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.

A slender drop in a nonlinear extensional flow

2016 ◽  
Vol 808 ◽  
pp. 337-361 ◽  
Author(s):  
Moshe Favelukis
Keyword(s):  
Stability Analysis ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Extensional Flow ◽  
Local Maximum ◽  
Creeping Flow ◽  
Time Dependent ◽  
Dimensionless Parameters ◽  
Breakup Mechanism ◽  
The One

The deformation of a slender drop in a nonlinear axisymmetric extensional and creeping flow has been theoretically studied. This problem, which was first suggested by Sherwood (J. Fluid Mech., vol. 144, 1984, pp. 281–295), is being revisited, and new results are presented. The problem is governed by three dimensionless parameters: the capillary number ($\mathit{Ca}\gg 1$), the viscosity ratio ($\unicode[STIX]{x1D706}\ll 1$), and the nonlinear intensity of the flow ($E\ll 1$). Contrary to linear extensional flow ($E=0$), where the local radius of the drop decreases monotonically (in the positive $z$ direction), in a nonlinear extensional flow ($E\neq 0$), two possible steady shapes exist: steady shapes (stable or unstable) with the local radius decreasing monotonically, and steady shapes (unstable) where the local radius of the drop has a local maximum, besides the one at the centre of the drop. Similar to linear extensional flow, the addition of nonlinear extensional effects does not change the end shape of the steady drop, which has pointed ends. A stability analysis has been done to distinguish between stable and unstable steady shapes and to determine the breakup point. Time-dependent studies reveal three types of breakup mechanism: a centre pinching mode, indefinite elongation, and a mechanism that remind us of tip-streaming, where a cusp is developed at the end of the drop.

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.

Shear thinning of the bulk metallic glass forming alloy Zr41.2 Ti13.8 Cu12.5 Ni10.0 Be22.5 close to the liquidus temperature.

2003 ◽  
Vol 806 ◽  
Author(s):  
Tyler Shaw ◽  
Christopher Way ◽  
Ralf Busch
Keyword(s):  
Metallic Glass ◽  
Bulk Metallic Glass ◽  
Power Law ◽  
Liquidus Temperature ◽  
Flow Behavior ◽  
Shear Thinning ◽  
Shear Rates ◽  
Glass Forming ◽  
Power Law Index ◽  
Type Response

ABSTRACTThe viscous properties of the multi component Zr41.2 Ti13.8 Cu12.5 Ni10.0 Be22.5 bulk metallic glass forming alloy was studied above the liquidus temperature. A shear thinning behavior for the molten alloy has been discovered. The shear thinning behavior can be characterized as a power law fluid with a power-law index of -0.5. Additionally, at low shear rates and temperatures near the liquidus temperature a visco-elastic type response in the flow behavior is observed.

Flow Inertia and Heat Transfer in Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Shear Thinning ◽  
Heat Transfer Augmentation ◽  
Flow And Heat Transfer ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
Annular Pipe ◽  
Flow Inertia ◽  
The Impact

The impact of flow inertia on flow and heat transfer in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. The equations governing conservation of mass, momentum, and energy, along with the power-law constitutive model are numerically solved using a finite-difference numerical scheme. The influence 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}; n = {1, 0.6}; and Pr = {1, 10, 100}. Heat transfer augmentation, downstream the plane of expansion, is only observed for Pr = 10 and 100. The extent and intensity of recirculation in the corner region, increases with inflow inertia. Higher Reynolds and Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane.

Computational Modeling of Enhanced Laminar Flow Heat Transfer in Viscoplastic Fluids in Corrugated-Plate Channels

2002 ◽  
Author(s):  
Hossam M. Metwally ◽  
Raj M. Manglik
Keyword(s):  
Heat Transfer ◽  
Yield Stress ◽  
Power Law ◽  
Flow Behavior ◽  
Shear Thinning ◽  
Bingham Plastic ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Colburn Factor ◽  
Power Law Index

The enhanced heat transfer in laminar viscoplastic, shear thinning, Herschel-Bulkley fluid flows in sinusoidal corrugated-plate channels is investigated. With uniform-temperature plate walls, periodically developed flows are considered for a wide range of flow rates (10 ≤ Reg ≤ 700) and pseudoplastic flow behavior indices (n = 0.54, 0.8, and 1.0; the latter representing a Bingham plastic). The effects of fluid yield stress are simulated for the case where τy = 1.59 N/m2, representing a 0.5% xantham gum aqueous solution. Typical velocity and temperature distributions, along with extended results for isothermal friction factor ƒ and Colburn factor j are presented. The effect of the yield stress is found to be most dominant at low Reg regardless of the power law index n, and the recirculation or swirl in the wall trough regions is weaker than in the cases of Newtonian and power-law liquids. At higher Reg, the performance of the Herschel-Bulkley fluid asymptotically approaches that of the non-yield-stress power-law fluid. At low Reg, the yield stress increases ƒ by an order of magnitude and j is enhanced because of the higher wall gradients imposed by the plug-like flow field. The relative heat transfer enhancement, represented by the ratio (j/ƒ), and the role of the fluid yield stress and shear-thinning (or pseudoplastic) behaviors are also discussed.

On the Flow of a Non-Newtonian Liquid Induced by Intestine-Like Contractions

1989 ◽  
Vol 111 (1) ◽  
pp. 1-8 ◽  
Author(s):  
N. Phan-Thien ◽  
H. T. Low
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Power Law ◽  
Flow Rate ◽  
Finite Amplitude ◽  
Newtonian Liquid ◽  
Peristaltic Motion ◽  
Positive Displacement ◽  
Displacement Pump ◽  
Power Law Index

This paper considers the flow of an inelastic liquid which is generated by contractions like those of the intestine. Unlike regular peristaltic motion, these contractions occur locally over a finite length and have a finite amplitude. We adopt a contraction model due to Macagno and Christensen and repeat their analysis for an inelastic liquid. Our analysis, which is based on a Boundary Element Method, indicates that the net flow rate depends very weakly on the power-law index. The pumping action is therefore similar to that of a positive displacement pump.

scholarly journals Effect of Wind Stress on the Dynamics and Stability of Nonisothermal Power-Law Film down an Inclined Plane

2012 ◽  
Vol 2012 ◽  
pp. 1-31 ◽  
Author(s):  
B. Uma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Multiple Scales ◽  
Critical Value ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Nonlinear Stability Analysis ◽  
Inclined Plane ◽  
Condensate Film ◽  
Power Law Index

Dynamics and stability of a nonisothermal power-law liquid film down an inclined plane is considered in the presence of interfacial shear. Linear stability characteristics of the power-law liquid film using normal mode approach reveal that isothermal and evaporating films are unstable for any value of power-law index while there exists a critical value of power-law index for the case of condensate film above which condensate film ow system is always stable. This critical value of power-law index increases with the increase in shear stress at the interface. Weakly nonlinear stability analysis using method of multiple scales divulges the existence of zones due to supercritical stability and subcritical instability. The nonlinear evolution equation is solved numerically in a periodic domain. The results reveal that (1) for an isothermal dilatant (pseudoplastic) liquids, the maximum wave amplitude is always smaller (larger) than that for a Newtonian liquid and the amplitude of permanent wave increases with the increase in interfacial shear; (2) condensation of pseudoplastic film happens for the earlier instant of time when the phase change parameter increases and the effect of interfacial shear makes the film more corrugated; (3) dilatant (pseudoplastic) evaporating liquid film attains rupture faster (slower) than that of Newtonian liquid film, and the interfacial shear does not influence the time at which rupture occurs.

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.

scholarly journals Hydrodynamic drag reduction of shear-thinning liquids in superhydrophobic textured microchannels

2021 ◽  
Vol 25 (9) ◽  
Author(s):  
Anvesh Gaddam ◽  
Himani Sharma ◽  
Ratan Ahuja ◽  
Stefan Dimov ◽  
Suhas Joshi ◽  
...  
Keyword(s):  
Friction Factor ◽  
Power Law ◽  
Shear Thinning ◽  
Flow Behaviour ◽  
Friction Reduction ◽  
Hydrodynamic Drag ◽  
Micro Channels ◽  
Factor Ratio ◽  
Newtonian Liquids ◽  
Power Law Index

AbstractSuper-hydrophobic textured surfaces reduce hydrodynamic drag in pressure-driven laminar flows in micro-channels. However, despite the wide usage of non-Newtonian liquids in microfluidic devices, the flow behaviour of such liquids was rarely examined so far in the context of friction reduction in textured super-hydrophobic micro-channels. Thus, we have investigated the influence of topologically different rough surfaces on friction reduction of shear-thinning liquids in micro-channels. First, the friction factor ratio (a ratio of friction factor on a textured surface to a plain surface) on generic surface textures, such as posts, holes, longitudinal and transverse ribs, was estimated numerically over a range of Carreau number as a function of microchannel constriction ratio, gas fraction and power-law exponent. Resembling the flow behaviour of Newtonian liquids, the longitudinal ribs and posts have exhibited significantly less flow friction than the transverse ribs and holes while the friction factor ratios of all textures has exhibited non-monotonic variation with the Carreau number. While the minima of the friction factor ratio were noticed at a constant Carreau number irrespective of the microchannel constriction ratio, the minima have shifted to a higher Carreau number with an increase in the power-law index and gas fraction. Experiments were also conducted with aqueous Xanthan Gum liquids in micro-channels. The flow enhancement (the flow rate with super-hydrophobic textures with respect to a smooth surface) exhibited a non-monotonic behaviour and attenuated with an increase in power-law index tantamount to simulations. The results will serve as a guide to design frictionless micro-channels when employing non-Newtonian liquids.

Power-Law Fluid Flow Passing Two Square Cylinders in Tandem Arrangement

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Izadpanah Ehsan ◽  
Sefid Mohammad ◽  
Nazari Mohammad Reza ◽  
Jafarizade Ali ◽  
Ebrahim Sharifi Tashnizi
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Power Law Fluid ◽  
Tandem Arrangement ◽  
Square Cylinders ◽  
Shear Thickening Fluids ◽  
Power Law Index

Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

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