Non-Newtonian Shear-Thinning Fluid Passing Through a Duct with an Obstacle, Using a Power Law Model

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.

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

Applied Rheology ◽

10.1515/arh-2020-0113 ◽

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.

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Static Rheological Study of Ocimum basilicum Seed Gum

International Journal of Food Engineering ◽

10.1515/ijfe-2014-0189 ◽

2015 ◽

Vol 11 (1) ◽

pp. 97-103 ◽

Cited By ~ 11

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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Heat Transfer and Flow Structures of Laminar Confined Slot Impingement Jet with Power-Law Non-Newtonian Fluid

Entropy ◽

10.3390/e20100800 ◽

2018 ◽

Vol 20 (10) ◽

pp. 800 ◽

Cited By ~ 1

Author(s):

Yan Qiang ◽

Liejiang Wei ◽

Xiaomei Luo ◽

Hongchao Jian ◽

Wenan Wang ◽

...

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Power Law ◽

Methyl Cellulose ◽

Shear Thickening ◽

Shear Thinning ◽

Working Fluid ◽

Flow Structures ◽

Inlet Velocity ◽

Shear Thinning Fluid

Heat transfer performances and flow structures of laminar impinging slot jets with power-law non-Newtonian fluids and corresponding typical industrial fluids (Carboxyl Methyl Cellulose (CMC) solutions and Xanthangum (XG) solutions) have been studied in this work. Investigations are performed for Reynolds number Re less than 200, power-law index n ranging from 0.5 to 1.5 and consistency index K varying from 0.001 to 0.5 to explore heat transfer and flow structure of shear-thinning fluid and shear-thickening fluid. Results indicate that with the increase of n, K for a given Re, wall Nusselt number increases mainly attributing to the increase of inlet velocity U. For a given inlet velocity, wall Nusselt number decreases with the increase of n and K, which mainly attributes to the increase of apparent viscosity and the reduction of momentum diffusion. For the same Re, U and Pr, wall Nusselt number decreases with the increase of n. Among the study of industrial power-law shear-thinning fluid, CMC solution with 100 ppm shows the best heat transfer performance at a given velocity. Moreover, new correlation of Nusselt number about industrial fluid is proposed. In general, for the heat transfer of laminar confined impinging jet, it is best to use the working fluid with low viscosity.

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Influence of Non-Newtonian Behavior of Blood on Flow in an Elastic Artery Model

Journal of Biomechanical Engineering ◽

10.1115/1.2795936 ◽

1996 ◽

Vol 118 (1) ◽

pp. 111-119 ◽

Cited By ~ 38

Author(s):

A. Dutta ◽

J. M. Tarbell

Keyword(s):

Shear Stress ◽

Pressure Gradient ◽

Power Law ◽

Flow Rate ◽

Wall Motion ◽

Flow Simulation ◽

Shear Thinning ◽

Power Law Model ◽

Viscous Shear ◽

Sinusoidal Flow

Two different non-Newtonian models for blood, one a simple power law model exhibiting shear thinning viscosity, and another a generalized Maxwell model displaying both shear thining viscosity and oscillatory flow viscoelasticity, were used along with a Newtonian model to simulate sinusoidal flow of blood in rigid and elastic straight arteries. When the spring elements were removed from the viscoelastic model resulting in a purely viscous shear thinning fluid, the predictions of flow rate and WSS were virtually unaltered. Hence, elasticity of blood does not appear to influence its flow behavior under physiological conditions in large arteries, and a purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions. When a power law model with a high shear rate Newtonian cutoff was used for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to a Newtonian fluid experiencing the same pressure gradient. The wall shear stress was found to be relatively insensitive to fluid rheology but strongly dependent on vessel wall motion for flows driven by the same pressure gradient. The effect of wall motion on wall shear stress could be greatly reduced by matching flow rate rather than pressure gradient. For physiological flow simulation in the aorta, an increase in mean WSS but a reduction in peak WSS were observed for the power law model compared to a Newtonian fluid model for a matched flow rate waveform.

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Asymptotics of slow flow of very small exponent power-law shear-thinning fluids in a wedge

European Journal of Applied Mathematics ◽

10.1017/s0956792500002060 ◽

1995 ◽

Vol 6 (6) ◽

pp. 559-571 ◽

Cited By ~ 7

Author(s):

M. E. Brewster ◽

S. J. Chapman ◽

A. D. Fitt ◽

C. P. Please

Keyword(s):

Boundary Layers ◽

Power Law ◽

Outer Region ◽

Shear Thinning ◽

Similarity Solutions ◽

Explicit Solutions ◽

Slow Flow ◽

Small Power ◽

Shear Thinning Fluids ◽

Shear Thinning Fluid

The incompressible slow viscous flow of a power-law shear-thinning fluid in a wedge-shaped region is considered in the specific instance where the stress is a very small power of the strain rate. Asymptotic analysis is used to determine the structure of similarity solutions. The flow is shown to possess an outer region with boundary layers at the walls. The boundary layers have an intricate structure consisting of a transition layer 0(ɛ) adjoining an inner layer O(ɛlnɛ), which further adjoins an inner-inner layer 0(ɛ) next to the wall. Explicit solutions are found in all the regions and the existence of ‘dead zones’ in the flow is discussed.

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The Hele-Shaw injection problem for an extremely shear-thinning fluid

European Journal of Applied Mathematics ◽

10.1017/s095679251500039x ◽

2015 ◽

Vol 26 (5) ◽

pp. 563-594 ◽

Cited By ~ 1

Author(s):

G. RICHARDSON ◽

J. R. KING

Keyword(s):

Surface Tension ◽

Approximate Solution ◽

Free Boundary ◽

Power Law ◽

Shear Thinning ◽

Small Region ◽

Power Law Fluid ◽

Injection Point ◽

Laplacian Equation ◽

Shear Thinning Fluid

We consider Hele-Shaw flows driven by injection of a highly shear-thinning power-law fluid (of exponentn) in the absence of surface tension. We formulate the problem in terms of the streamfunction ψ, which satisfies thep-Laplacian equation ∇·(|∇ψ|p−2∇ψ) = 0 (withp= (n+1)/n) and use the method of matched asymptotic expansions in the largen(extreme-shear-thinning) limit to find an approximate solution. The results show that significant flow occurs only in (I) segments of a (single) circle centred on the injection point, whose perimeters comprise the portion of free boundary closest to the injection point and (II) an exponentially small region around the injection point and (III) a transition region to the rest of the fluid: while the flow in the latter is exponentially slow it can be characterised in detail.

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