On the effect of a large cloud of rigid particles on the motion of an incompressible non--Newtonian fluid

2024/04/10 by Eduard Feireisl, Arnab Roy, Feireisl, Eduard +3
Chemical Engineering · Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Particle Dynamics in Fluid Flows #Rheology and Fluid Dynamics Studies #Sports Dynamics and Biomechanics

paper · pdf · doi:10.48550/arxiv.2404.06782

openalex publication_date 2024/04/10 · openalex created_date 2024/04/12 · openalex updated_date 2026/07/29

Abstract

We show that the collective effect of N rigid bodies (S_n,N)_n=1^N of diameters (r_n,N)_n=1^N immersed in an incompressible non--Newtonian fluid is negligible in the asymptotic limit N → ∞ as long as their total packing volume ∑_n=1^N r_n,N^d, d=2,3 tends to zero exponentially -- ∑_n=1^N r_n,N^d ≈ A^-N -- for a certain constant A > 1. The result is rather surprising and in a sharp contrast with the associated homogenization problem, where the same number of obstacles can completely stop the fluid motion in the case of shear thickening viscosity. A large class of non--Newtonian fluids is included, for which the viscous stress is a subdifferential of a convex potential.

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