AUTHOR=Talon Laurent , Auradou Harold , Hansen Alex 

TITLE=Effective rheology of Bingham fluids in a rough channel

JOURNAL=Frontiers in Physics

VOLUME=Volume 2 - 2014

YEAR=2014

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2014.00024

DOI=10.3389/fphy.2014.00024

ISSN=2296-424X

ABSTRACT=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.