Abstract
Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids.Graphic abstract
Highlights
Recent years have seen a surge of interest in the study of viscoelastic fluids, due to increased experimental understanding and several intriguing results that were obtained in these media
Microswimmers in viscoelastic fluids show a richer set of behaviors than possible in simple (Newtonian) fluids, which include the self-propulsion of a microswimmer with a single hinge [1,2], which is forbidden in a Newtonian fluid at low Reynolds number by Purcell’s scallop theorem [3]; enhanced rotational diffusion of thermophoretic Janus swimmers, due to time-delayed translation–rotation coupling in polymer suspensions [4]; a peak in the motility of Escheria coli bacteria as a function of the polymer concentration and complexity of the fluid [5]; and a fundamental change in the way a microorganism propels in response to the rheology of the medium [6]
Examples of such solvers applied to microfluidic problems include the finite volume method [12,13], the finite element method [14,15], multi-particle collision dynamics (MPCD) [16,17], dissipative particle dynamics [18], the immersed boundary method [6], smoothedparticle hydrodynamics [19,20], as well as explicitpolymer models based on Stokesian dynamics [21] and MPCD [22]
Summary
Recent years have seen a surge of interest in the study of viscoelastic fluids, due to increased experimental understanding and several intriguing results that were obtained in these media. Our method is inspired by the Su et al [43] algorithm for an Oldroyd-B fluid, which we re-derive as a finite volume scheme similar to that of Oliveira et al [46]. This ensures momentum conservation and allows us to introduce a boundary coupling that makes no assumptions on the stress at the boundary. 2 and laying out our numerical method, we benchmark our algorithm using several standard rheological tests: time dependence of the planar Poiseuille flow, steady shear flow, the instabilities in lid-driven-cavity flow, and extensional flow in the four-roll mill in Sect.
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