title: Soft Objects in Newtonian and Non-Newtonian Fluids : a Computational Study of Bubbles and Capsules in Flow
Creators: name: Häusl, Fabian
Publisher: name: University of Bayreuth
Year: 2021
Subjects: subject: lattice Boltzmann method
subject: viscoelasticity
subject: non-Newtonian fluids
subject: bubbles
subject: Hoshen-Kopelman
subject: microcapsule
subject: bioprinting
subject: microfluidics
subject: GPU
subject: high performance computing
subject: OpenCL
subject: FENE-P
subject: Oldroyd-B
subject: polymer suspension
subject: biofabrication
subject: 004
subject: 500
subject: 530
subject: 570
subject: 610

description: Most biological fluids are viscoelastic, giving rise to complex phenomena like shear-dependent viscosities or non-zero storage moduli. Soft objects suspended in these fluids cause complicated flow geometries and stress distributions, where computational models can help to understand the underlying interactions. To this end, a hybrid algorithm combining the lattice Boltzmann method (LBM) with the finite volume (FV) scheme is proposed, where the former is used to solve the hydrodynamic equations while the latter models the polymer dynamics. To be able to separate the different viscoelasticity properties within a polymeric liquid, the kinetics of the dissolved polymers is captured by two different constitutive equations, modeling viscoelastic fluids consisting of linear dumbbells (Oldroyd-B) or finitely extensible non-linear elastic dumbbells with Peterlin closure (FENE-P). By carefully adapting the algorithm for compatibility with various types of LBM boundary conditions, the correct rheological behavior in several validation setups is reproduced with high accuracy, including oscillatory shear, onset of poiseuille flow, elongational flow and cessation of steady shear. Coupling this algorithm to the immersed boundary method (IBM) allows for the modeling of immersed capsules, which are shown to match well with literature data both in Newtonian and Oldroyd-B shear flow. With this basis, this thesis proposes numerical simulations of capsules in FENE-P fluids, where the capabilities of the IB-LBM were never quantified before. Here, the well-known drop of the dimensionless rotational frequency of capsules at Weissenberg number Wi ≈ 1 is reproduced, the time-dependent capsule deformation under shear is explored and a prediction on the behavior of cells under bioprinting conditions is made. Increasing the complexity, the model is extended to capsules with differing interior and exterior fluid properties, whilst at the same time accounting for both conservation of stress and high advection accuracy at the capsule boundary. In the case of bubbles suspended in Newtonian fluids, no biological boundary is needed to separate the two phases. Instead, surface tension now plays a dominant role, which is integrated into the LBM using a Volume-of-Fluid (VoF) approach, reducing the problem of a liquid-gas two-phase flow to a single-phase fluid with a free interface. The change in pressure due to (de-)compression of the bubble volume is approximated by incorporation of the ideal gas equation. Especially in the presence of multiple bubbles, tracking the topological changes of the free surface while accounting for merging or splitting of bubbles becomes a difficult task. This thesis presents an algorithm based on the Hoshen-Kopelman algorithm to efficiently manage merge/split processes, significantly reducing the computational load compared to purely CPU-based approaches by triggering these processes via GPU-compatible criteria. The accuracy of the algorithm is benchmarked using the Rayleigh-Plesset equation. Furthermore, its capability of reproducing the correct shape and speed of bubbles rising to the atmospheric surface is investigated over a long range of Morton and Bond numbers. Together with the simulation of a bursting bubble, this tests the model for its application in microplastics research, where bubbles are believed to play an important role in the exchange of particles at the air-water interface.