Numerical simulation of viscous fingering of shear‐thinning fluids

The viscous fingering instability of miscible shear‐thinning fluids has been examined using a pseudo‐spectral numerical technique based on the Hartley transform. The instability was studied for a flow in a rectilinear Hele‐Shaw cell, and the shear‐thinning character of the fluids has been modelied using the Carreau equation. New mechanisms of viscous fingering not previously observed in the case of similar Newtonian flow displacements have been identified. These mechanisms, which are reminiscent of the fractal patterns observed in experimental studies, were interpreted in terms of the velocity‐dependent mobility of the flow.     

The effect of shear‐thickening on the stability of slot‐die coating

Slot‐die coating is an economical roll‐to‐roll processing technique with potential to revolutionize the fabrication of nano‐patterned thin films at high throughput. In this study, the impact of shear‐thickening of the coating fluid on the stability of slot‐die coating was investigated. For the coating fluid, a model system fumed silica nanoparticles dispersed in polypropylene glycol was chosen. These dispersions exhibit shear and extensional thickening characterized through steady shear and capillary break‐up measurements. The critical web velocity for the onset of coating defect for different flow rates was measured, while the type of coating defect was visualized using a high speed camera. For the shear thickening particle dispersions, the coating failed through the onset of a ribbing instability. The critical web velocity for the onset of coating defect was found to decrease with increasing particle concentration and increasing fluid viscosity. The minimum wet thickness was studied as a function of capillary number for the particle dispersions and compared with a series of Newtonian fluids with similar viscosities. In all cases, shear‐thickening behavior was found to stabilize coating by reducing the minimum wet coating thickness when compared against a Newtonian fluid with similar viscosity at the same capillary number. Conversely, the shear‐thinning fluids tested destabilized the coating by increasing the minimum wet thickness when compared against a Newtonian at the same capillary number. The impact of shear‐thickening on slot‐die coating was further studied by quantifying the evolution of the ribbing instability with increasing web speed and by conducting tests over a wide range of coating gaps. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4536–4547, 2016     

Characterization of viscoelastic fluid flow in a periodically driven cavity: Flow structure,frequency response,and phase lag

Transport phenomena in periodically driven cavities are important because of their relevance in polymer processing and microfluidics. The transient periodic flow of viscoelastic fluids in a cuboidal cavity, with periodic motion of top plate, was studied in this work. Flow with a characteristic time scale was achieved through the simple harmonic motion of the top plate. The flow in the cavity was characterized by measuring planar velocity fields using particle image velocimetry (PIV). Temporal variation of velocity except at central vertical plane showed predominance of the plate frequency. The temporal point variations, though seemingly similar to those for Newtonian and purely viscous non‐Newtonian fluids, led to rich varieties of spatial flow structures in case of the viscoelastic fluids. The overall flow behavior was characterized using spatial variations, phase trajectories, and streamline patterns. The transition from low Reynolds number steady‐lid driven type flow to complex vortical patterned flow was observed during a cycle of periodic motion of viscoelastic fluids. The effects of elasticity and inertia on the flow fields were analyzed. Computational fluid dynamics simulations with purely viscous shear thinning fluid (power law) and Newtonian fluid showed significant differences with experimental measurements on viscoelastic fluids. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Mixing of a lignin‐based slurry fuel

Lignin‐based slurry fuels are a potential alternative to fossil fuels in kraft pulp mills. Lignogels — mixtures of lignin, fuel oil, water and surfactant — are non‐Newtonian fluids, with shear‐thinning and thixotropic behaviour. Their mixing was investigated in tanks with volumes of 3 and 30 L. An A310 hydrofoil impeller was used in all experiments. Results were compared with measurements in Newtonian fluids, used to characterize the impeller over a broad range of Reynolds numbers (1–500 000). An aqueous CMC solution was also used for characterization of the impeller and estimation of the Metzner‐Otto constant. Results in the transition region were corrected by introduction of two empirical parameters.     

An examination of the shear‐thickening behavior of high molecular weight polymers dissolved in low‐viscosity Newtonian solvents

The anomaly of shear thickening at high shear rates can be observed under certain conditions for high molecular weight polymers dissolved in low‐viscosity Newtonian solvents despite the fact that shear‐thinning behavior is considered the norm for these fluids. The nature of the shear‐thickening region of the flow curve is examined herein through the application of a recent rheological model that has the capability of quantifying not only the rheological properties of the material, but its internal microstructural state as well. The results of this examination provide a self‐consistent explanation of the full flow characterization of this anomalous behavior, including both rheological and optical experimental measurements. The results presented herein suggest that the shear‐thickening behavior is actually caused by the destruction of structures formed during shear at lower shear rates, not by their formation, as previously assumed. The linear birefringence and linear dichroism observed experimentally in correlation with the shear‐thickening behavior are well described by the rheological model and give predictions in line with experimental measurements. Furthermore, quantitative predictions are made for rheological characteristic functions, such as the first and second normal‐stress coefficients, for which experimental measurements for these solutions have not yet been made. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 1714–1735, 2002     

Experimental and numerical analysis of heat transfer including viscous dissipation in a scraped surface heat exchanger

Viscous dissipation plays an important role in the dynamics of fluids with strongly temperature-dependent viscosity because of the coupling between the energy and momentum equations. The heat generated by viscous friction causes a local temperature increase in the high shearing zone with a consequent decrease of the viscosity which may dramatically change the temperature and velocity distribution. These processes are mainly controlled by the Brinkman number, the rotating velocity and the thermal boundary conditions. This work analyses forced convection heat transfer including the viscous dissipation in a scraped surface heat exchanger (SSHE). In this study the increase of the temperature due to the viscous dissipation is analysed both experimentally and numerically for Newtonian and non-Newtonian fluids. Heat transfer simulations including viscous dissipation were carried out by means of the CFD code of the software Fluent, version 6.3, with solving momentum and energy equations. Two thermal boundary conditions were considered: pseudo-adiabatic wall and constant temperature on the stator wall exchange. In the case of Newtonian fluid (pure HV45), for both considered thermal boundary conditions, an important increase of the temperature was obtained. In the case of non-Newtonian shear thinning fluid (2 wt% CMC solution), viscous dissipation is neglected. The developed numerical model agrees well with experimental results. The validated numerical model was then used to study the effect of index and consistency behaviour of shear thinning fluid using power-law rheological behaviour on the viscous dissipation, and correlation using dimensionless analysis expressed with different dimensionless process numbers is proposed for Newtonian and non-Newtonian shear thinning fluid.     

Influence of Shear‐Thinning Rheology on the Mixing Dynamics in Taylor‐Couette Flow

Non‐Newtonian rheology can have a significant effect on mixing efficiency, which remains poorly understood. The effect of shear‐thinning rheology in a Taylor‐Couette reactor is studied using a combination of particle image velocimetry and flow visualization. Shear‐thinning is found to alter the critical Reynolds numbers for the formation of Taylor vortices and the higher‐order wavy instability, and is associated with an increase in the axial wavelength. Strong shear‐thinning and weak viscoelasticity can also lead to sudden transitions in wavelength as the Reynolds number is varied. Finally, it is shown that shear‐thinning causes an increase in the mixing time within vortices, due to a reduction in their circulation, but enhances the axial dispersion of fluid in the reactor.     

The effect of surfactants on deformation of falling non‐Newtonian drops in a Newtonian liquid

Deformation of settling non‐Newtonian ellipsoidal drops in a Newtonian liquid was experimentally observed. Corn oil was used as the Newtonian phase and solutions of polyacrylamide in aqueous glycerine as the non‐Newtonian phase. The shear‐thinning behaviour of the drops fluid was controlled by the amount of polymer dissolved, while the effect of interfacial tension was examined using different concentrations of sodium dodecyl sulphate (SDS). In the range of 1 < E < 2.9, 0.2 < Eo, < 23, and 0 < Ma < 17.2, drop eccentricity increased linearly with a modified Eötvös number taking into account the effect of surfactants. For the range of experimental conditions tested, drop deformation was mainly controlled by viscous and interfacial tension forces, while shear‐thinning and inertia effects were negligible.     

Experimental investigations of non‐Newtonian/Newtonian liquid‐liquid flows in microchannels

The plug flow of a non‐Newtonian and a Newtonian liquid was experimentally investigated in a quartz microchannel (200‐µm internal diameter). Two aqueous glycerol solutions containing xanthan gum at 1000 and 2000 ppm were the non‐Newtonian fluids and 0.0046 Pa s silicone oil was the Newtonian phase forming the dispersed plugs. Two‐color particle image velocimetry was used to obtain the hydrodynamic characteristics and the velocity profiles in both phases under different fluid flow rates. The experimental results revealed that the increase in xanthan gum concentration produced longer, bullet‐shaped plugs, and increased the thickness of the film surrounding them. From the shear rate and viscosity profiles, it was found that the polymer solution was in the shear‐thinning region while the viscosity was higher in the middle of the channel compared to the region close to the wall. Circulation times in the aqueous phase increased with the concentration of xanthan gum. © 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 3599–3609, 2017     

POD analysis of oscillating grid turbulence in water and shear thinning polymer solution

Oscillating grids are frequently used with water and Newtonian fluids to generate controlled turbulence and mixing. Yet, their use with shear thinning fluids still requires experimental characterization. Proper orthogonal decomposition (POD) is applied to PIV measurements of the flow generated by an oscillating grid in water and a shear thinning dilute polymer solution (DPS) of xanthan gum. The aims are to investigate the ability of POD to isolate periodic flow structures, and to use it to describe the effects of the shear thinning property. A dominance of the low order POD modes is evidenced in DPS. The methods applied in blade stirred tanks to identify oscillatory motion fail here. However, a strong mode coupling in the grid swept region is observed, determined by the working fluid and by an underlying chaotic nature of the flow. Possibilities of reconstructing turbulence properties using high order modes are discussed.     

Influence of Rheological Behavior of Purely Viscous Fluids on Analytical Residence Time Distribution in Straight Tubes

In an effort to better understand the homogeneity of heat treatment of foodstuffs in holding tubes, the cumulative residence time distribution function is derived for a Herschel‐Bulkley fluid from fully developed laminar flow in a straight circular tube under isothermal conditions when diffusional effects are negligible. The proposed analytical solution can be reduced to solutions for Newtonian, shear‐thinning, dilatant, Bingham fluids by setting particular rheological parameters, and consequently, it is possible to successfully explain the dependence of residence time distribution on fluid properties for almost all of the rheological models used for time‐independent purely viscous fluids.     

A new expression of the Ks factor for helical ribbon agitators

The purpose of this note is to present a new model that is able to predict an effective shear rate in a vessel equipped with helical ribbon agitators, when mixing shear‐thinning fluids. This model is based on well established results obtained for non‐Newtonian flow in cylindrical ducts.     

A QUASI NEWTONIAN MODEL FOR SIMULATING THE FLOW OF DILUTE POLYMER SOLUTIONS THROUGH A SUDDEN CONTRACTION

The flow of a quasi Newtonian model fluid, which allows shear thinning as well as extension thickening, through a sudden planar 4:1 contraction is studied numerically. Comparing with numerical results for a purely shear thinning fluid differences show up which follow the trend of experimental data.     

A QUASI NEWTONIAN MODEL FOR SIMULATING THE FLOW OF DILUTE POLYMER SOLUTIONS THROUGH A SUDDEN CONTRACTION

The flow of a quasi Newtonian model fluid, which allows shear thinning as well as extension thickening, through a sudden planar 4:1 contraction is studied numerically. Comparing with numerical results for a purely shear thinning fluid differences show up which follow the trend of experimental data.     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Power Requirement when Mixing a Shear‐Thickening Fluid with a Helical Ribbon Impeller Type

The optimal design of close clearance impellers requires the knowledge of the power demand of the mixing equipment. In non‐Newtonian mixing, this can be readily obtained using the Metzner and Otto concept [1]. In this work, this concept and the determination of the K_s value for an atypical helical agitator (PARAVISC system from Ekato firm) have been revised in the case of shear‐thinning fluids and a shear‐thickening fluid. For poor shear‐thinning fluids, it has been shown that for our mixing system the K_s value does not vary strongly with the flow behavior index, and may be regarded as a constant for the mixing purpose design. By contrast, for the shear‐thickening fluid, power consumption measurements indicate that the relationship between the K_s values and the flow behavior index is much more complex due to a partial solidification of the product around the impeller.     

Influence of carrier fluid on the electrokinetic and rheological properties of shear thickening fluids

This paper presents a study on the influence of hydroxyl groups and oxygen atoms together with chain length and branching of carrier fluid on the rheological and electrokinetic properties of shear thickening fluid (STF). An STF is non-Newtonian fluid behaviour in which the increase of viscosity increases with the applied shear rate. Ethylene glycol, triethylene glycol, 1,3-propanediol, glycerin, poly(propylene glycol) of different molecular weight and poly(propylene glycol) triol were used as the carrier fluids (dispersants). Silica powder with an average particle size of 100 nm was used as the solid phase. Zeta potential, particle size distribution (by DLS technique), steady-state and dynamic rheological measurements were conducted. Experimental results indicate that a different amount of hydroxyl groups and oxygen atoms together with chain length and branching of carrier fluids have a significant influence on the intermolecular interactions thereby and on the rheological properties of suspensions. Depending on the composition, it is possible to control rheological properties. The use of a suitable carrier fluid allows the required pattern flow to be obtained, from Newtonian through shear thinning to shear thickening, given specific shear conditions.     

Pressure drop in a split‐and‐recombine caterpillar micromixer in case of newtonian and non‐newtonian fluids

Microreactors are very promising tools for the design of future chemical processes. For example, emulsions of very narrow size distribution are obtained at much lower energy consumption than the one spent with usual processes. Micromixers play thereby an eminent role. The goal of this study is to better understand the hydrodynamic properties of a split‐and‐recombine Caterpillar micromixer (CPMM) specially with regard to handling viscoelastic fluids, a topic hardly addressed so far in the context of micromixers in general, although industrial fluids like detergent, cosmetic, or food emulsions are non‐Newtonian. Friction factor was measured in a CPMM for both Newtonian and non‐Newtonian fluids. For Newtonian fluids, the friction factor in the laminar regime is f/2 = 24/Re. The laminar regime exists up to Reynolds numbers of 15. For shear‐thinning fluids like Carbopol 940 or viscoelastic fluids like Poly Acryl Amide (PAAm) aqueous solutions, the friction factor scales identically within statistical errors up to a generalized Reynolds number of 10 and 0.01, respectively. Above that limit, there is an excess pressure drop for the viscoelastic PAAm solution. This excess pressure drop multiplies the friction factor by more than a decade over a decade of Reynolds numbers. The origin of this excess pressure drop is the high elongational flow present in the Caterpillar static mixer applied to a highly viscoelastic fluid. This result can be extended to almost all static mixers, because their flows are generally highly elongational. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2679–2685, 2013     

Power Requirement for Mixing Shear‐Thinning Fluids with a Planetary Mixer

The optimal control of processes dealing with non‐Newtonian liquids requires the knowledge and control of the power demand of the mixing equipment. In this context, an extension of the Metzner and Otto concept to planetary mixers is proposed to adapt this concept to planetary mixers. The theoretical part of this work defines modified expressions of Reynolds and power numbers. These definitions introduce a characteristic velocity u_ch that is used to define the parameter K_s. A planetary mixer is employed to experimentally ascertain this guideline. Power consumption measurements carried out by mixing shear‐thinning fluids permit to determine the K_s factor. This factor varies only slightly with the flow behavior index and may be regarded as a defined constant for this geometry. Finally, experiments with an additional shear‐thickening fluid confirm the validity of this approach.     

A model viscoelastic fluid

Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Flow pattern observations in circular die entry flows in conjunction with independent shear and normal stress measurement strongly suggest that these fluids would make excellent model fluids for melt studies. Studies in which the influence of elasticity in the absence of shear thinning and fluid inertia can easily be made. Furthermore it is clearly shown that a realistic solution to the die entry flow problem is not obtained using second order flow theory. In the second order region the secondary cell is observed to be almost identical in size to the cell observed for an inelastic Newtonian fluid in creeping flow. Marked growth in the secondary cell as a function of elasticity is not observed until the shear rates exceed the region of second order behavior. This growth in cell size as a result of elasticity is followed at higher shear rates by a spiraling flow instability like that observed for some polymer melts.