The Effect of Microstructure on Models for the Flow of a Bingham Fluid in Porous Media: One-Dimensional Flows

Abstract

The Buckingham-Reiner models for the one-dimensional flow of a Bingham fluid along a uniform pipe or channel are well-known, but are modified here to cover much more general one-dimensional configurations. These include selections of channels with different widths, and five different probability density functions describing distributions of channel widths. It is found that the manner in which breakthrough occurs at the threshold pressure gradient depends very strongly on the type of distribution of pores and that a pseudo-threshold pressure gradient, which might be inferred from measurements of flow at relatively high pressure gradients, may be more than twice the magnitude of the true threshold gradient.

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

“…In this case the initial rise in the flow is quadratic immediately post-threshold, as opposed to linear in Pascal's model. We also note that more sedate transitions to flow were found by Nash and Rees (2017) who considered distributions of channels/pores. In the present paper, we will adopt Pascal's piecewise-linear form.…”

Flow of yield stress and Carreau fluids through rough‐walled rock fractures: Prediction and experiments

“…[], who stated that u scales linearly as ( ) in the case of a Bingham fluid (n = 1) flowing at high u through a one‐dimensional channel. Also, Nash and Rees [] showed that the manner in which flow begins once the threshold pressure gradient is exceeded strongly depends on the channel‐size distribution of the porous media. The same authors [ Talon et al ., ; Nash and Rees , ] proved that is higher than the actual threshold pressure, which is consistent with our results given that increases as u tends to zero (Figure ).…”

The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

“…One of the most frequently used is the Buckingham-Reiner model (Buckingham [5] and Reiner [6]) which, strictly speaking, corresponds to the Hagen-Poiseuille flow of a Bingham fluid, but it may be applied to a porous medium by assuming a unidirectional flow within a medium consisting of identical pores. More complicated scenarios may be envisaged, and it is worth mentioning that Nash and Rees [7] performed an analytical study of the effect of having distributions of pore diameters. In general this was found to 'soften' the initial stages of flow post-threshold, and each distribution of pores has its own analogue of a Buckingham-Reiner law.…”

“…In general this was found to 'soften' the initial stages of flow post-threshold, and each distribution of pores has its own analogue of a Buckingham-Reiner law. The work of Malvault et al [8] relaxes the assumptions of [7] that the pores have a uniform cross-section.…”