Simulating gas bubble shape during its rise in a confined polymeric solution by WC-SPH

In this study, rising and deformation of a single bubble in a viscoelastic fluid obeying the Giesekus model are numerically simulated by a modified version of weakly compressible smoothed particle hydrodynamics (WC-SPH). It is shown that the developed algorithm is robust enough to simulate two-phase flow with large density and viscosity ratios (up to 1000 and 100, respectively) not only in Newtonian cases but also in viscoelastic ones. After quantitative and qualitative verification of the developed code against previously published results, it is applied for simulating the rising bubble in the Giesekus fluid as a realistic model for polymeric solutions. Several simulations are performed to investigate the effects of mobility factor (0 ≤α≤ 1), polymer concentration (2.5 ≤c_l≤ 20), relaxation time (1.14 ≤ De ≤ 114), density ratio (10 ≤ρ_l∕ρ_b≤1000) as well as domain width (6.6 ≤ W/D₀≤ 16.6). It is found that in contrast to relaxation and polymer concentration parameters which have dramatic effects on the rising bubble, the mobility factor has no significant effect on the rising bubble in high viscous polymeric solution. Also, the cusp trailing edge is postponed by decreasing the domain width.