Coaxial Mixer Hydrodynamics with Newtonian and non‐Newtonian Fluids

The performance of several combinations of a wall scraping impeller and dispersing impellers in a coaxial mixer operated in counter‐ and co‐rotating mode were assessed with Newtonian and non‐Newtonian fluids. Using the power consumption and the mixing time as the efficiency criteria, impellers in co‐rotating mode were found to be a better choice for Newtonian and non‐Newtonian fluids. The hybrid impeller‐anchor combination was found to be the most efficient for mixing in counter‐rotating or co‐rotating mode regardless of the fluid rheology. For both rotating modes, it was shown that the anchor speed does not have any effect on the power draw of the dispersing turbines. However, the impeller speed was shown to affect the anchor power consumption. The determination of the minimum agitation conditions to achieve the just suspended state of solid particles (N_js) was also determined. It was found that N_js had lower values with the impellers having the best axial pumping capabilities.     

Using Tomography to Characterize the Mixing of Non‐Newtonian Fluids with a Maxblend Impeller

The flow field inside a cylindrical mixing vessel was visualized by electrical resistance tomography (ERT), a non‐intrusive measurement technique. Six tomography planes, each containing 16 sensing electrodes, measured the mixing time in the agitation of pseudoplastic fluid exhibiting yield stress. The effects of various parameters such as impeller types, impeller speed, fluid rheology, power consumption, Reynolds number, and absence of baffles on the mixing time were investigated. The Maxblend impeller was able to improve the mixing performance of non‐Newtonian fluids in a batch reactor. The mixing quality could be further enhanced by decreasing the xanthan gum concentration and using baffles in the mixing vessel.     

Measuring Mixing Time in the Agitation of Non‐Newtonian Fluids through Electrical Resistance Tomography

Electrical resistance tomography (ERT), which is a non‐invasive and robust measurement technique, was employed to visualize, in three dimensions, the concentration field inside a cylindrical mixing vessel equipped with a radial‐flow Scaba 6SRGT impeller. The ability of ERT to work in opaque fluids makes this technique very attractive from an industrial perspective. An ERT system with a 4‐plane assembly of peripheral sensing rings, each containing 16 electrodes, was used to measure the mixing time in agitation of xanthan gum solution which is a pseudoplastic fluid with yield stress. An image reconstruction algorithm was used to generate images of the tracer distribution within the sensing zone. In this study, the effect of impeller speed, fluid rheology, power consumption, and Reynolds number on the mixing time was investigated.     

Computational Fluid Dynamics Simulation of Generation and Coalescence of Bubbles in Non‐Newtonian Fluids

The successive generation and coalescence behaviors of bubbles from two parallel nozzles in non‐Newtonian fluids were numerically simulated by using the volume of fluid (VOF) method. Three flow patterns for bubbles and the related flow regime transition lines were obtained. Two critical nozzle intervals exist: one for the bubble coalescence before pinch‐off, and another for alternating bubble formation then in‐line coalescence under different conditions. Two correlations were proposed to predict the dimensionless critical nozzle intervals for the transition of bubble‐flow patterns. The influences of nozzle diameter, gas flow rate, nozzle interval, and rheological properties of fluid on bubble‐flow patterns were investigated systematically.     

Non‐Newtonian Heat Transfer on a Plate Heat Exchanger with Generalized Configurations

For the configuration optimization of plate heat exchangers (PHEs), the mathematical models for heat transfer and pressure drop must be valid for a wide range of operational conditions of all configurations of the exchanger or the design results may be compromised. In this investigation, the thermal model of a PHE is adjusted to fit experimental data obtained from non‐Newtonian heat transfer for eight different configurations, using carboxymethylcellulose solutions (CMC) as test fluid. Although it is possible to successfully adjust the model parameters, Newtonian and non‐Newtonian heat transfer cannot be represented by a single generalized correlation. In addition, the specific heat, thermal conductivity and power‐law rheological parameters of CMC solutions were correlated with temperature, over a range compatible with a continuous pasteurization process.     

Bubble Volume and Aspect Ratio Generated in Non‐Newtonian Fluids

Bubble formation from an orifice submerged in quiescent polyacrylamide aqueous solution was investigated numerically with a sharp‐interface coupled level‐set/volume‐of‐fluid method based on the rheological characteristics of the fluid. In both non‐Newtonian fluids and Newtonian fluids, the numerical approach was able to capture accurately the deformation of the bubble surface, validated by comparison with experimental results. The effects of orifice diameter, solution mass concentration, and gas flow rate on bubble volume and aspect ratio were evaluated. Both the instantaneous and detached volume decrease with the orifice diameter but increase with mass concentration and gas flow rate. The aspect ratio at the departing point tends to rise with the orifice diameter and mass concentration and falls with the gas flow rate.     

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.     

Characterization of Bubble Shapes in Non‐Newtonian Fluids by Parametric Equations

Based on experiments with single air bubbles rising in stagnant non‐Newtonian fluids, an innovative model containing the aspect ratio (E) and two parameters (α, β) was proposed and proved to be capable of characterizing the bubble shape from spherical/ellipsoidal to prolate/oblate‐tear with good accuracy. Several impacts on bubble deformation were investigated, involving the rheological properties of the fluids and different forces exerted on the bubble, which were quantified by multiple dimensionless numbers (e.g., Reynolds, Eötvös, and Deborah number). Within a wide range, the empirical correlations were obtained for parameter β, and between α and β. Together with the shape model, a complete system was set up for bubble shape characterization and prediction that will provide new ideas for future studies on bubble hydrodynamics.     

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.     

Volumetric Mass Transfer Coefficient in non‐Newtonian Fluids in Spout Fluid Beds

The volumetric liquid‐phase mass transfer coefficient, k_La, was determined by absorption of oxygen in air using six different carboxy‐methyl cellulose (CMC) solutions with different rheological values in three phase spout‐fluid beds operated continuously with respect to both gas and liquid. Three cylindrical columns of 7.4 cm, 11.4 cm, and 14.4 cm diameters were used. Gas velocity was varied between 0.00154–0.00563 m/s, liquid velocity between 0.0116–0.0387 m/s, surface tension between 0.00416–0.0189 N/m, static bed height between 6.0–10.8 cm, and spherical glass particles of 1.75 mm diameter were used as packing material. A single nozzle sparger of 1.0 cm diameter was used in the spouting line. The volumetric mass transfer coefficient was found to increase with gas velocity, liquid velocity, and static bed height and to decrease with the increase of the effective liquid viscosity of the CMC solution. A dimensionless correlation was developed and compared with those listed in the literature.     

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.     

Predicting Power for a Scaled‐up Non‐Newtonian Biomass Slurry

High‐solids biomass slurries exhibit non‐Newtonian behavior with a yield stress and require high power input for mixing. The goals were to determine the effect of scale and geometry on power number P₀, and estimate the power for mixing a pretreated biomass slurry in a 3.8 million L hydrolysis reactor of conventional design. A lab‐scale computational fluid dynamics model was validated against experimental data and then scaled up. A pitched‐blade turbine and A310 hydrofoil were tested for various geometric arrangements. Flow was transitional; laminar and turbulence models resulted in equivalent P₀ which increased with scale. The ratio of impeller diameter to tank diameter affected P₀ for both impellers, but impeller clearance to tank diameter affected P₀ only for the A310. At least 2 MW is required to operate at this scale.     

Predicting the Viscosity of Non‐Newtonian Water‐in‐Oil Emulsions Based on the Lederer Model

The accurate prediction of the viscosity of emulsions is highly important for oil well exploitation. Commonly used models for predicting the viscosity of water‐in‐oil (W/O) emulsions composed by two or three factors cannot always fit well the viscosity of W/O emulsions, especially in the case of non‐Newtonian W/O emulsions. An innovative and comprehensive method for predicting the viscosity of such emulsions was developed based on the Lederer, Arrhenius, and Einstein models, using experimental data. Compared with the commonly applied W/O emulsion viscosity models, the proposed method considers more factors, including temperature, volume fraction of water, shear rate, and viscosity of the continuous (oil) and dispersed phase (water). Numerous published data points were collected from the literature to verify the accuracy and reliability of the method. The calculation results prove the high accuracy of the model.     

Assessing Blending of Non‐Newtonian Fluids in Static Mixers by Planar Laser‐Induced Fluorescence and Electrical Resistance Tomography

Planar laser‐induced fluorescence (PLIF) and electrical resistance tomography (ERT) were applied simultaneously to monitor the mixing performance of a KM static mixer for the blending of non‐Newtonian fluids of dissimilar rheologies in the laminar regime. The areal distribution method was used to obtain quantitative information from the ERT tomograms and the PLIF images. Comparison of the ERT and PLIF results demonstrates the ability of ERT to detect the mixing performance in cases of poor mixing within the resolution of the measurement, though the accuracy decreases as the condition of perfect mixing is approached. Thus, ERT has the potential to detect poor mixing within the confines of its resolution limit and the required conductivity contrast, providing potential rapid at‐line measurement for industrial practitioners.     

Gas Holdup and Solid‐Liquid Mass Transfer in Newtonian and non‐Newtonian Fluids in Bubble Columns

Gas holdup and surface‐liquid mass transfer rate in a bubble column have been experimentally investigated. De‐mineralized water, 0.5 and 1.0% aqueous solutions of carboxy methyl cellulose (CMC), and 60% aqueous propylene glycol have been used as the test liquids. Effects of column diameter, liquid height to column diameter ratio, superficial gas velocity and liquid phase viscosity on gas holdup and mass transfer rate are studied. Generalized correlations for the average gas holdup and wall to liquid heat and mass transfer coefficients are proposed. These are valid for both Newtonian and pseudoplastic non‐Newtonian fluids.     

Frictional Pressure Drop of Air Non‐Newtonian Liquid Flow through Helical Coils in Horizontal Orientation

Investigations have been carried out to evaluate the two‐phase frictional pressure drop for air non‐Newtonian liquid flow through helical coils in horizontal orientation. The experiments performed using 36 different helical coils and 4 different concentrations of sodium salt of carboxymethyl—cellulose (SCMC) as non‐Newtonian liquids. The effects of air and liquid flow rate, coil diameter, helix angle and liquid properties‐ on two‐phase frictional pressure drop have been discussed. An attempt has been made to fit the experimental two‐phase frictional pressure drop data by the Lockhart and Martinelli, Chem. Eng. Prog. 45 , 39–48 (1949) correlation and the modified Lockhart‐Martinelli correlation as presented by different authors. In another approach, friction factor method was adopted to correlate the experimental data by dimensional analysis. The correlation developed predicts the two‐phase frictional pressure drop with acceptable statistical accuracy.     

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.     

CFD Investigation of the Mixing of Yield‐Pseudoplastic Fluids with Anchor Impellers

The study was carried out to simulate the 3D flow domain in the mixing of pseudoplastic fluids possessing yield stress with anchor impellers, using a computational fluid dynamics (CFD) package. The multiple reference frames (MRF) technique was employed to model the rotation of the impellers. The rheology of the fluid was approximated using the Herschel–Bulkley model. To validate the model, the CFD results for the power consumption were compared to the experimental data. After the flow fields were calculated, the simulations for tracer homogenization were performed to simulate the mixing time. The effects of impeller speed, fluid rheology, and impeller geometry on power consumption, mixing time, and flow pattern were explored. The optimum values of c/D (impeller clearance to tank diameter) and w/D (impeller blade width to tank diameter) ratios were determined on the basis of minimum mixing time.     

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.