scholarly journals Capsules Rheology in Carreau–Yasuda Fluids

Nanomaterials ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 2190
Author(s):  
Alessandro Coclite ◽  
Giuseppe Coclite ◽  
Domenico De Tommasi
Keyword(s):  
Reynolds Number ◽  
Shear Zones ◽  
Shear Thinning ◽  
Lateral Position ◽  
Momentum Equation ◽  
Viscosity Model ◽  
Immersed Boundary ◽  
Forcing Term ◽  
Neutrally Buoyant ◽  
The Revolution

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, n = 0.25, 0.50, 0.75, 1.0, and 1.5. Then, the flow within a squared lid-driven cavity for Re = 1000 and 5000 (being Re the Reynolds number) is computed as a function of n for a shear-thinning (n < 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 (AR = 2 and 3) is analyzed for shear-thinning (n < 1), Newtonian (n = 1), and shear-thickening (n > 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, Rec, after which the tumbling is inhibited in confirmed also for non-Newtonian fluids. Analogously, the equilibrium lateral position yeq of such neutrally buoyant capsules when transported in a plane-Couette flow is studied detailing the variation of yeq as a function of the Reynolds number as well as of the exponent n.

scholarly journals A finite-difference convective model for Jupiter's equatorial jet

2006 ◽  
Vol 2 (S239) ◽  
pp. 230-232 ◽  
Author(s):  
Kwing L. Chan
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Finite Difference ◽  
Spherical Shell ◽  
Reynolds Stress ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Zonal Momentum Balance ◽  
Zonal Momentum ◽  
Convective Model

AbstractWe present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.

Improved compressor corner separation prediction using the quadratic constitutive relation

2017 ◽  
Vol 231 (7) ◽  
pp. 618-630 ◽  
Author(s):  
Xinrong Su ◽  
Xin Yuan
Keyword(s):  
Constitutive Relation ◽  
Eddy Viscosity ◽  
Pressure Coefficient ◽  
Momentum Equation ◽  
Viscosity Model ◽  
Corner Separation ◽  
Pressure Loss Coefficient ◽  
Eddy Viscosity Model ◽  
Relation Model ◽  
Separation Size

This work presents the implementation and study of the quadratic constitutive relation nonlinear eddy-viscosity model with representative compressor application, for which the corner separation has been poorly predicted with the widely used linear Boussinesq eddy-viscosity model. With the introduction of the Reynolds stress anisotropy, the secondary flow of the second kind and its effect on the corner flow can be well captured and this results in greatly improved prediction of pressure coefficient, total pressure loss coefficient and the corner separation size. Without the quadratic constitutive relation model, the separation size and loss are generally over-estimated. The mechanism of the improvement is studied using both the vortex dynamics and the momentum equation. It is proved that quadratic constitutive relation model consumes low CPU time and provides much improved compressor corner separation prediction without worsening the convergence property.

Effect of surfactants on hydrodynamics characteristics of bubble in shear thinning fluids at low Reynolds number

2018 ◽  
Vol 25 (4) ◽  
pp. 805-811 ◽  
Author(s):  
Shao-bai Li ◽  
Jun-geng Fan ◽  
Run-dong Li ◽  
Lei Wang ◽  
Jing-de Luan
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Shear Thinning ◽  
Shear Thinning Fluids ◽  
Low Reynolds

Dynamics of a macroscopic elastic fibre in a polymeric cellular flow

2017 ◽  
Vol 817 ◽  
pp. 388-405 ◽  
Author(s):  
Qiang Yang ◽  
Lisa Fauci
Keyword(s):  
Reynolds Number ◽  
Viscoelastic Fluid ◽  
Relaxation Times ◽  
Elastic Fibre ◽  
Weissenberg Number ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
Multiple Cells

We study the dynamics and transport of an elastic fibre in a polymeric cellular flow. The macroscopic fibre is much larger than the infinitesimal immersed polymer coils distributed in the surrounding viscoelastic fluid. Here we consider low-Reynolds-number flow using the Navier–Stokes/Fene-P equations in a two-dimensional, doubly periodic domain. The macroscopic fibre supports both tensile and bending forces, and is fully coupled to the viscoelastic fluid using an immersed boundary framework. We examine the effects of fibre flexibility and polymeric relaxation times on fibre buckling and transport as well as the evolution of polymer stress. Non-dimensional control parameters include the Reynolds number, the Weissenberg number, and the elasto-viscous number of the macroscopic fibre. We find that large polymer stresses occur in the fluid near the ends of the fibre when it is compressed. In addition, we find that viscoelasticity hinders a fibre’s ability to traverse multiple cells in the domain.

The hydrodynamic lift of a slender, neutrally buoyant fibre in a wall-bounded shear flow at small Reynolds number

2019 ◽  
Vol 879 ◽  
pp. 121-146 ◽  
Author(s):  
Johnson Dhanasekaran ◽  
Donald L. Koch
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Solid Body ◽  
Rotational Motion ◽  
Fibre Orientation ◽  
Reciprocal Theorem ◽  
Microfluidic Channels ◽  
Slender Body Theory ◽  
Cross Flow Filtration ◽  
Neutrally Buoyant

The hydrodynamic lift velocity of a neutrally buoyant fibre in a simple shear flow near a wall is determined for small, but non-zero, fibre Reynolds number, illustrating the role of non-sphericity in lift. The rotational motion and effects of fibre orientation on lift are treated for fibre positions that induce and do not induce solid-body wall contacts. When the fibre does not contact the wall its lift velocity can be obtained in terms of the Stokes flow field by using a generalized reciprocal theorem. The Stokes velocity field is determined using slender-body theory with the no-slip velocity at the wall enforced using the method of images. To leading order the lift velocity at distances large compared with the fibre length and small compared with the Oseen length is found to be $0.0303\unicode[STIX]{x1D70C}\dot{\unicode[STIX]{x1D6FE}}^{2}l^{2}a/(\unicode[STIX]{x1D707}\ln [2l/a])$, where $l$ and $a$ are the fibre half-length and radius, $\unicode[STIX]{x1D70C}$ is the density, $\dot{\unicode[STIX]{x1D6FE}}$ is the shear rate and $\unicode[STIX]{x1D707}$ is the viscosity of the fluid. When the fibre is close enough to the wall to make solid-body contact during its rotational motion, a process known as pole vaulting coupled with inertially induced changes of fibre orientation determines the lift velocity. The order of magnitude of the lift in this case is larger by a factor of $l/a$ than when the fibre does not contact the wall and it reaches a maximum of $0.013\unicode[STIX]{x1D70C}\dot{\unicode[STIX]{x1D6FE}}^{2}l^{3}/(\unicode[STIX]{x1D707}\ln [l/a])$ for the case of a highly frictional contact and about half that value for a frictionless contact. These results are used to illustrate how particle shape can contribute to separation methods such as those in microfluidic channels or cross-flow filtration processes.

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