Shear-thinning Power-law Fluid Research Articles

Flow rheology of light foams generated from aqueous solutions of polyvinyl alcohol

Recent studies have shown that foam-assisted application of additives into a wet web has advantages over the conventional way of adding the chemicals into the pulp suspension before forming, e.g., increased mechanical retention as well as high dosage giving increased wet strength without impairing the sheet uniformity. To engineer processes utilizing this new technology, the complex flow behavior of applied foams must be quantified. At the minimum, the foam viscosity and the slip velocity at the solid surfaces need to be known to build practical models that can be used in analyzing and upscaling unit processes of the foam-assisted application. In this study, the rheological behavior was quantified for foams having polyvinyl alcohol (PVOH), a widely used strength additive chemical, as the surfactant. The foam density was varied between 100 g/L and 300 g/L, and the concentration of the PVOH solution was varied between 0.5% and 6.0% (w/w). The foams were generated with a commercial foam generator, and the rheological properties of the foams were measured by using a horizontal pipe bank. At the outlet from the generator, the volumetric flow rate, the absolute pressure, and the bubble size distribution of the foam were measured. In the measurement pipe section, the viscous pressure gradient and the slip velocity were measured, after which the foam was discharged to ambient air pressure. The viscosity and the dynamic surface tension of the PVOH solutions were quantified with commercial laboratory devices. In the viscosity analysis, the apparent shear rate was calculated from the volumetric flow rate, and the resulting apparent viscosity was translated to real material viscosity data by applying the Weissenberg-Rabinowitsch correction. The results indicated that PVOH foams can be described with high accuracy as shear-thinning power-law fluids where the detailed behavior depends on the foam density and the PVOH concentration. Slip flow, as usual, increased with increasing wall shear stress, but it was also dependent on the PVOH concentration, the air content, and the bubble size. For both the foam viscosity and the slip flow, a correlation was found that described the quantitative behavior of all the studied foams with good accuracy.

Investigation on drag reduction of aqueous foam for transporting thermally produced high viscosity oil

An innovative idea is proposed for facilitating the transportation of thermally produced high-viscosity oil by injecting temperature tolerant aqueous foam. To this aim, experimental investigations of the flow characteristics of heated highly viscous oil flowing through a 25 mm i.d. horizontal rough-wall tempered borosilicate glass pipe were conducted. Measurements were made for the superficial oil and foam velocities in the range of 0.05–0.40 m/s and 0.04–0.39 m/s, respectively. Eccentric core annular flow configurations detected by a high-speed camera were found to be particularly dominant throughout the entire tested range. A two-fluid, three-zone mechanistic model for horizontal foam-oil flows was implemented for the case of shear thinning power-law fluid in the annulus, which is in accordance with the foam rheological behavior at the tested elevated temperature. Good agreement was achieved between the predicted and measured data over a wide range of operational conditions. When a complete foam annulus encapsulating the oil core is formed, a critical value of input foam volume fraction can be determined for the maximum drag reduction ratio. An optimal oil core-to-pipe radius ratio range was determined for the highest oil-transport operational coefficient. The drag reduction performance of the tested hot oil-foam system is better than that obtained with the oil-foam system employed at room temperature.

Characterization of silver nanoparticle inks toward stable roll-to-roll gravure printing

The rheological properties of silver inks are analyzed, and the printing results are presented based on the inks and roll-to-roll (R2R) printing speed. The shear viscosity, shear modulus, and extensional viscosity of the inks are measured using rotational and extensional rheometers. The inks exhibit the shear thinning power law fluids because the concentration of dispersed nanoparticles in the solvent is sufficiently low, which minimizes elasticity. After the inks are printed on a flexible substrate through gravure printing, the optical images, surface profiles, and electric resistances of the printed pattern are obtained. The width and height of the printed pattern change depending on the ink viscosity, whereas the printing speed does not significantly affect the widening. The drag-out tail is reduced at high ink viscosities and fast printing speeds, thereby improving the printed pattern quality in the R2R process. Based on the results obtained, we suggest ink and printing conditions that result in high printing quality for complicated printings, such as overlay printing registration accuracy, which imposes pattern widening and drag-out tails in printed patterns.

Stratified Shear-Thinning Fluid Flow Past Tandem Cylinders in the Presence of Mixed Convection Heat Transfer With a Channel-Confined Configuration

Abstract The article examines the consequence of thermal buoyancy-driven cross-flow and heat transfer for shear-thinning power-law fluids on the tandem orientation of two cylinders. Finite volume methodology is used to investigate the effect of the gap ratio (2.5 ≤ S/D ≤ 5.5), power-law index (0.2 ≤ n ≤ 1), and Richardson number (0 ≤ Ri ≤ 1) on flow and thermal output parameters at Reynolds number Re = 100 and Prandtl number Pr = 50 in a confined channel. An unprecedented jump has been witnessed in the flow/thermal parameters at the critical gap ratio (critical spacing). At forced convection (Ri = 0), this critical spacing keeps on increasing with shear-thinning character, from S/D = 3.9 (at n = 1) to 4.9 (at n = 0.2). On the contrary, an increase in shear-thinning characteristic leads to a decrease in critical spacing from S/D = 3.9 (at n = 1) to 2.8 (at n = 0.4) for Ri = 1 (mixed convection). The heat transfer rate increases with shear-thinning behavior, with a maximum heat transfer, noted at n = 0.2. A higher unprecedented increment for flow/thermal parameters is seen at critical spacing for the downstream cylinder than the upstream cylinder. At the highest gap ratio, the output parameters for the upstream cylinder approximate that of an isolated cylinder. The time-variant fluctuations in lift coefficients for a shear-thinning flow in a tandem arrangement provide a new understanding of coshedding and extended body flow regimes.

CFD analysis of flow field and power consumption of in-line high shear mixers with different stator structures

As a new type of process enhancement equipment, the high shear mixer (HSMs) has very complicated structure, high strain rate, and very complicated internal flow, makes it more difficult to understand the flow and mixing characteristics. Although the relationships between the power consumption and operating parameters of HSMs have been obtained, there are too many factors to be considered, and there is still a lack in how the model parameters depend on the design parameter size, such as the geometric structure sizes of the rotor and stator. In this study, Computational fluid dynamics (CFD) is used to study the effect of different number of stator slots and stator tooth thicknesses on the flow field and power characteristics of in-line HSMs under the same stator opening area. Through the CFD simulation of Newtonian fluid and shear thinning power-law fluid, the functional relationship between power consumption constant KP , strain rate constant Ks , stator tooth thickness and the number of stator slots is studied. The results show that with the decrease of the number of stator slots ns and the thickness of stator teeth Ts, the jet intensity from the outermost stator tooth slots increases, and the circulating flow behind the jet increases, so the influence of the jet on the tangential movement is more obvious. With the increase of stator tooth thickness, KP decreases and Ks increases. With the increase of the number of stator slots, KP and Ks increase. Based on the correlation between KP and Ks and stator structure parameters, a new correlation with tip-to-base clearance, shear gap width, stator thickness and the number of stator slots for the power number is established. A new correlation can be provided as a unified correlation for viscous fluid in the laminar regime.

Micromechanics-based assessment of the effective viscosity of suspensions of generalized-Newtonian fluids embedding noncolloidal angular/spheroidal pores and particles

The viscosity of suspensions depends on the properties of the fluid, i.e., the matrix material as well as on the volume fraction and shape of embedded inclusions. Regarding this dependence, a micromechanics-based homogenization approach is presented, giving access to the resulting effective viscous properties, starting from well established homogenization schemes originally proposed for the linear-elastic material response. In order to incorporate nonlinear matrix behavior, i.e., non-Newtonian fluids, the secant method of nonlinear homogenization is employed. The effect of nonsphericity of inclusions is considered by substituting the Eshelby tensor by a replacement tensor (replacement Eshelby tensor) determined by linear-elastic finite element simulations in Traxl and Lackner [Mech. Mater. 126, 126–139 (2018)]. In total, suspensions consisting of four different types of matrix materials, namely, (i) Newtonian, (ii) shear thickening, (iii) shear thinning power-law fluids, and (iv) Bingham or Herschel–Bulkley yield-stress fluids are considered embedding spherical, cubical, and tetrahedral inclusions (rigid particles and pores). The performance of the model is assessed by finite element simulations of respective representative volume elements, showing good agreement between model predictions and numerical results for small and moderate inclusion volume fractions.

An Experimental Setup to Investigate Non-Newtonian Fluid Flow in Variable Aperture Channels

Non-Newtonian fluid flow in porous and fractured media is of considerable technical and environmental interest. Here, the flow of a non-Newtonian fluid in a variable aperture fracture is studied theoretically, experimentally and numerically. We consider a shear-thinning power-law fluid with flow behavior index n. The natural logarithm of the fracture aperture is a two-dimensional, spatially homogeneous and correlated Gaussian random field. An experimental device has been conceived and realized to allow the validation of the theory, and several tests are conducted with Newtonian and shear-thinning fluids and different combinations of parameters to validate the model. For Newtonian fluids, experimental results match quite well the theoretical predictions, mostly with a slight overestimation. For non-Newtonian fluids, the discrepancy between experiments and theory is larger, with an underestimation of the experimental flow rate. We bear in mind the high shear-rates involved in the experiments, covering a large range where simple models seldom are effective in reproducing the process, and possible interferences like slip at the wall. For all test conditions, the comparison between analytical and numerical model is fairly good.

The liquid of aloe extract with shear-thinning Carreau fluids

In the analysis of plant extracts, rheological and heat transfer characteristics are of great significance for one to study regarding applications, such as in the biorheology or pharmaceutical industries. In this paper, we examine the aloe extract experimentally and test its rheological properties. To gain a better understanding of the extract's fluid properties, numerical simulations using FEM are performed on a square channel. Results show that, under a large shear rate, such a fluid behavior closely to the shear-thinning power-law fluid. Combining with numerical simulations, we analyze the influence of the Pr number and the material coefficient λ on the motion of the fluid. We also discuss the effects of other parameter values. • We studied the aloe extract experimentally and tested its rheological properties. • Results show that, under the large shear rate, it is close to the shear-thinning power law fluid. • To gain a better understanding of these fluid properties, a numerical simulation is performed on a square channel. • The influence of Pr number and material coefficient on the motion state of fluid are analyzed.

Pipe rheology of microfibrillated cellulose suspensions

The shear rheology of two mechanically manufactured microfibrillated cellulose (MFC) suspensions was studied in a consistency range of 0.2–2.0% with a pipe rheometer combined with ultrasound velocity profiling. The MFC suspensions behaved at all consistencies as shear thinning power law fluids. Despite their significantly different particle size, the viscous behavior of the suspensions was quantitatively similar. For both suspensions, the dependence of yield stress and the consistency index on consistency was a power law with an exponent of 2.4, similar to some pulp suspensions. The dependence of flow index on consistency was also a power law, with an exponent of − 0.36. The slip flow was very strong for both MFCs and contributed up to 95% to the flow rate. When wall shear stress exceeded two times the yield stress, slip flow caused drag reduction with consistencies higher than 0.8%. When inspecting the slip velocities of both suspensions as a function of wall shear stress scaled with the yield stress, a good data collapse was obtained. The observed similarities in the shear rheology of both the MFC suspensions and the similar behavior of some pulp fiber suspensions suggests that the shear rheology of MFC suspensions might be more universal than has previously been realized.

Pulsatile flow and heat transfer of shear-thinning power-law fluids over a confined semi-circular cylinder

This work is an attempt to simulate the effects of pulsating flow upon the thermal and hydrodynamic behavior of shear-thinning non-Newtonian fluid (approximated as power-law fluid) while it flows past a semi-circular cylinder fixed in a symmetrically confining channel and deduces the optimum oscillating frequencies and amplitude for a particular power-law index (n) and Reynolds number (Re). The semi-circular cylinder studied has a fixed temperature while the wall confinement is insulating. The ranges of control parameters varied are ${\rm Re}=10$ -100 (based on object's diameter), the amplitude of oscillation (A) = 0-0.6, the Strouhal number (St) = 0-2 and the n ranging from 0.2 to 1. The Prandtl number has been kept fixed at $({\rm Pr})=50$ (which corresponds to several fluids of industrial importance like n-butanol, etc.). The isotherms and streamlines give a qualitative insight into the heat and flow transfer behavior as various parameters are varied, while the Nusselt number, overall drag and lift coefficients have been calculated to get a quantitative insight. Further, the augmentation in heat transfer and the decline in drag upon using a pulsating non-Newtonian fluid inlet as opposed to using a steady Newtonian flow have been established. Lastly, the temporal variations and the frequency of vortex shedding have been studied using a fast Fourier transform.

Electroosmotic flow of a non-Newtonian fluid in a microchannel with heterogeneous surface potential

Based on the Nernst–Planck model for ion transport, the electroosmotic flow of a non-Newtonian fluid near a surface potential heterogeneity is studied numerically. The objectives of this study are to highlight the limitations of the linear slip-model and the nonlinear Poisson–Boltzmann model at various flow conditions as well as to develop vortical flow to promote mixing of neutral solutes within the micro-channel. A power-law fluid, both shear-thinning and shear-thickening, for the pseudoplastic behavior of the non-Newtonian fluid or viscoplastic fluid with yield stress is adopted to describe the transport of electrolyte, which is coupled with the ion transport equations governed by the Nernst–Planck equations and the Poisson equation for electric field. The viscoplastic fluid is modeled as either Casson, Bingham or Hershel–Buckley fluid. A pressure-correction based control volume approach has been adopted for the numerical computations of the governing equations. The nonlinear effects are found to be pronounced for a shear thinning liquid, whereas, the electroosmotic flow is dominated by the diffusion mechanisms for the shear thickening liquid. A maximum difference of 39% between the existing analytic solution based on the Debye–Hu¨ckel approximation and the present numerical model is found for a shear thinning power-law fluid. A vortex, which resembles a Lamb vortex, develops over the potential patch when the patch potential is of opposite sign to that of the homogeneous surface potential. Enhanced mixing of a neutral solute is also analyzed in the present analysis. The yield stress reduces the electroosmotic flow however, promotes solute mixing.

Experimental investigation on rheological property of foamy oil in Venezuela

ABSTRACTSome heavy oil reservoirs present foamy oil flow behavior under primary production, and the foamy oil viscosity and rheological property are important factors that influence the efficiency of the process. The variation of the foamy oil viscosity during the depletion process is complicated due to the generation and migration of dispersed gas bubbles within the oil phase, and still remains as a controversial topic. This study aims to investigate this issue by measuring the foamy oil viscosity at different pressure, temperature and flow rate with a capillary viscometer system equipped with a specially designed foamy oil generator to guarantee the generation and stable flow of gas-in-oil dispersions. Meanwhile, the dead oil and live oil viscosities were also measured for comparison. Based on the results from all the tests the following conclusions can be drawn. Below the bubble point pressure, the dispersed gas-bubble volume fraction and foamy oil viscosity increase with pressure decline; the viscosity of foamy oil is higher than that of live oil, and the gap between them widens with pressure decline. Moreover, foamy oil behaves as shear-thinning power-law fluid, and the shear-thinning effect becomes stronger with the decrease of pressure. The foamy oil rheology is also affected by temperature, and the shear-thinning effect becomes milder with the increase of temperature. Based on the experimental data, a formula was established for estimating foamy oil apparent viscosity within porous media, which took flow rate, shear-thinning flow parameters, permeability, porosity and other factors into consideration.

Numerical study on dynamics of single bubble rising in shear-thinning power-law fluid in different gravity environment

The bubble dynamics in non-Newtonian fluids play an important role in industrial processes, such as petroleum process, fermentation, wastewater treatment, boiling heat transfer, etc. To understand the bubble dynamics, the single bubble rising in the shear-thinning non-Newtonian fluid is detailedly studied with the volume of fluid (VOF) method, in which the continuous surface tension model and the Carreau model are used to calculate surface tension and liquid viscosity, respectively. Studies are performed on the influence of the rheological index, the Eötvös and Galilei numbers on bubble shape, wake characteristic, terminal velocity and liquid apparent viscosity. The present results show that, the bubble deformation and the circulating region in the bubble wake increase with increasing the Eötvös and Galilei numbers or with decreasing the rheological index. With the decrease of the rheological index, one confined region with the high viscosity exists in the bubble rear, and this region gradually detaches from the bubble rear. The detachment becomes fast with the increase of the Galilei number. In addition, the bubble terminal velocity depends on the bubble shape, the shear-thinning effect of liquid and the gravity level.

The effect of yield stress on pipe flow turbulence for generalised newtonian fluids

The effect of modifying yield stress on turbulent pipe flow of generalised Newtonian fluids at a friction Reynolds number of 323 is investigated using direct numerical simulations. Simulations are carried out for Bingham and Herschel–Bulkley fluids with the yield stress varying from 0% to 20% of the mean wall shear stress. Results show that the effect of increasing yield stress is mostly similar to shear thinning in power-law fluids. The turbulent viscous stress which arises due to viscosity fluctuations is negative for a yield stress fluid and is higher in magnitude for higher yield stress. An analysis of the turbulent kinetic energy budget showed that the effect of yield stress is mainly significant near the wall for y+≲60 which was also seen for shear-thinning power-law fluids at similar Reτ. Additional shear thinning enhances the yield stress effect. The main difference between shear thinning and yield stress is that the effect of yield stress is maximum outside the viscous sublayer whereas shear thinning has a more significant effect inside the viscous sublayer.

Viscoelastic bending model for continuous fiber-reinforced thermoplastic composites in melt

Bending of single plies or stacks of multiple plies is an essential deformation mechanism during thermoforming of thermoplastic composites. A reliable prediction of the forming process requires an accurate description of the bending behavior. To this end, a characterization method for the bending of composites under thermoforming conditions has been developed. Experiments are performed with an in-house developed bending setup and are analyzed with an analytical model, which is derived in this paper. The model describes the composite with linear elastic fibers and a matrix material that behaves as a shear thinning power law fluid. The model can represent the characteristic behavior that is measured in bending experiments with unidirectional carbon fiber reinforced PA6 composites.

Dip coating in the presence of an opposing Marangoni stress.

Theoretical analysis of the dip coating process of uniformly wetting and selectively wetting substrates with a shear-thinning power-law fluid is presented. The viscosity is modeled by a three-constant Ellis model that allows for Newtonian and power-law fluids at low and high shear, respectively. The effect of an opposing Marangoni stress is studied on the entrained film thickness. Ellis number and Marangoni number are the important parameters in the analysis that control the film thickness. Numerical results show that the film thickness is a monotonically decreasing function of these two parameters. A correlation between the parameters is found for both the surfaces to obtain an apparent "dry" substrate with a microscopically thin film attached to the surfaces.

On the stability of the BEK family of rotating boundary-layer flows for power-law fluids

We consider the convective instability of the BEK family of rotating boundary-layer flows for shear-thinning power-law fluids. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. A linear stability analysis is conducted using a Chebyshev polynomial method in order to investigate the effect of shear-thinning fluids on the convective type I (inviscid crossflow) and type II (viscous streamline curvature) modes of instability. The results reveal that an increase in shear-thinning has a universal stabilising effect across the entire BEK family. Our results are presented in terms of neutral curves, growth rates and an analysis of the energy balance. The newly-derived governing equations for both the steady mean flow and unsteady perturbation equations are given in full.

Laminar flow and forced convective heat transfer of shear-thinning power-law fluids in dimpled and protruded microchannels

The three dimensional laminar flow structures and forced convective heat transfer of shear-thinning power-law fluids in dimpled and protruded microchannel were investigated in this study. The CMC (Carboxyl Methyl Cellulose) aqueous solutions with various concentrations were employed as the working substances. The dimples and protrusions with relative depth δ/D of 0.1, 0.2 and 0.3 were vertically aligned to arrange on the opposite walls. The results reveal that the modes of separation flow near protruded walls, observed at some cases with δ/D=0.2 and 0.3, obviously differ from that near dimpled walls. Both the scale and intensity of all the separation bubbles are strengthened with the increase of flow rate and CMC concentration, except 4000ppm. While, the results at cases of 4000ppm show the variable geometrical structure of protrusion can overcome the negative effect of large CMC concentration on heat and mass transfer. Moreover, the heat and mass transfer of main flow and near-wall flow, as well as the strengthened secondary flow in the passage, are enhanced by the dynamic viscosity distinction of working substance, differing from the Newtonian flow. Furthermore, relative Fanning friction factor f/f0 increases with the increase of depth of dimple/protrusion and flow rate and the decrease of CMC concentration. Relative Nusselt number Nu/Nu0 continuously increases with the increase of flow rate and depth of dimple/protrusion. And then the maximum and minimum thermal performance TP are observed at the case 2000ppm with δ/D=0.3 and CMC100 with δ/D=0.1, respectively. At last, new correlations of f/f0 and Nu/Nu0 are proposed based on the results in this study with a well-established data fitting.

Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids

We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of contact with sidewalls. The solution without sidewalls is a simple generalisation of that found by Robison (JFM, 648, 363), allowing us to obtain the equilibrium grounding line thickness using a simple computer model and to get an analytic approximation. For laterally confined shelves, we obtain an asymptotic theory valid for long shelves and define when this is. Our theory is based on the velocity profile across the channel being a generalised version of Poiseuille flow, which works when lateral shear dominates the force balance. We conducted experiments using a laboratory model for ice. This was an aqueous suspension of $0.5\%$ mass concentration xanthan, yielding $n \approx 3.8$ (similar to ice). Our theories agreed extremely well with our experiments for all relevant parameters (front position, thickness profile, lateral velocity profile, longitudinal velocity gradient and grounding line thickness). This strongly suggests that we have understood the dominant force balance in both types of ice shelf. In the real world, ice tongues are unlikely to rapidly disintegrate but can be shortened until they no longer exist, at which point the sheet becomes unstable and ultimately the grounding line should retreat above sea level. Prior to that point, the flow of ice into it should not be speeded up and the grounding line should also not retreat, assuming that only oceanic conditions change. However, laterally confined ice shelves experience significant buttressing. If removed, this leads to a rapid speedup of the sheet and a much smaller equilibrium grounding line thickness. Something similar may have occurred to the Larsen B ice shelf.

Planar contraction flow of a nematic PPTA solution

Planar contraction flow of a nematic solution of poly-paraphenylene terephthalamide (PPTA) in sulphuric acid (H2SO4) was studied experimentally and compared with the flow of an isotropic model fluid, a poly-ethyleneglycol–poly-ethyleneoxide (PEG-PEO) Boger fluid, in the same geometry. The dimensions and deformation rates in our experiments are relevant for industrial polymer extrusion processes, such as fiber spinning. Under these conditions, viscoelastic lip vortices arise at the re-entrant corners in the nematic flow. The experimental results show that the vortex growth behavior in the nematic PPTA solution closely resembles that in isotropic viscoelastic fluids, such as the PEG-PEO Boger fluid that was used as a reference. The velocity field in the nematic flow is characteristic of Hele-Shaw flow of a shear-thinning power-law fluid, although locally, the influence of the nematic defect structure was observed, especially for the first minutes after starting the flow. Furthermore, the lateral movement of the extruded jet, downstream of the contraction, was shown to be coupled with velocity fluctuations in the upstream flow. Our experiments give detailed insight in the complex flow behavior of a nematic polymer solution under flow conditions that are relevant to practical applications. The results can be applied in the optimization of nematic polymer extrusion processes.