Thus, different flow regimes are encountered as the angular velocity of the experiment is increased. When the rim shear stress τ_R is below the slip yield stress, the exerted torque is not sufficient to rotate the disk and the material remains still. When τ_c<τ_R<τ_0 the material is still unyielded but exhibits wall slip and rotates as a solid at half the angular velocity of the rotating disk. Finally, when τ_R>τ_0, the material exhibits slip everywhere and yields only in the annulus r_0<r<R, where r_0 is the critical radius at which the shear stress is equal to the yield stress and R is the radius of the disks. In the general case, the slip velocity, which varies with the radial distance, can be calculated numerically and then all quantities of interest, such as the true shear rate, and the two branches of the apparent flow curve can be computed by means of closed form expressions. Analytical solutions have also been obtained for certain values of the power-law exponent. In order to illustrate the effect of wall slip on the apparent flow curve and on the torque, results have been obtained for different gap sizes between the disks choosing the values of the rheological and slip parameters to be similar to reported values for certain colloidal suspensions. The computed apparent flow curves reproduce the patterns observed in the experiments. |
| title | Torsional parallel plate flow of Herschel-Bulkley fluids with wall slip |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2403.14700 |