Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow

Abstract

Bubble suspensions can be found in many different fields and studying their rheology is crucial in order to improve manufacturing processes. When bubbles are added to a liquid, the magnitude of the viscosity changes and the behavior of the material is modified, giving it viscoelastic properties. For the purpose of this work, the suspended bubbles are considered to be monodisperse. It is assumed that Brownian motion and inertia can be neglected and that the fluid of the matrix is Newtonian and incompressible. The suspension is subject to an oscillatory strain while remaining in the linear regime. The resulting equations are solved in 3D with direct numerical simulation using a finite element discretization. Results of an ordered and random distribution of bubbles of volume fractions up to 40% are presented. The presence of bubbles has an opposite effect on the rheology of the suspension depending on the applied frequency. When the frequency is low, bubbles act as rigid fillers giving a rise to viscosity. On the contrary, when the frequency is high, the strain rate is being accommodated by the gaseous phase. Hence, bubbles deform, leading to a decrease of the viscosity.

On the use of a diffuse-interface model for the simulation of rigid particles in two-phase Newtonian and viscoelastic fluids

“…Although we only employ 2D meshes in this paper, this appraoch can be fairly easily extended to full 3D problems with multiple interfaces (see e.g. [41]). For both models, we employ adaptive meshing to ensure that the mesh close to the particle and fluid-fluid interface is refined, whereas it is coarser in the rest of the domain.…”

Simulation of bubble growth during the foaming process and mechanics of the solid foam

“…After manipulation of Eq. ( 9), the velocity of the interface is implemented in normal direction [18,19] x…”

“…where k is a constant diffusion coefficient and ∆d are the nodal mesh displacements [18,22]. The movement of the outer boundaries, denoted by δx| Γi is, unlike δx| Si , not known after solving the system of equations.…”

“…In the initial structure, bubbles are randomly distributed in the RVE. The nodes on the surface mesh are moved outside of the bubbles in an iterative process, to prevent intersection with the bubbles, which creates the initial random box similar to [18]. Microstructures with one bubble in the computational domain are simulated until a volume fraction f = 0.55 is reached, with a time step of ∆t = 5 × 10 −3 .…”

Head-on collision of Newtonian drops in a viscoelastic medium

“…(18) as a boundary condition. The implementation is similar as in Mitrias et al (2017), but now the whole domain is perturbed. In this way, our scheme is not limited by the characteristic mesh size time limit.…”