Convoluted models and high-Weissenberg predictions for micellar thixotropic fluids in contraction–expansion flows

Abstract

a b s t r a c tThis study is concerned with finite element/volume modelling of contraction-expansion axisymmetric pipe flows for thixotropic and non-thixotropic viscoelastic models. To obtain solutions at highBautista-Manero micellar and non-thixotropic EPTT f -functionals have been investigated. Here, three key modifications have been implemented: first, that of convoluting EPTT and micellar Bautista-Manero ffunctionals, either in a multiplicative ( Conv * ) or additive ( Conv + ) form; second, by adopting f -functionals in absolute form (ABS-f -correction); and third, by imposing pure uniaxial-extension velocity-gradient components at the pure-stretch flow-centreline (VGR-correction). With this combination of strategies, highly non-linear solutions have been obtained to impressively high Wi [ = O(50 0 0 + )].This capability permits analysis of industrial applications, typically displaying non-linear features such as thixotropy, yield stress and shear banding. The scope of applications covers enhanced oil-recovery, industrial processing of plastics and foods, as well as in biological and microfluidic flows. The impact of rheological properties across convoluted models (moderate-hardening, shear-thinning) has been observed through steady-state solutions and their excess pressure-drop ( epd ) production, stress, f -functional field structure, and vortex dynamics. Three phases of vortex-behaviour have been observed with rise in elasticity, along with upstream-downstream Moffatt vortices and plateauing epd -behaviour at high-Wi levels. Moreover, enhancement of positive-definiteness in stress has improved high-Wi solution attenuation.

Viscoelastic surfactant fluids filtration in porous media: A pore‐scale study

“…The uniaxial extension viscosity, η Ext , was calculated following the convoluted models 45 . The simple uniaxial extension viscosity is derived as expressed in Equation ). …”

Predictions for circular contraction-expansion flows with viscoelastoplastic & thixotropic fluids

“…The theme of this predictive study is that of thixotropic-viscoelastoplastic flow in complex deformation. The constitutive equations employed reflect this and are model variants from the classes of Bautista-Manero [1][2][3][4][5][6][7][8] and . The study is conducted under a flow-rate (Q)-increase protocol, and hence, under fixed fluid relaxation-time (Maxwellian averaged, 1).…”

“…On constitutive modelling Typical and representative constitutive equations for these thixotropic and viscoelastoplastic fluids are constructed upon coupled stress and fluidstructure equations. Bautista-Manero model fluids were originally proposed to approximate the rheology of wormlike micellar solutions [1][2][3][4][5]8]. That is, so-called 'smart fluidsviscoelastic surfactants', given their ability to break and reform their internal structure, subject to the changing environmental conditions of deformation they are exposed to.…”

“…The first normal-stress difference response in shear-deformation N1Shear is highly non-linear, with a second upturn at high shear-rates. Nevertheless, some essential differences between the models are apparent: (i) through the nature of the structure parameter -the Bautista- structure-destruction term of the structure-parameter equation, the factor driving the nonlinear evolution features differsthis being the dissipation-function for Bautista-Manero models; whilst correspondingly, De Souza model early variants contain a dimensionless stress-tensor second-invariant [9][10] (latterly replaced by unity in a corrected De Souza version [11]); (iv) elasticity in the structure equation: whilst some Bautista-Manero model variants have an explicit contribution from the fluid relaxation-time 1 in the destruction-term [4][5][6][7][8], De Souza forms are devoid of this [9][10][11]. Naturally, such similarities and differences motivate the present investigation.…”

“…In this, VGR-correction imposes shear-free extensional deformation along the symmetry-line and a discrete correction for continuity; whilst ABS-f-correction to the constitutive-model structure-functional f, guarantees thermodynamic consistency and ensures positive viscosity estimation in complex flow (see [5]). These corrections are devised to constrain the loss of initial-value-problem (IVP) evolution and its consequent lack of positive definiteness in the system, alongside error propagation (see [5,8] and Section 3 below). Such corrections have been implemented successfully in a number of applications, as exemplified through the simulation of -wormlike micellar fluids in complex flow in non-banding [5,8] and banding conditions [38], the flow of viscoelastoplastic fluids in contraction-expansions (rounded-corner, =4; [6][7]), and the flow of Boger fluids in contraction-type flows.…”