A new mathematical model to predict cavern diameters in highly shear thinning, power law liquids using axial flow impellers

1998 ◽  
Vol 53 (3) ◽  
pp. 455-469 ◽  
Author(s):  
A. Amanullah ◽  
S.A. Hjorth ◽  
A.W. Nienow
Keyword(s):  
Mathematical Model ◽  
Power Law ◽  
Axial Flow ◽  
Shear Thinning

A novel formulation for blood trauma prediction by a modified power-law mathematical model

2005 ◽  
Vol 4 (4) ◽  
pp. 249-260 ◽  
Author(s):  
Mauro Grigioni ◽  
Umberto Morbiducci ◽  
Giuseppe D’Avenio ◽  
Giacomo Di Benedetto ◽  
Costantino Del Gaudio
Keyword(s):  
Mathematical Model ◽  
Power Law ◽  
Modified Power Law ◽  
Blood Trauma

Drag on a Sphere in Poiseuille Flow of Shear-Thinning Power-Law Fluids

2011 ◽  
Vol 50 (23) ◽  
pp. 13105-13115 ◽  
Author(s):  
Daoyun Song ◽  
Rakesh K. Gupta ◽  
Rajendra P. Chhabra
Keyword(s):  
Power Law ◽  
Poiseuille Flow ◽  
Shear Thinning ◽  
Power Law Fluids

Heat Transfer Enhancement in Annular Shear-Thinning Flows Over a Sudden Pipe Expansion

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Power Law ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Transfer Enhancement ◽  
Heat Transfer Augmentation ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
The Impact

Heat transfer enhancement in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers, Nu, higher than the fully developed value, in the downstream pipe, is observed only for Pr = 10 and 100. Higher Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane. Heat transfer augmentation for Pr = 10 and 100, is more dramatic for suddenly expanding annular flows, in comparison with suddenly expanding pipe flow. For a given annular diameter ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, for both Newtonian and shear-thinning non-Newtonian flows.

Non-Newtonian slender drops in a nonlinear extensional flow

2019 ◽  
Vol 877 ◽  
pp. 561-581 ◽  
Author(s):  
Moshe Favelukis
Keyword(s):  
Stability Analysis ◽  
Power Law ◽  
Analytical Solutions ◽  
Viscosity Ratio ◽  
Extensional Flow ◽  
Shear Thinning ◽  
Newtonian Liquid ◽  
Creeping Flow ◽  
Stationary States ◽  
Power Law Index

In this theoretical report we explore the deformation and stability of a power-law non-Newtonian slender drop embedded in a Newtonian liquid undergoing a nonlinear extensional creeping flow. The dimensionless parameters describing this problem are: the capillary number $(Ca\gg 1)$, the viscosity ratio $(\unicode[STIX]{x1D706}\ll 1)$, the power-law index $(n)$ and the nonlinear intensity of the flow $(|E|\ll 1)$. Asymptotic analytical solutions were obtained near the centre and close to the end of the drop suggesting that only Newtonian and shear thinning drops $(n\leqslant 1)$ with pointed ends are possible. We described the shape of the drop as a series expansion about the centre of the drop, and performed a stability analysis in order to distinguish between stable and unstable stationary states and to establish the breakup point. Our findings suggest: (i) shear thinning drops are less elongated than Newtonian drops, (ii) as non-Newtonian effects increase or as $n$ decreases, breakup becomes more difficult, and (iii) as the flow becomes more nonlinear, breakup is facilitated.

Fully Developed Flow of Power-Law Fluid Through a Cylindrical Microfluidic Pipe: Pressure Drop and Electroviscous Effects

2008 ◽  
Author(s):  
Ram P. Bharti ◽  
Dalton J. E. Harvie ◽  
Malcolm R. Davidson
Keyword(s):  
Pressure Drop ◽  
Field Strength ◽  
Charge Density ◽  
Power Law ◽  
Maximum Velocity ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Electrical Field ◽  
Electrical Field Strength ◽  
Fluid Behaviour

Pressure drop and electroviscous effects in the axisymmetric, steady, fully developed, pressure-driven flow of incompressible power-law fluids through a cylindrical microchannel at low Reynolds number (Re = 0.01) have been investigated. The Poisson-Boltzmann equation (describing the electrical potential) and the momentum equations in conjunction with electrical force and power-law fluid rheology have been solved numerically using the finite difference method. The pipe wall is considered to have uniform surface charge density (S = 4) and the liquid is assumed to be a symmetric electrolyte solution. In particular, the influence of the dimensionless inverse Debye length (K = 2, 20) and power-law flow behaviour index (n = 0.2, 1, 1.8) on the EDL potential, ion concentrations and charge density profiles, induced electrical field strength, velocity and viscosity profiles and pressure drop have been studied. As expected, the local EDL potential, local charge density and electrical field strength increases with decreasing K and/or increasing S. The velocity profiles cross-over away from the charged pipe wall with increasing K and/or decreasing n. The maximum velocity at the center of the pipe increases with increasing n and/or increasing S and/or decreasing K. The shear-thinning fluid viscosity is strongly dependent on K and S, whereas the shear-thickening viscosity is very weakly dependent on K and S. For fixed K, as the fluid behaviour changes from Newtonian (n = 1) to shear-thinning (n < 1), the induced electrical field strength increases and maximum velocity reduces. On the other hand, the change in fluid behaviour from Newtonian (n = 1) to shear-thickening (n > 1) decreases the electrical field strength and increases the maximum velocity. The non-Newtonian effects on maximum velocity and pressure drop are stronger in shear-thinning fluids at small K and large S, the shear-thickening fluids show opposite influence. Electroviscous effects enhance with decreasing K and/or increasing S. The electroviscous effects show complex dependence on the non-Newtonian tendency of the fluids. The shear-thickening (n > 1) fluids and/or smaller K show stronger influence on the pressure drop and thus, enhance the electroviscous effects than that in shear-thinning (n < 1) fluids and/or large K where EDL is very thin.

Rheology of Polyaniline-Dinonylnaphthalene Disulfonic Acid (DNNDSA) Montmorillonite Clay Nanocomposites in the Sol State: Shear Thinning versus Pseudo-Solid Behavior

2008 ◽  
Vol 8 (4) ◽  
pp. 1842-1851 ◽  
Author(s):  
Ashesh Garai ◽  
Arun K. Nandi
Keyword(s):  
Shear Rate ◽  
Storage Modulus ◽  
Power Law ◽  
Network Formation ◽  
Loss Modulus ◽  
Shear Thinning ◽  
Disulfonic Acid ◽  
Clay Nanocomposites ◽  
Crossover Point ◽  
Clay Concentration

The melt rheology of polyaniline (PANI)-dinonylnaphthalenedisulfonic acid (DNNDSA) gel nanocomposites (GNCs) with organically modified (modified with cetyl trimethylammonium bromide)-montmorillonite (om-MMT) clay has been studied for three different clay concentrations at the temperature range 120–160 °C. Field emission scanning electron microscopy (FE-SEM), wide angle X-ray scattering (WAXS), differential scanning calorimetry (DSC) and dc-conductivity data (∼10–3 S/cm) indicate that the PANI-DNNDSA melt is in sol state and it is not de-doped at that condition. The WAXS data indicate that in GNC-1 sol clay tactoids are in exfoliated state but in the other sols they are in intercalated state. The zero shear viscosity (η0), storage modulus (G′) and loss modulus (G″) increase than that of pure gel in the GNCs. The pure sol and the sols of gel nanocomposites (GNCs) exhibit Newtonian behavior for low shear rate (<6 × 10–3 s–1) and power law variation for the higher shear rate region. The characteristic time (λ) increase with increasing clay concentration and the power law index (n) decreases with increase in clay concentration in the GNCs indicating increased shear thinning for the clay addition. Thus the sols of om-clay nanocomposites of PANI-DNNDSA system are easily processible. The storage modulus (G′) of GNC sols are higher than that of pure PANI-DNNDSA sol, GNC1 sol shows a maximum of 733% increase in storage modulus and the percent increase decreases with increase in temperature. Exfoliated nature of clay tactoids has been attributed for the above dramatic increase of G′. The PANI-DNNDSA sol nanocomposites behave as a pseudo-solid at higher frequency where G′ and loss modulus (G′′) show a crossover point in the frequency sweep experiment at a fixed temperature. The crossover frequency decreases with increase in clay concentration and it increases with increase in temperature for GNC sols. The pseudo-solid behavior has been explained from jamming or network formation of clay tactoids under shear. A probable explanation of the two apparently contradictory phenomena of shear thinning versus pseudo-solid behavior of the nanocomposite sols is discussed.

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.

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