Numerical simulation of the motion and deformation of a non-Newtonian shear-thinning drop suspended in a Newtonian circular Couette flow using DR-BEM

Giraldo, Mauricio; Power, H.; Florez, W. F.

doi:10.1016/j.enganabound.2008.03.003

Cited by 12 publications

(7 citation statements)

References 31 publications

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“…Even though this is by far the simplest and computational less expensive method, it was found to diverge when the power law index was smaller than ≈0.8, and therefore not used here. A good alternative is to use the Newton-Raphson method as presented by Giraldo et al [31].…”

Section: Iterative Solution Of the Nonlinear System Of Equationsmentioning

confidence: 99%

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Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

Giraldo

Power

Florez

2010

Numer. Methods Partial Differential Eq.

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An efficient indirect boundary integral formulation for the evaluation of inelastic non-Newtonian shearthinning flows at low Reynolds number is presented in this article. The formulation is based on the solution of a homogeneous Stokes flow field and the use of a particular solution for the nonlinear non-Newtonian terms that yields the complete solution to the problem. Matrix multiplications are reduced in comparison to other means of handling nonlinear terms in boundary integral formulations such as the dual reciprocity method. The iterative solution of the nonlinear system of equations has been performed with a modified Newton-Raphson method obtaining accurate results for values of the power law index as low as 0.4 without domain partitioning. Geometries such as Couette flow and a typical industrial polymer mixer have been analyzed with the proposed method obtaining good results with a reduction in computational cost compared with other equivalent formulations.

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Section: Iterative Solution Of the Nonlinear System Of Equationsmentioning

confidence: 99%

“…However, domain partitioning techniques have drawbacks when evaluating problems with moving boundaries, as they require complex remeshing algorithms. Single domain approaches, on the other hand, require only the repositioning of surface nodes as shown in [31], greatly reducing computational cost. …”

Section: A Couette Flowmentioning

confidence: 99%

Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

Giraldo

Power

Florez

2010

Numer. Methods Partial Differential Eq.

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“…Regarding shear thinning drops, one has to distinguish whether the comparison with Newtonian drops is done at the same zero-shear viscosity or the same viscosity at the applied shear stress. If the zero-shear viscosity is considered, the deformation of shear thinning drops is higher than the deformation of the corresponding Newtonian liquid [28]. If instead the viscosity at the applied shear stress is considered, shear thinning drops are less deformed and breakup occurs at a higher capillary number in comparison to Newtonian liquids [29][30][31][32].…”

Section: Introductionmentioning

confidence: 96%

“…As reason for the divergent behavior, the inhomogeneous viscosity profile inside a shear thinning drop under shear is reported. Because of the shear thinning properties of the drop, the viscosity profile inside the drop shows a strong increase from the liquid-liquid interface towards the center of the drop [28,33]. De Bruijn showed that the breakup behavior of shear thinning liquids can be described by the theory developed for Newtonian liquids provided that the inhomogeneous drop viscosity profile is taken into account by calculating the viscosity ratio with an adjusted effective disperse phase viscosity [27].…”

Section: Introductionmentioning

confidence: 98%

Emulsification of particle loaded drops in simple shear flow

Merkel

Henne

Hecht

et al. 2015

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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“…One of the alternatives is the Dual Reciprocity Method (DRM) which is used together with the NewtonRaphson iterative technique. It turned out to be an efficient way for the numerical investigation of the deformation of a non-Newtonian drop in the Newtonian fluid flow [13]. The truncated power law model has been used.…”

Section: Introductionmentioning

confidence: 99%

The indirect boundary element method for the two-dimensional pressure- and gravity-driven free surface Stokes flow

Ponomareva¹,

Filina²,

Yakutenok³

2014

WIT Transactions on Modelling and Simulation

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The indirect boundary element method (IBEM) is formulated for a two-dimensional Stokes flow with moving boundary in the presence of gravity. For simulation of the non-Newtonian fluid flow an iterative scheme for solving a nonlinear system of algebraic equation is used to calculate nonlinear viscous terms. The selected scheme requires values of pseudo forces in each boundary element and each internal collocation point obtained from boundary conditions (for velocities and tractions) and velocity field found at the previous iteration. Boundary element integrals are calculated analytically with a singularity extraction and internal cells integrals are evaluated by using the standard Gaussian quadratures. Internal cells sources are estimated numerically within a finite difference approach to velocity derivatives calculation. The Poiseuille flow of power law fluid in a channel is calculated for a benchmark of the IBEM algorithm. The accuracy and convergence tests are presented for a wide range of power law index (0.2-1.2). In the presence of a free surface, no analytical solution is available. The problem of channel filling with power law fluid is analyzed. The shape and the movement of the free surface are investigated through a special numerical front tracking algorithm based on mesh refinement for the free surface and for the solution domain. Elements of high performance computing are presented. The obtained results coincide with those of other authors. It confirms that the presented algorithm and corresponding software can be applied to study a number of low Reynolds flows, for example in a mould filling technology.

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Numerical simulation of the motion and deformation of a non-Newtonian shear-thinning drop suspended in a Newtonian circular Couette flow using DR-BEM

Cited by 12 publications

References 31 publications

Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

Emulsification of particle loaded drops in simple shear flow

The indirect boundary element method for the two-dimensional pressure- and gravity-driven free surface Stokes flow

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