Flow of shear-thinning fluids through porous media

Abstract

Porous media Homogeniz.adon Adjoint theory Carreau fluids Pseudo-plastic fluids exhibit a non-Jinear stress-strain relationship which can provoke large, localized viscosity gradients. For the fl ow of such fl uids in porous media the consequence is a strong varia b ility of the effective permeability with poroeity, angle of the macroscopic pressure gradien t, and meological parameters of the fluid. Such a variability is investigated on the basis of ad j oint homogenization theory for a Carreau fluid in an idealized porous medium geometty, highlighting differences with respect to the Newtonian case. It is shown in particular that the more we de part from Newtonian conditions, the more the (often used) hypothesis of an effective viscosity in Darc y' s law is a poor approximation, for the effective permeability tensor becomes strongly anisotropie.

Macroscopic model for unsteady generalized Newtonian fluid flow in homogeneous porous media

“…This observation is relevant because it allows for the closure problem defined in Eqs. (31) to reduce, under non-inertial and steady-state conditions, to the one reported in Section 3 in [38].…”

“…For example, the macroscopic flux to force relationship has been inferred from simplified representations of the porous structure under the form of bundles of capillaries [18,19] and pore-network models [20,21]. More formal approaches have also been employed, including the thermodynamically https://doi.org/10.1016/j.jnnfm.2022.104840 constrained averaging theory (TCAT) [22], the classical [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] and adjoint [38] homogenization techniques and the volume averaging method [39][40][41][42]. In the following paragraphs a brief literature review, mainly focused on applications of the homogenization and volume averaging methods, is presented.…”

“…Using the adjoint homogenization approach [47], Airiau and Bottaro [38] considered the steady creeping flow of a shear-thinning incompressible fluid in the bulk of a porous medium. They proposed to first solve for the zeroth-order velocity in the power-series expansion and then substitute this field into the viscosity term of the auxiliary problem in order to avoid an iterative scheme.…”

Reliable fluid‐mechanical characterization of haemofilters: Addressing the deficiencies of current standards and practices

“…14 The same experiments have shown that the inertia coefficients ζ i also depend on viscosity; this appears reasonable for relatively small Reynolds number flows. 21 However, no theory exists, to deal with the rather complicated geometry of headers (and the complicated flow distribution therein), allowing the extrapolation of the results to liquids of different viscosities.…”

Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects

“…The two closure problems I and II are coupled both between themselves and also with the macroscale model solution due to the convective terms in Equations ( 29c) and (30c). This becomes clear when, in these two last equations, the representation given in Equation ( 28a) is used to expressṽ and v in terms of ∇ p β and f. This issue is often encountered while upscaling non-linear processes (see, for instance, Valdés-Parada et al, 2009;Airiau and Bottaro, 2020) and it will be addressed later in section 6.3. At this point, it is pertinent to derive the closed form of the upscaled model.…”