scholarly journals On the convergence rate of the Kačanov scheme for shear-thinning fluids

CALCOLO ◽  
2021 ◽  
Vol 59 (1) ◽  
Author(s):  
Pascal Heid ◽  
Endre Süli
Keyword(s):  
Convergence Rate ◽  
Power Law ◽  
Shear Thinning ◽  
Energy Difference ◽  
Iteration Scheme ◽  
Power Law Model ◽  
A Posteriori ◽  
Shear Thinning Fluids ◽  
Finite Dimensional ◽  
Contraction Factor

AbstractWe explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves, on finite-dimensional Galerkin spaces, previously derived bounds on the contraction factor in the context of the power-law model. Significantly, this factor is shown to be independent of the choice of the cut-off parameters whose use was proposed in the literature for the Kačanov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

Inflow Conditions and Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Inflow Velocity ◽  
Flow Recirculation ◽  
Shear Thinning Fluids ◽  
Power Law Index ◽  
The Impact ◽  
Inflow Conditions

The impact of inflow conditions on the flow structure and evolution characteristics of annular flows of Newtonian and shear-thinning fluids through a sudden pipe expansion are studied. Numerical solutions to the elliptic form of the governing equations along with the power-law constitutive equation were obtained using a finite-difference scheme. A parametric study is performed to reveal the influence of inflow velocity profiles, annular diameter ratio, k, and power-law index, n, over the following range of parameters: inflow velocity profile = {fully-developed, uniform}, k = {0, 0.5, 0.7} and n = {1, 0.8, 0.6}. Flow separation and entrainment, downstream of the expansion plane, creates central and a much larger outer recirculation regions. The results demonstrate the influence of inflow conditions, annular diameter ratio, and rheology on the extent and intensity of both flow recirculation regions, the wall shear stress distribution, and the evolution and redevelopment characteristics of the flow downstream the expansion plane. Fully-developed inflows result in larger reattachment and redevelopment lengths as well as more intense recirculation, within the central and corner regions, in comparison with uniform inflow conditions.

Extrusion of power-law shear-thinning fluids with small exponent

1997 ◽  
Vol 32 (1) ◽  
pp. 187-199 ◽  
Author(s):  
S.J. Chapman ◽  
A.D. Fitt ◽  
C.P. Please
Keyword(s):  
Power Law ◽  
Shear Thinning ◽  
Shear Thinning Fluids

scholarly journals Modeling the Deformation of Shear Thinning Droplets Suspended in a Newtonian Fluid

2020 ◽  
Vol 30 (1) ◽  
pp. 151-165
Author(s):  
Abdulwahab S. Almusallam ◽  
Isameldeen E. Daffallah ◽  
Lazhar Benyahia
Keyword(s):  
Experimental Data ◽  
Numerical Modeling ◽  
Large Deformation ◽  
Power Law ◽  
Simple Shear ◽  
Shear Thinning ◽  
Power Law Model ◽  
Flow Strength ◽  
Volume Model ◽  
Droplet Phase

Abstract In this work, we carried out numerical modeling of the large deformation of a shear thinning droplet suspended in a Newtonian matrix using the constrained volume model. The adopted approach was to consider making incremental corrections to the evolution of the droplet anisotropy equation in order to capture the experimental behavior of a shear thinning droplet when subjected to deformation due to imposed flow. The constrained volume model was modified by using different models to describe the viscosity of droplet phase: the Bautista et al. model, the Carreau-Yasuda model and the Power-law model. We found that by combining the constrained volume model with a simple shear thinning viscosity model we were able to describe the available experimental data for large deformation of a shear thinning droplet suspended in a Newtonian matrix. Moreover, we developed an equation approximating flow strength during droplet retraction, and we found that the model can accurately describe the experimental data of the retraction of a shear thinning droplet.

Evolution of a hairpin vortex in a shear-thinning fluid governed by a power-law model

2013 ◽  
Vol 25 (10) ◽  
pp. 101703 ◽  
Author(s):  
Ni Zhen ◽  
Robert A. Handler ◽  
Qi Zhang ◽  
Cassandra Oeth
Keyword(s):  
Power Law ◽  
Shear Thinning ◽  
Hairpin Vortex ◽  
Power Law Model ◽  
Shear Thinning Fluid

scholarly journals Linear stability of Taylor–Couette flow of shear-thinning fluids: modal and non-modal approaches

2015 ◽  
Vol 776 ◽  
pp. 354-389 ◽  
Author(s):  
Y. Agbessi ◽  
B. Alibenyahia ◽  
C. Nouar ◽  
C. Lemaitre ◽  
L. Choplin
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Base Flow ◽  
Newtonian Fluids ◽  
Transient Growth ◽  
Time Behaviour ◽  
Optimal Perturbation ◽  
Shear Thinning Fluids

In this paper, the response of circular Couette flow of shear-thinning fluids between two infinitely long coaxial cylinders to weak disturbances is addressed. It is highlighted by transient growth analysis. Both power-law and Carreau models are used to describe the rheological behaviour of the fluid. The first part of the paper deals with the asymptotic long-time behaviour of three-dimensional infinitesimal perturbations. Using the normal-mode approach, an eigenvalue problem is derived and solved by means of the spectral collocation method. An extensive description and the classification of eigenspectra are presented. The influence of shear-thinning effects on the critical Reynolds numbers as well as on the critical azimuthal and axial wavenumbers is analysed. It is shown that with a reference viscosity defined with the characteristic scales $\hat{{\it\mu}}_{ref}=\hat{K}(\hat{R}_{1}\hat{{\it\Omega}}_{1}/\hat{d})^{(n-1)}$ for a power-law fluid and $\hat{{\it\mu}}_{ref}=\hat{{\it\mu}}_{0}$ for a Carreau fluid, the shear-thinning character is destabilizing for counter-rotating cylinders. Moreover, the axial wavenumber increases with $\mathit{Re}_{2}$ and with shear-thinning effects. The second part investigates the short-time behaviour of the disturbance using the non-modal approach. For the same inner and outer Reynolds numbers, the amplification of the kinetic energy perturbation becomes much more important with increasing shear-thinning effects. Two different mechanisms are used to explain the transient growth, depending on whether or not there is a stratification of the angular momentum. On the Rayleigh line and for Newtonian fluids, the optimal perturbation is in the form of azimuthal streaks, which transform into Taylor vortices through the anti-lift-up mechanism. In the other cases, the optimal perturbation is initially oriented against the base flow, then it tilts to align with the base flow at optimal time. The scaling laws for the optimal energy amplification proposed in the literature for Newtonian fluids are extended to shear-thinning fluids.

Static Rheological Study of Ocimum basilicum Seed Gum

2015 ◽  
Vol 11 (1) ◽  
pp. 97-103 ◽  
Author(s):  
Fakhreddin Salehi ◽  
Mahdi Kashaninejad
Keyword(s):  
Power Law ◽  
Flow Behavior ◽  
Shear Thinning ◽  
Power Law Model ◽  
Rotational Viscometer ◽  
Flow Behavior Index ◽  
Consistency Coefficient ◽  
Salt Addition ◽  
Seed Gum ◽  
Behavior Index

Abstract A rotational viscometer was used to investigate the effect of different sugars (sucrose, glucose, fructose and lactose, 1–4% w/w) and salts (NaCl and CaCl2, 0.1–1% w/w), on rheological properties of Basil seed gum (BSG). The viscosity was dependent on type of sugar and salt addition. Interactions between BSG gum and sugars improved the viscosity of solutions, whereas the viscosity of the BSG solutions decreased in the presence of salts. Power law model well-described non-Newtonian shear thinning behavior of BSG. The consistency index was influenced by the sugars and salts content. Addition of sucrose, glucose, lactose and salts to BSG led to increases in flow behavior index (less shear thinning solutions), whereas fructose increased shear thinning of solutions. Flow behavior index values of the power law model vary as follows: 0.43–0.49, 0.53–0.64, 0.21–0.26, and 0.57–0.67 for sucrose, glucose, fructose and lactose, respectively. The consistency coefficient (k) of BSG was affected by sugars and salts. It decreased from 0.14 to 0.09 Pa.sn with increasing CaCl2 from 0 to 4% w/w (20°C, 0.2% w/w BSG). The consistency coefficient values vary as follows: 0.094–0.119, 0.075–0.098, 0.257–0.484, and 0.056–0.074 for sucrose, glucose, fructose and lactose, respectively.

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