Capsules Rheology in Carreau–Yasuda Fluids

• Main Authors: Alessandro Coclite, Giuseppe Maria Coclite, Domenico De Tommasi
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Nanomaterials
• Subjects: immersed boundary method (IBM); dynamic forcing IBM; multi relaxation time (MRT); moving least squares; non-Newtonian rheology; particle margination
• Online Access: https://www.mdpi.com/2079-4991/10/11/2190

In this paper, a Multi Relaxation Time Lattice Boltzmann scheme is used to describe the evolution of a non-Newtonian fluid. Such method is coupled with an Immersed-Boundary technique for the transport of arbitrarily shaped objects navigating the flow. The no-slip boundary conditions on immersed bodies are imposed through a convenient forcing term accounting for the hydrodynamic force generated by the presence of immersed geometries added to momentum equation. Moreover, such forcing term accounts also for the force induced by the shear-dependent viscosity model characterizing the non-Newtonian behavior of the considered fluid. Firstly, the present model is validated against well-known benchmarks, namely the parabolic velocity profile obtained for the flow within two infinite laminae for five values of the viscosity model exponent, <i>n</i> = 0.25, 0.50, 0.75, 1.0, and 1.5. Then, the flow within a squared lid-driven cavity for <i>Re</i> = 1000 and 5000 (being <i>Re</i> the Reynolds number) is computed as a function of <i>n</i> for a shear-thinning (<i>n</i> < 1) fluid. Indeed, the local decrements in the viscosity field achieved in high-shear zones implies the increment in the local Reynolds number, thus moving the position of near-walls minima towards lateral walls. Moreover, the revolution under shear of neutrally buoyant plain elliptical capsules with different Aspect Ratio (<i>AR</i> = 2 and 3) is analyzed for shear-thinning (<i>n</i> < 1), Newtonian (<i>n</i> = 1), and shear-thickening (<i>n</i> > 1) surrounding fluids. Interestingly, the power law by Huang et al. describing the revolution period of such capsules as a function of the Reynolds number and the existence of a critical value, <i>Re</i><inline-formula><math display="inline"><semantics><msub><mrow></mrow><mi>c</mi></msub></semantics></math></inline-formula>, after which the tumbling is inhibited in confirmed also for non-Newtonian fluids. Analogously, the equilibrium lateral position <inline-formula><math display="inline"><semantics><msub><mi>y</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub></semantics></math></inline-formula> of such neutrally buoyant capsules when transported in a plane-Couette flow is studied detailing the variation of <inline-formula><math display="inline"><semantics><msub><mi>y</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub></semantics></math></inline-formula> as a function of the Reynolds number as well as of the exponent <i>n</i>.