Viscoelastic Liquids in Stirred Vessels – Part I: Power Consumption in Unaerated Vessels

Different shear‐thinning and elastic fluids (STE fluids) have been stirred under unaerated conditions, in vessels equipped with Rushton disc turbines. Their power consumption has been evaluated over a wide range of stirring rates and their Metzner‐Otto constant (k_s) has been measured. A correlation has then been proposed to predict k_s values for a Rushton turbine operating in non‐Newtonian solutions. Power curves of STE fluids have been drawn and compared with reference curves (Newtonian, shear‐thinning inelastic and elastic with constant shear viscosity fluids). The STE fluids have thus been divided into two categories. The STE fluids of the first category (STE I fluids), which are concentrated viscous solutions of polymers (guar, CMC) reducing the power consumption at the beginning of the transitional region and connecting with the Newtonian reference at higher Reynolds numbers. In contrast, STE solutions of the second category (STE II fluids), which are solutions of drag reducing polymers (PAA), are less viscous and more elastic. They reduce the power consumption at the end of the transitional region and do not connect with the Newtonian reference, at least until Re = 6000. A general correlation has finally been proposed to model the power curve of STE fluids stirred by a Rushton turbine from the laminar to the turbulent regions, as a function of their elasticity.     

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.     

Erweiterung der Auslegungsverfahren von Rührern und Anwendung an einem Propellerviskosimeter

The design procedure of mixers to agitate non‐Newtonian flow is commonly based on several correlation methods that associate the power consumption of agitating newtonian flow with the power of agitating non‐Newtonian flow. Therefore, the knowledge of the viscosity function of the non‐Newtonian fluid is necessary. For the agitation of fluids with solid fractions, the viscosity is usually unknown and the methods are not applicable. Here, a method to determine the viscosity of pseudoplastic fluids with a solid fraction is presented.     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

Centrifugal pump performance calculation for homogeneous suspensions

Centrifugal pumps are widely used for transporting suspensions, but their head performance is derated when non‐Newtonian fluids and/or coarse solids are present. Some head deration methods are available for high viscosity Newtonian fluids, Bingham plastic fluids and for coarse solids in water. This paper presents a modification of the Hydraulic Institute head deration method that is suitable for any homogeneous non‐Newtonian rheology. A modification of the Walker and Goulas method is also considered. Possible anomalous behaviour of kaolin slurries in centrifugal pumps is discussed.     

Determination of Mixing Times with Helical Ribbon Impeller for Non‐Newtonian Viscous Fluids Using an Advanced Imaging Method

New results on mixing times for viscous Newtonian and non‐Newtonian fluids being homogenized with a helical ribbon impeller are presented. In particular, a recently developed technique to determine the macromixing kinetics of an impeller in a transparent vessel was applied to investigate the effects of rheological properties on mixing times. Significant differences were observed in the mixing times for viscous Newtonian and non‐Newtonian fluids. Based on the new data obtained in this work, a correlation incorporating the elastic effects is proposed in terms of a Weissenberg number for predicting the mixing time as a function of the Reynolds number and the system geometry.     

Analytical models for predicting penetration depth during slot die coating onto porous media

A series of analytical models have been developed to predict the penetration depth during slot die coating on porous media. Analytical models for both Newtonian and non‐Newtonian fluids were derived based on Lubrication Theory, Darcy's law, and a modified Blake–Kozeny equation. Using these models, the penetration depth can be quickly solved and the effects of material properties and processing conditions on penetration depth can be easily investigated. Experiments of coating Newtonian glycerin and non‐Newtonian blackstrap molasses onto Toray series carbon paper were conducted to validate developed models. The overall relative error between the predicted and measured penetration depth was found to be typically lower than 20%, which demonstrates the relative accuracy of developed models. Furthermore, based on a parametric study, it was found that the effect of capillary pressure on penetration depth is less than 10% when the ratio of coating bead pressure and capillary pressure is larger than 10. © 2014 American Institute of Chemical Engineers AIChE J 60: 4241–4252, 2014     

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     

Experimental study of film thickness and free surface velocity around a rotating roll for non-newtonian fluids

Measurements are performed on film thickness and free surface velocity around a rotating roll for Newtonian, non-Newtonian inelastic, and viscoelastic fluids by using noncontact methods of a capacitance probe and a laser Doppler velocimeter probe. The film thickness decreases with increasing inspection angle for Newtonian fluids. For non-Newtonian fluids, it retains an approximately constant value, owing to shear-thinning of viscosity, except for a meniscus region development, which is dependent on fluid elasticity. Comparison of current results with the film thickness from a previous work is also made. With the increment of inspection angle, the free surface velocity increases rapidly in the meniscus region and maintains a constant value almost equal to a roll speed in the other region for viscoelastic fluids, while it increases linearly for Newtonian fluids. The shear rate at a roll surface is presented assuming that the velocity distribution in the liquid film is a polynomial equation. It is found that viscoelastic fluids exhibit different behavior from that of Newtonian and non-Newtonian inelastic fluids. Evaluation of the force acting on the liquid film for Newtonian fluids implies that the velocity gradient at a roll surface in an ascending region may be steeper than the parabolic form assumed in this study.     

Pressure Drop Models for Gas/Non‐Newtonian Power‐Law Fluids Flow in Horizontal Pipes

Models commonly used in literature are evaluated versus 696 data points to predict the pressure drop of gas/non‐Newtonian power‐law fluids flow in horizontal pipes. Suitable models are recommended. A new correlation is developed by ignoring the pressure drop across the gas slug and adopting the liquid slug holdup of gas/non‐Newtonian fluid flow into the homogeneous model. The theoretical curves can capture the test data trends and the overall agreement of predicted values with experimental data is sufficient to be practically applied in industry.     

Gas Dispersion in Rheologically‐Evolving Model Fluids by Hybrid Dual Mixing Systems

Gas dispersion experiments (0.18 ≤ Fr ≤ 0.71, 0.02 ≤ F1 ≤ 0.09) were carried out using a hybrid dual mixing system, which included a helical ribbon impeller and either a Smith or a Rushton turbine. Newtonian and non‐Newtonian model fluids were used as rheologically‐evolving fluids to evaluate changes in gas dispersion performance. A motionless helical ribbon agitator was used as a baffle in low‐viscosity Newtonian fluids. Both Smith and Rushton turbines produced a vortex, which was eliminated by the motionless helical ribbon impeller. Gas dispersion in low‐viscosity fluids was enhanced when the helical ribbon agitator and turbine of the dual hybrid mixing system was kept at a rotational speed ratio of 10 (N_T/N_HR = 10), which allowed dispersion at a lower Fr than the turbine alone. For moderate‐viscosity Newtonian fluids, gas dispersion was achieved at Fr ≤ 0.71 and F1 ≤ 0.05. Flow properties of non‐Newtonian fluids played an important role in gas dispersion; transition from dispersing to flooding stages was observed for the fluids that were more shear‐thinning (n ≤ 0.38).     

Investigations of heat transfer and pressure drop between parallel channels with pseudoplastic and dilatant fluids

Central to the problem of heat exchangers design is the prediction of pressure drop and heat transfer in the noncircular exchanger duct passages such as parallel channels. Numerical solutions for laminar fully developed flow are presented for the pressure drop (friction factor times Reynolds number) and heat transfer (Nusselt numbers) with thermal boundary conditions [constant heat flux (CHF) and constant wall temperature (CWT) ] for a pseudoplastic and dilatant non‐Newtonian fluid flowing between infinite parallel channels. A shear rate parameter could be used for the prediction of the shear rate range for a specified set of operating conditions that has Newtonian behavior at low shear rates, power law behavior at high shear rates, and a transition region in between. Numerical results of the Nusselt number [constant heat flux (CHF) and constant wall temperature (CWT) ] and the product of the friction factor and Reynolds number for the Newtonian region were compared with the literature values showing agreement within 0.36% in the Newtonian region. For pseudoplastic and dilatant non‐Newtonian fluids, the modified power law model is recommended to use because the fluid properties have big discrepancies between the power law model and the actual values in low and medium range of shear rates. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3601–3608, 2003     

Residence Time Distribution Models Derived from Non‐Ideal Laminar Velocity Profiles in Tubes

The theoretical E‐curve for the laminar flow of non‐Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks‐in‐series models of residence time distribution (RTD). In this work, four RTD models derived from non‐ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.     

Blade-coating of a viscoelastic fluid

A theory is presented which describes the dynamics of blade-coating of a viscoelstic fluid onto a moving sheet. The method begins with the usual “lubrication” approximation, and develops the solution as a perturbation about the Newtonian case. Viscoelasticity is described by an empirical constitutive equation which shows non-Newtonian viscosity and finite normal stress behavior consistent with typical observations of polymeric fluids. Theoretical results indicate a small increase in coating thickness due to departure from Newtonian behavior, and a significant decrease in the magnitude of the pressure developed under the blade. Consequently, the blade loading can be reduced significantly by viscoelastic effects. The results for the loading may be an artifact of the specific constitutive model, since it can be shown that some viscoelastic fluids, specifically an “elastic Newtonian” fluid, would exhibit increased loading relative to the inelastic Newtonian case.     

Experimental and Numerical Analysis of the Viscous Fingering Instability of Shear‐Thinning Fluids

Miscible flow displacements in a rectilinear Hele‐Shaw cell of Newtonian as well as rheologically well‐characterized shear‐thinning fluids are examined through experimental measurements and numerical modelling. Water is used as a displacing fluid while the displaced fluid consists of either a reference Newtonian glycerol solution or shear‐thinning solutions of Alcoflood? polymers of different molecular weights. The experimental measurements revealed that the shear‐thinning behaviour of the non‐Newtonian solutions resulted in more complex instability patterns and new finger structures not previously observed in the case of Newtonian displacements are identified and characterized. An analysis of the effects of the rheological behaviour of the shear‐thinning fluids on instability characteristics such as the finger width and finger tip velocity is presented. Numerical simulations using a pseudo‐spectral method are conducted and allowed to compare the predictions of the mathematical model based on an effective Darcy's law with the experimental measurements.     

Breakup dynamics of slender bubbles in non‐newtonian fluids in microfluidic flow‐focusing devices

This study aims to investigate the breakup of slender bubbles in non‐Newtonian fluids in microfluidic flow‐focusing devices using a high‐speed camera and a microparticle image velocimetry (micro‐PIV) system. Experiments were conducted in 400‐ and 600‐μm square microchannels. The variation of the minimum width of gaseous thread with the remaining time before pinch‐off could be scaled as a power‐law relationship with an exponent less than 1/3, obtained for the pinch‐off of bubbles in Newtonian fluids. The velocity field and spatial viscosity distribution in the liquid phase around the gaseous thread were determined by micro‐PIV to understand the bubble breakup mechanism. A scaling law was proposed to describe the size of bubbles generated in these non‐Newtonian fluids at microscale. The results revealed that the rheological properties of the continuous phase affect significantly the bubble breakup in such microdevices. © 2012 American Institute of Chemical Engineers AIChE J,, 2012     

New generalized Newtonian fluid models for quantitative description of complex viscous behavior in shear flows

Two semiempirical models of generalized Newtonian fluid are discussed. Special attention was focused on the stress dependent model based on the free volume theory. However, the strain‐rate dependent model in form of a modified viscosity function resulting from Oldroyd equation is also presented. Both models (along with specific cases) reflecting pseudoplastic or dilatant behavior of liquids in shear flows are generalized to multimode models (defined as products of two or more basic models), which are able to describe quantitatively the behavior of more complex systems, for example, systems with pseudoplastic and dilatant properties in different shear stress (shear rate) ranges. A number of practical examples for viscosity curves of non‐Newtonian fluids described by these models are given. The questions of inverse models and model efficiency are also discussed. POLYM. ENG. SCI., 58:1446–1455, 2018. © 2017 Society of Plastics Engineers     

Gelled Fuel Simulant Droplet Impact onto a Solid Surface

The dynamics of the impact process of a non‐Newtonian gelled fuel simulant droplet was studied experimentally. A comparison between the impact process of the gel simulant and that of a neat Newtonian fluid reveals a similar behaviour during the kinematic phase of the droplet impact. However, significant differences, both quantitatively and qualitatively, between the investigated fluids were found during the later spreading, relaxation and equilibrium phases of the impact process. Numerical simulations for the neat Newtonian fluid were found to accurately predict the centreline height during the kinematic phase for both of the fluids. A novel dynamic model for drop shape based on elastic spring and dashpot elements using the Bessel function to describe the periodic term is presented. Very good agreement of the dynamic model with the experimental data was obtained.     

Withdrawal of cylinders from non-newtonian fluids

The cylinder withdrawal theory for power-law fluids proposed by Tallmadge has been compared with continuous withdrawal data in this work. Calculated withdrawal speeds differ greatly from measured values, although Tallmadge's gravity-corrected theory for Newtonian fluids is in agreement with the present data on Newtonian fluids. Correlations similar to that of Goucher and Ward have been developed with the experimental data over a 400-fold range of dimensionless withdrawal speeds. These correlations are applicable for prediction of non-Newtonian liquid film thicknesses on vertical wires and also apparently for viscoelastic fluids like CMC solutions, but are not applicable for inelastic fluids like Carbopol 934.     

Energy Dissipation Rates of Newtonian and Non‐Newtonian Fluids in a Stirred Vessel

Energy dissipation rates of water and glycerol as Newtonian fluids and carboxyl methyl carbonate solution as non‐Newtonian fluid in a stirred vessel are investigated by 2D particle image velocimetry and compared. Mean velocity profiles reflect the Reynolds (Re) number similarity of two flow fields with different rheological properties, but the root mean square velocity profiles differ in rheology at the same Re‐number. Energy dissipation rates are estimated by direct calculation of fluctuating velocity gradients. The varying energy dissipation rates of Newtonian and non‐Newtonian fluids result from the difference in fluid rheology and apparent viscosity distribution which decides largely the flow pattern, circulation intensity, and rate of turbulence generation.