Foam Flow: Darcy vs NS Equation

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Foam is identified as a Bingham plastic, and Darcy's equation with Bingham's extension is proposed for modeling its flow. The discussion questions the appropriateness of using Darcy's equation for foam flow compared to the Navier-Stokes equations, which are limited to Newtonian fluids. Concerns are raised about the accuracy of certain equations in the referenced article, suggesting potential flaws in the analysis. The unique pressure drop-flow rate behavior of non-Newtonian fluids like foam complicates the application of traditional fluid dynamics equations. Overall, the suitability of Darcy's equation for foam flow remains debated, highlighting the complexities of modeling non-Newtonian fluids.
Talal
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According to the attached article, Foam is a Bingham plastic. Darcy's equation with Bingham's extension can be used to describe the flow. My question is, for foam flow, does utilising Darcy's equation a reasonable approach ? What benefits does it have, or better yet, why not use Navier stockes equation ? Also in the attached article foam is treated as a single phase.
 

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Talal said:
According to the attached article, Foam is a Bingham plastic. Darcy's equation with Bingham's extension can be used to describe the flow. My question is, for foam flow, does utilising Darcy's equation a reasonable approach ? What benefits does it have, or better yet, why not use Navier stockes equation ? Also in the attached article foam is treated as a single phase.
The Navier Stokes equations only apply to a Newtonian fluid. This fluid is non-Newtonian, so its pressure drop-flow rate behavior will be different. I have problems with this paper, particularly Eqns. 22 and 23, which are definitely incorrect.
 
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Thank you very much for your answer.
 

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