Effective Rheology of Bingham Fluids in a Rough Channel
We derive the volumetric flow rate versus pressure drop of a Bingham <br/>fluid in one-dimensional channels of variable apertures in the lubrication <br/>approximation. A characteristic length scale, $a^*$ characterizing the flow<br/>is introduced in order to distinguish between a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2014-04-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00024/full |
| Summary: | We derive the volumetric flow rate versus pressure drop of a Bingham <br/>fluid in one-dimensional channels of variable apertures in the lubrication <br/>approximation. A characteristic length scale, $a^*$ characterizing the flow<br/>is introduced in order to distinguish between a high and a low flow rate <br/>regime. We illustrate the calculation for channels with periodically varying <br/>apertures. We then go on to consider apertures that are self affine. We <br/>determine how the scaling properties of the aperture field is reflected<br/>in the effective flow equations.<br/>Finally, a series expansion for high and low flow rates that <br/>works very well over the entire range of flow rates is proposed.<br/>This truncated expansion allows us to predict the domain of <br/>validity of the two expansions by comparing $a^*$ to the <br/>aperture distribution. |
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| ISSN: | 2296-424X |