INTERIOR ESTIMATES FOR POWER-LAW SHEAR-THICKENING FLUIDS

2021 ◽  
Vol 26 (1) ◽  
pp. 49-66
Author(s):  
Gilberlandio J. Dias
Keyword(s):  
Power Law ◽  
Shear Thickening ◽  
Interior Estimates ◽  
Shear Thickening Fluids

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.

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.

Two Dimensional Unsteady Laminar Flow of Power Law Fluids Past a Square Cylinder: A Numerical Study

2008 ◽  
Author(s):  
Akhilesh K. Sahu ◽  
Raj P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
Edge Separation

The two-dimensional and unsteady flow of power-law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time for Newtonian fluids. However, no such information is available for power law fluids. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The macroscopic quantities such as drag coefficients, Strouhal number, lift coefficient as well as the detailed kinematic variables like stream function, vorticity and so on, have been calculated as functions of the pertinent dimension-less groups. In particular, the effects of Reynolds number and of the power-law index have been investigated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening behaviour delays the leading edge separation. So, the drag coefficient in the above-mentioned range of Reynolds number, Re, in shear-thinning fluids (n &lt; 1) initially decreases but at high values of the Reynolds number, it increases. As expected, on the other hand, in case of shear-thickening fluids (n &gt; 1) drag coefficient reduces with Reynolds number, Re. Furthermore, the present results also suggest the transition from steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thickening fluids than that in Newtonian fluids. Also, the spectra of lift signal for shear-thickening fluids show that the flow is truly periodic in nature with a single dominant frequency in the above range of Reynolds number. In shear-thinning fluids at higher Re, quasi-periodicity sets in with additional frequencies, which indicate the transition from the 2-D to 3-D flows.

Flow of power-law fluids in fixed beds of cylinders or spheres

2012 ◽  
Vol 713 ◽  
pp. 491-527 ◽  
Author(s):  
John P. Singh ◽  
Sourav Padhy ◽  
Eric S. G. Shaqfeh ◽  
Donald L. Koch
Keyword(s):  
Drag Force ◽  
Newtonian Fluid ◽  
Power Law ◽  
Test Particle ◽  
Body Force ◽  
Equations Of Motion ◽  
Fixed Bed ◽  
Shear Thickening ◽  
Length Scale ◽  
Shear Thickening Fluids

AbstractAn ensemble average of the equations of motion for a Newtonian fluid over particle configurations in a dilute fixed bed of spheres or cylinders yields Brinkman’s equations of motion, where the disturbance velocity produced by a test particle is influenced by the Newtonian fluid stress and a body force representing the linear drag on the surrounding particles. We consider a similar analysis for a power-law fluid where the stress $\boldsymbol{\tau} $ is related to the rate of strain $ \mathbisf{e} $ by $\boldsymbol{\tau} = 2m \mathop{ \vert \mathbisf{e} \vert }\nolimits ^{n\ensuremath{-} 1} \mathbisf{e} $, where $m$ and $n$ are constants. In this case, the ensemble-averaged momentum equation includes a body force resulting from the nonlinear drag exerted on the surrounding particles, a power-law stress associated with the disturbance velocity of the test particle, and a stress term that is linear with respect to the test particle’s disturbance velocity. The latter term results from the interaction of the test particle’s velocity disturbance with the random straining motions produced by the neighbouring particles and is important only in shear-thickening fluids where the velocity disturbances of the particles are long-ranged. The solutions to these equations using scaling analyses for dilute beds and numerical simulations using the finite element method are presented. We show that the drag force acting on a particle in a fixed bed can be written as a function of a particle-concentration-dependent length scale at which the fluid velocity disturbance produced by a particle is modified by hydrodynamic interactions with its neighbours. This is also true of the drag on a particle in a periodic array where the length scale is the lattice spacing. The effects of particle interactions on the drag in dilute arrays (periodic or random) of cylinders and spheres in shear-thickening fluids is dramatic, where it arrests the algebraic growth of the disturbance velocity with radial position when $n\geq 1$ for cylinders and $n\geq 2$ for spheres. For concentrated random arrays of particles, we adopt an effective medium theory in which the drag force per unit volume in the medium surrounding a test particle is assumed to be proportional to the local volume fraction of the neighbouring particles, which is derived from the hard-particle packing. The predictions of the averaged equations of motion are validated by comparison with simulations of randomly distributed hydrodynamically interacting cylinders.

Bifurcation Analysis for Peristaltic Transport of a Power-Law Fluid

2019 ◽  
Vol 74 (3) ◽  
pp. 213-225 ◽  
Author(s):  
Nasir Ali ◽  
Kaleem Ullah
Keyword(s):  
Power Law ◽  
Global Bifurcation ◽  
Shear Thickening ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Autonomous Differential Equations ◽  
Fluid Behaviour ◽  
Behaviour Index

AbstractIn this work, the streamline topologies and their bifurcations for peristaltic transport of shear-thinning and shear-thickening fluids characterised by power-law model are analysed. The flow is assumed in a two-dimensional symmetric channel. The analytical solution is obtained in a wave frame of reference under low Reynolds number and long wavelength approximations. To study the streamline topologies, a system of non-linear autonomous differential equations is formed and the method of dynamical system is employed to investigate the bifurcations and their changes. Three different types of flow situations occur: backward flow, trapping and augmented flow. The conversions of backward flow to trapping and then trapping to augmented flow correspond to bifurcations. The stability and nature of bifurcations and their topological changes are explained graphically. For this purpose, a global bifurcation diagram is constructed. The backward flow and trapping regions are significantly affected by fluid behaviour index. In fact, the trapping region expands and the backward region shrinks by increasing the fluid behaviour index. Theoretical results are verified by comparing them with the experimental data, which is available in the literature.

Spread of a non-Newtonian liquid jet over a horizontal plate

2008 ◽  
Vol 613 ◽  
pp. 411-443 ◽  
Author(s):  
JIANGANG ZHAO ◽  
ROGER E. KHAYAT
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Hydraulic Jump ◽  
Shear Thickening ◽  
Flow Region ◽  
Shear Thinning ◽  
Similarity Solutions ◽  
Viscous Boundary Layer ◽  
Power Law Fluids ◽  
Shear Thickening Fluids

The flow of an impinging non-Newtonian jet onto a solid flat plate is examined theoretically in this study. Similarity solutions are sought for both shear-thinning and shear-thickening fluids of the power-law type. The jet is assumed to spread out in a thin layer bounded by a hydraulic jump. In addition to the stagnation-flow region, the flow domain is divided into three main regions: a developing boundary layer, fully viscous boundary layer and hydraulic jump. The anomalous behaviour of power-law fluids at small shear rate is remedied by seeking a two-layer solution in each domain. Such anomalies include the singularity of viscosity for shear-thinning fluids, and the vanishing of viscosity as well the overshoot in velocity for shear-thickening fluids. Although the rate of shear-thinning appears to affect significantly the film profile and velocity, only the overall viscosity influences the position of the hydraulic jump.

Research and Applications of Shear Thickening Fluids

2011 ◽  
Vol 4 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Jie Ding ◽  
Weihua Li ◽  
Shirley Z. Shen
Keyword(s):  
Shear Thickening ◽  
Shear Thickening Fluids

Dynamic compressive response of 3D GFRP composites with shear thickening fluid (STF) matrix as cushioning materials

2021 ◽  
pp. 002199832098424
Author(s):  
Mohsen Jeddi ◽  
Mojtaba Yazdani
Keyword(s):  
Shear Thickening ◽  
Low Velocity Impact ◽  
Gfrp Composites ◽  
High Concentration ◽  
Low Velocity ◽  
Shear Thickening Fluid ◽  
Compressive Response ◽  
Reinforced Polymer ◽  
Glass Fiber Reinforced ◽  
Shear Thickening Fluids

Whereas most previous studies have focused on improving the penetration resistance of Shear Thickening Fluids (STFs) treated composites, in this study, the dynamic compressive response of single and multi-ply 3 D E-Glass Fiber Reinforced Polymer (GFRP) composites with the STF matrix was investigated by using a drop-weight low-velocity impact test. The experimental results revealed the STF improved the compressive and cushioning performance of the composites such that with increasing its concentration, further improvement was observed. The five-ply composite containing the STF of 30 wt% silica nanoparticles and 1 wt% carbon nanotubes (CNTs) reduced the applied peak force by 56% and 26% compared to a steel plate and five-ply neat samples, respectively. A series of repeated impacts was performed, and it was found that the performance of high-concentration composites is further decreased under this type of loading.

scholarly journals Pre- and post-transition behavior of shear-thickening fluids in oscillating shear

2007 ◽  
Vol 46 (8) ◽  
pp. 1099-1108 ◽  
Author(s):  
Christian Fischer ◽  
Christopher J. G. Plummer ◽  
Véronique Michaud ◽  
Pierre-Etienne Bourban ◽  
Jan-Anders E. Månson
Keyword(s):  
Shear Thickening ◽  
Transition Behavior ◽  
Shear Thickening Fluids
Sign in / Sign up

Export Citation Format

Share Document