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

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch

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.

Author(s):  
Akhilesh K. Sahu ◽  
Raj P. Chhabra ◽  
V. Eswaran

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 < 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 > 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.


Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.


Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow; however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.


2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Izadpanah Ehsan ◽  
Sefid Mohammad ◽  
Nazari Mohammad Reza ◽  
Jafarizade Ali ◽  
Ebrahim Sharifi Tashnizi

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.


2008 ◽  
Vol 613 ◽  
pp. 411-443 ◽  
Author(s):  
JIANGANG ZHAO ◽  
ROGER E. KHAYAT

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.


2017 ◽  
Vol 826 ◽  
pp. 918-941 ◽  
Author(s):  
A. Bougouin ◽  
L. Lacaze ◽  
T. Bonometti

Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$, the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$, the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$, the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$. Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$. This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.


2011 ◽  
Vol 676 ◽  
pp. 145-171 ◽  
Author(s):  
R. LIU ◽  
Q. S. LIU

In this paper, we study the linear stability of a plane Couette flow of a power-law fluid. The influence of shear-thinning effect on the stability is investigated using the classical eigenvalue analysis, the energy method and the non-modal stability theory. For the plane Couette flow, there is no stratification of viscosity. Thus, for the stability problem the stress tensor is anisotropic aligned with the strain rate perturbation. The results of the eigenvalue analysis and the energy method show that the shear-thinning effect is destabilizing. We focus on the effect of non-Newtonian viscosity on the transition from laminar flow towards turbulence in the framework of non-modal stability theory. Response to external excitations and initial conditions has been studied by examining the ε-pseudospectrum and the transient energy growth. For both Newtonian and non-Newtonian fluids, it is found that there can be a rather large transient growth even though the linear operator of the Couette flow has no unstable eigenvalue. The results show that shear-thinning significantly increases the amplitude of response to external excitations and initial conditions.


Author(s):  
Purushotam Kumar ◽  
Kai Jin ◽  
Surya Pratap Vanka

Abstract In this paper, we have applied a recently-developed numerical technique to study the three-dimensional dynamics of a confined air bubble rising in shear thinning and shear-thickening power-law fluids. The method is a blend of Volume of Fluid and Level Set methods and incorporates a Sharp Surface Force Method (SSF) for surface tension forces by solving a second Pressure Poisson Equation (PPE). The gas-liquid interface is captured by an equation for the liquid volume fraction and advected using the geometry reconstruction method. The interface normal and curvature are computed using level-set and height function methods. The accurate representation of the interface and interfacial forces significantly suppressed the spurious velocities commonly observed with conventional volume of fluid method and the Continuum Surface Force (CSF). The algorithm is implemented in a in-house code called CUFLOW and runs on multiple GPUs platform. We explored the effects of fluid rheology, Bond number, and wall confinement on bubble’s transient shape, rise velocity, rise path, and generated vortex structures. The power-law index is varied from 0.25 to 1.50 covering shear-thinning and shear-thickening regimes. Three Bond numbers (Bo = 2, 10 and 50) and three confinement ratios (Cr = 4, 6 and 8) are considered, and their impacts on bubble’s dynamics are analyzed. For the range of parameters examined here, bubble motion in a shear-thinning fluid is seen to be unsteady with significant shape oscillations. The bubble rises with a secondary motion in the cross-sectional plane along with its primary vertical rise. However, in the Newtonian and shear-thickening fluids, the bubble’s shape is seen to reach a steady-state in a relatively short time and rise with only minor deviations from the vertical path.


2019 ◽  
Vol 74 (3) ◽  
pp. 213-225 ◽  
Author(s):  
Nasir Ali ◽  
Kaleem Ullah

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.


Author(s):  
Jaspinder Kaur ◽  
Roderick Melnik ◽  
Anurag Kumar Tiwari

Abstract In this present work, forced convection heat transfer from a heated blunt-headed cylinder in power-law fluids has been investigated numerically over the range of parameters, namely, Reynolds number (Re): 1–40, Prandtl number (Pr): 10–100 and power-law index (n): 0.3–1.8. The results are expressed in terms of local parameters, like streamline, isotherm, pressure coefficient, and local Nusselt number and global parameters, like wake length, drag coefficient, and average Nusselt number. The length of the recirculation zone on the rear side of the cylinder increases with the increasing value of Re and n. The effect of the total drag coefficient acting on the cylinder is seen to be higher at the low value of Re and its effect significant in shear-thinning fluids (n < 1). On the heat transfer aspect, the rate of heat transfer in fluids is increased by increasing the value of Re and Pr. The effect of heat transfer is enhanced in shear-thinning fluids up to ∼ 40% and it impedes it’s to ∼20% shear-thickening fluids. In the end, the numerical results of the total drag coefficient and average Nusselt number (in terms of J H −factor) have been correlated by simple expression to estimate the intermediate value for the new application.


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