“…For the more elastic EVP droplet, the material continuosly unyields and yields when passing through boundaries of solid zones, while the solid zones remain at same place in steady state. This shows that the solid regions of the droplet are pseudoplugs, which have been observed in EVP flow in porous media [14,42]. We can also observe that the velocity vectors do not show any change in direction or character when entering or leaving the pseudoplug.…”
Section: B Time Evolution Of the Yielding Processsupporting
The dynamics of a single elastoviscoplastic drop immersed in plane shear flow of a Newtonian fluid is studied by three-dimensional direct numerical simulations using a finite-difference/level set method combined with the Saramito model for the elastoviscoplastic fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimensional parameters on the yielding process; in particular, the Bingham number, the capillary number, the Weissenberg number and the ratio of solvent and total drop viscosity are varied. We find that all of these parameters have a significant influence on the drop dynamics, and not only the Bingham number. Numerical simulations predict that the volume of the unyielded region inside the droplet increases with the Bingham number and the Weissenberg number, while it decreases with the capillary number at low Weissenberg and Bingham numbers. A new regime map is obtained for the prediction of the yielded, unyielded and partly yielded modes as a function of the Bingham and Weissenberg numbers. The drop deformation is studied and explained by examining the stresses in the vicinity of the drop interface. The deformation has a complex dependence on the Bingham and Weissenberg numbers. At low Bingham numbers, the droplet deformation shows a non-monotonic behaviour with an increasing drop viscoelasticity. In contrast, at moderate and high Bingham numbers, droplet deformation always increases with drop viscoelasticity. Moreover, it is found that the deformation increases with the capillary number and with the solvent to total drop viscosity ratio. A simple ordinary differential equation model is developed to explain the various behaviours observed numerically. The presented results are in contrast with the heuristic idea that viscoelasticity in the dispersed phase always inhibits deformation.
“…For the more elastic EVP droplet, the material continuosly unyields and yields when passing through boundaries of solid zones, while the solid zones remain at same place in steady state. This shows that the solid regions of the droplet are pseudoplugs, which have been observed in EVP flow in porous media [14,42]. We can also observe that the velocity vectors do not show any change in direction or character when entering or leaving the pseudoplug.…”
Section: B Time Evolution Of the Yielding Processsupporting
The dynamics of a single elastoviscoplastic drop immersed in plane shear flow of a Newtonian fluid is studied by three-dimensional direct numerical simulations using a finite-difference/level set method combined with the Saramito model for the elastoviscoplastic fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimensional parameters on the yielding process; in particular, the Bingham number, the capillary number, the Weissenberg number and the ratio of solvent and total drop viscosity are varied. We find that all of these parameters have a significant influence on the drop dynamics, and not only the Bingham number. Numerical simulations predict that the volume of the unyielded region inside the droplet increases with the Bingham number and the Weissenberg number, while it decreases with the capillary number at low Weissenberg and Bingham numbers. A new regime map is obtained for the prediction of the yielded, unyielded and partly yielded modes as a function of the Bingham and Weissenberg numbers. The drop deformation is studied and explained by examining the stresses in the vicinity of the drop interface. The deformation has a complex dependence on the Bingham and Weissenberg numbers. At low Bingham numbers, the droplet deformation shows a non-monotonic behaviour with an increasing drop viscoelasticity. In contrast, at moderate and high Bingham numbers, droplet deformation always increases with drop viscoelasticity. Moreover, it is found that the deformation increases with the capillary number and with the solvent to total drop viscosity ratio. A simple ordinary differential equation model is developed to explain the various behaviours observed numerically. The presented results are in contrast with the heuristic idea that viscoelasticity in the dispersed phase always inhibits deformation.
“…In this study, we implement the entire numerical algorithm in an open-source C finite element environment – FreeFEM (Hecht 2012). We have previously validated our numerical implementation and mesh adaptation widely within various studies (Chaparian & Frigaard 2017 b ; Chaparian & Tammisola 2019; Chaparian et al. 2020).…”
Section: Slip Law and The Numerical Algorithm Beyond 1-dmentioning
confidence: 96%
“…It is clear that the velocity distribution after adaptation (red line) is much closer to the analytical solution (red circles) than the solution of the initial mesh (blue line), and also yields a fine resolution of the yield surfaces – see figure 3( d ). We shall mention that the focus of the present study is not on quantifying these improvements by the mesh adaptation, as it has been previously studied in detail (Roquet & Saramito 2003, 2008; Chaparian & Tammisola 2019). Figure 3.The [M] problem features: ( a ) velocity profile of the case (fully sliding plug); ( b ) velocity profile of the case (deforming regime); ( c ) the mesh after five cycles of adaptation associated with panel ( b ); ( d ) velocity contour associated with panel ( b ), the green lines show the yield surfaces; ( e , f ) close-up of the cyan windows in the panels ( b , c ), respectively.…”
“…In the case of more complex models, e.g. elastoviscoplastic models, one needs more effort – please see Chaparian & Tammisola (2019). In the following, as an example, we consider the 2-D circular Couette flow between two infinitely long cylinders of radii and – see figure 19.…”
mentioning
confidence: 99%
“…In the case of more complex models, e.g. elastoviscoplastic models, one needs more effort – please see Chaparian & Tammisola (2019).…”
A numerical study of yield-stress fluids flowing in porous media is presented. The porous media is randomly constructed by non-overlapping mono-dispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yield-stress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence.
Graphical abstract
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