Stochastic particle level set simulations of buoyancy-driven droplets in non-Newtonian fluids

Computational modeling of multiphase viscoelastic and elastoviscoplastic flows

“…The droplet interface shapes that we obtained at t = 0.13 s together with the ones by Zainali et al and Vahabi and Sadeghy are depicted in Figure . It can be seen in the figure that the present result is consistent with the one reported by Vahabi and Sadeghy; on the contrary, Zainali et al have not observed the cusped trailing edge, which is however a common feature for the case of Newtonian droplet in viscoelastic medium at high polymer concentrations …”

“…The no‐slip boundary conditions are applied at the horizontal walls. It should be noted that Prieto used the free‐slip boundary conditions on the vertical walls, whereas Zainali et al and Vahabi and Sadeghy imposed the no‐slip boundary conditions. The nondimensional parameters pertaining to this problem are defined as the Reynolds number R e = ρ 1 U g L / μ 1 , the E tv s number , the Weissenberg number W i = λ U g / L , the Bingham number B i = τ y / ρ g L , the viscosity ratio k μ = μ 2 / μ 1 , the density ratio k ρ = ρ 2 / ρ 1 , and the confinement ratio χ = 2 R / L x .…”

“…First, we show a comparison of rising droplets to the computational study of Prieto in two cases. (NV) denotes a Newtonian droplet in a viscoelastic medium ( W i = 1, β = 0.5), and (N) denotes a Newtonian droplet in a Newtonian medium ( W i = 0, β = 1).…”

“…A, the terminal velocity versus the nondimensional time; B, its respective steady state shape. The symbols represent the present results, whereas the solid lines are those by Prieto . Our results are obtained using a 128 × 256 grid (N case: R e = 35, E o = 10, B i = 0, k ρ = 0.1, k μ = 0.1, and χ = 0.5; NV case: R e = 35, E o = 10, W i = 1, B i = 0, β = 0.5, k ρ = 0.1, k μ = 0.1, and χ = 0.5) [Colour figure can be viewed at wileyonlinelibrary.com]…”

“…It can be seen in the figure that the present result is consistent with the one reported by Vahabi and Sadeghy 103 ; on the contrary, Zainali et al 102 have not observed the cusped trailing edge, which is however a common feature for the case of Newtonian droplet in viscoelastic medium at high polymer concentrations. 44,101,[105][106][107] Finally, some sample simulations are presented for a Newtonian droplet moving in an EVP fluid. The physical properties pertinent to the problem are the same as in the work of Zainali et al 102 and Vahabi and Sadeghy 103 except for a nonzero Bingham number; indeed, the Bingham number is varied between Bi = 0 and 0.1.…”