non-Newtonian Systems Research Articles

A computational study of the dynamic motion of a bubble rising in Carreau model fluids

We present the results of three-dimensional direct numerical simulations of the dynamic motion of a gas bubble rising in Carreau model fluids. The simulations are carried out by a coupled level-set/volume-of-fluid (CLSVOF) method, which combines some of the advantages of the volume-of-fluid (VOF) method with the level-set (LS) method. In our study, it is shown that the motion of a rising gas bubble largely depends on the Carreau model parameters, n and B (n, the slope of decreasing viscosity and B, time constant). Both the model parameters, n and B, have considerable influence on the bubble rise motion. Using numerical analysis, we can understand in detail the bubble morphology for non-Newtonian two-phase flow systems. We also discuss bubble rise motion in shear-thinning fluids in terms of the effective viscosity, ηeff, the effective Reynolds number, Reeff and the effective Morton number, Meff.

Mixing studies of non-Newtonian fluids in an anchor agitated vessel

The success of any mixing operation involving liquid–liquid, gas–liquid and gas–liquid–solid systems depends mainly on the geometry of the vessel and impeller, operating conditions and properties of the system. Transformation of laboratory results to commercial scale unit is very difficult due to the complexity of flow phenomena and the scale up is being done by adopting a conservative approach which is based on the geometric, kinematic and dynamic similarities. This approach does not take into account the non-ideal flow behavior of the fluid and the design of commercial unit will be more rational if this information is included in the design of the unit. An attempt has been made to generate the data on non-ideal flow by carrying out the tracer experiments in an anchor agitated vessel. The fluids studied include water, castor oil, castor oil methyl esters and carboxy methyl cellulose (0.5 and 1 wt%), paper-pulp suspension (0.5 and 2 wt%) and starch suspension (2 and 4 wt%) in presence and absence of aeration. The data is analyzed for characterizing the flow by employing mixed model and dispersion model. Increase in the fraction of well-mixed zone ‘ g’ from 0.7 to 0.95 with increase in impeller speed has been observed for both Newtonian and non-Newtonian systems but the increase is small for viscous fluids. A correlation between the model parameter ‘ g’ and impeller speed, aeration and properties of system has been developed. Incorporating the value of ‘ g’ in different scale up rules a commercial scale stirred vessel is designed. Constant tip speed resulted in large well-mixed zone with minimum power consumption.

Development of Correlations for Overall Gas Hold-up, Volumetric Mass Transfer Coefficient, and Effective Interfacial Area in Bubble Column Reactors Using Hybrid Genetic Algorithm-Support Vector Regression Technique: Viscous Newtonian and Non-Newtonian Liquids

The objective of this study was to develop hybrid genetic algorithm−support vector regression (GA-SVR)-based correlations for overall gas hold-up (ϵG), volumetric mass-transfer coefficient (kLa), and effective interfacial area (a) in bubble column reactors for gas−liquid systems employing viscous Newtonian and non-Newtonian systems as the liquid phase. The hybrid GA-SVR is a novel technique based on the feature generation approach using genetic algorithm (GA). In the present study, GA has been used for nonlinear rescaling of attributes. These, exponentially scaled, are eventually subjected to SVR training. The technique is an extension of conventional SVR technique, showing relatively enhanced results. For this purpose an extensive literature search was done. From the published literature, 1629 data points for viscous Newtonian and 845 data points for viscous non-Newtonian systems for ϵG, 500 data points for viscous Newtonian and 556 data points for viscous non-Newtonian systems for kLa, and 208 data poin...

Trickle bed hydrodynamics for (non-)Newtonian foaming liquids in non-ambient conditions

Abstract Hydrodynamic studies on trickle-bed reactors at non-ambient conditions overwhelmingly addressed coalescing systems despite numerous industrial applications concern the processing of foaming liquids for which engineering data are scantier. To fill this gap, the effects of temperature and moderate pressure (non-ambient conditions) are reported in this study on the shift of the transition from trickle-to-foaming-pulsing flow regimes, on the two-phase pressure drop, the liquid holdup, and the pulse frequency and velocity for Newtonian (air–cetyltrimethylammoniumbromide (CTAB)) foaming and non-Newtonian (air–0.25% CTAB–carboxymethylcellulose (CMC)) foaming systems. At constant superficial gas velocity, the trickle-to-foaming-pulsing flow transition boundary was observed at lower superficial liquid velocity in comparison to non-foaming systems. The transition boundary shifted towards higher gas and liquid superficial velocities with increasingly temperatures and pressures. The pulse frequency increased with temperature and/or pressure whereas the pulse velocity increased with temperature but it decreased with increasing pressure. Respective comparisons with the coalescing alter ego, namely, air–water and air–CMC/water systems, showed that Newtonian and non-Newtonian foaming systems behaved qualitatively similarly regarding the effects of temperature and pressure as the coalescing systems.

Average shear rate for non-Newtonian fluids in a concentric-tube airlift bioreactor

In the present study, a simple methodology for evaluating the average shear rate ( γ ˙ av ) in an internal concentric-tube airlift reactor has been developed for non-Newtonian systems. The volumetric oxygen transfer coefficient ( k L a) was chosen as the appropriate characteristic parameter to evaluate the average shear rate ( γ ˙ av ) because the oxygen transfer occurs through the interfacial area of the air bubbles distributed evenly throughout the bioreactor. The average shear rate ( γ ˙ av ) values of up to 9300 s −1 were estimated as a function of the gas velocity in the riser (0.0094 ≤ U GR ≤ 0.0943 m s −1), of the rheological parameters of the fluid (0.180 ≤ K ≤ 1.833 Pa s n and 0.234 ≤ n ≤ 0.461), and of the volumetric oxygen transfer coefficient (0.0056 ≤ k L a ≤ 0.0609 s −1). Profiles of the γ ˙ av as a function of the gas velocity in the riser ( U GR) displayed different behaviors from those of the literature since γ ˙ av increased up to a maximum value and then decreased with an increase in the U GR. The shear rate estimated by the proposed methodology lay within the range of the correlation values in the literature. Unlike other correlations in the literature, the average shear rate in the present study ( γ ˙ av ) is estimated considering the rheological parameters of the fluid, the volumetric oxygen transfer coefficient ( k L a), and the mass transfer parameter, which is a function of the operating conditions and the geometry of the bioreactor.

Computations of the Breakup of a Jet into Drops in Non-Newtonian Liquid-Liquid Systems

The breakup of a laminar liquid jet into drops in non-Newtonian immiscible liquid systems has been studied using a two-dimensional cylindrical axisymmetric front-tracking/finite difference method with the Carreau–Yasuda model for non-Newtonian viscosities. For co-flow condition, where the continuous phase flows with the same velocity as the jet injection velocity, the lengths of the jet and the sizes of the drops are in good agreement between numerical simulations and experiments reported previously. Non-Newtonian effects are discussed by visualizing the distribution of viscosity. The breakup length of the jet becomes large when shear thinning occurs inside the jet, while the jet becomes short when shear thinning occurs in a continuous phase.

A kinetic approach to the rheology of inhomogeneous systems with account for the interaction of disperse-phase particles

By measuring the optical characteristics of a flow the rheology of a viscous non-Newtonian fluid — an aqueous solution of hydrolyzed polyacrylonitrile — has been studied. The loss of stability by the system with chaotic fluctuations of transparency has been established. A kinetic model, as well as kinetic equations that describe the flow of heterogeneous systems, have been suggested. It is expected that this approach will be used in calculations in oil-and gas production and filtration of non-Newtonian systems in porous media.

Identification of hydrodynamics characteristics in bubble columns through analysis of acoustic sound measurements—Influence of the liquid phase properties

The effects of liquid properties on the hydrodynamics of bubble columns were investigated experimentally through analysis of acoustic sound measurements, using coalescence and non-coalescence mediums. The hydrodynamics parameters such as gas holdup, average bubble radius, gas bubbling rate, root mean square of the sound pressure and damping ratio of the bubble pulsation were investigated at the sparger and bulk regions. The acoustic study revealed that the addition of carboxymethyl cellulose (CMC) and xanthan gum (XG) in small percentage increased the overall gas holdup and reduced the average bubble radius. Moreover, the bubbling rate for these solutions is lower than that for water at low superficial gas velocities. These observations were more apparent in the CMC case. The injection of KCl and silicon polymer substances however, resulted in reduction of the gas holdup and enlargement of the bubble size. In addition, the bubbling rate for the KCl and silicon polymer solutions is found to be superior to that for water. In addition, it is found that acoustic measurements can be used to detect sparger activity for both air–water and non-Newtonian solutions systems. At low superficial gas velocity, the sparger acts as a nozzle, hence heterogeneous bubble size distribution was observed and detected. At high superficial gas velocity, the sparger becomes fully activated and consequently homogeneous size distribution was detected.

Onset of pulsing in trickle beds with non-Newtonian liquids at elevated temperature and pressure—Modeling and experimental verification

The onset of pulse flow in trickle-bed reactors involving gas–non-Newtonian liquid systems was predicted from a stability analysis of the solutions around equilibrium steady-state trickle flow of a transient two-fluid model based on the volume–average mass and momentum balance equations. The model was developed for the versatile Herschel–Bulkley constitutive rheological equation from which special solutions for plastic Bingham fluids, power-law shear-thinning and thickening fluids, as well as Newtonian fluids were derived. The impact of yield stress, consistency and power-law indices, and temperature and reactor pressure on the trickle-to-pulse flow transition was analyzed theoretically. Model predictions of the trickle-to-pulse transition for gas–non-Newtonian liquid systems were confronted with elevated temperature and pressure experimental transition data obtained for air–0.25 and 0.5 mass(carboxymethylcellulose) CMC solution systems measured by means of an electrical conductivity technique. In addition the model version offspring corresponding to the Newton case ( n = 1 , k = μ ℓ , τ 0 = 0 ) , confronted with measured high temperature/pressure-transition data from this work and high-pressure transition data from Wammes et al. [1990. The transition between trickle flow and pulse flow in a cocurrent gas–liquid trickle-bed reactor at elevated pressure. Chemical Engineering Science 45, 3149; 1991. Hydrodynamics in a cocurrent gas–liquid trickle bed at elevated pressures. A.I.Ch.E. J. 37, 1849] and Burghardt et al. [2002. Hydrodynamics of a tree-phase fixed-bed reactor operating in the pulsing flow regime at an elevated pressure. Chemical Engineering Science 57, 4855] proved equally successful.

Mass Transfer in a Rotating Packed Bed with Various Radii of the Bed

This work examined the mass transfer efficiency of a rotating packed bed with various radii of the packed bed. Experimental results showed that kLa increased with decreasing volume of the packed bed. This may contribute to the significant end effects as the volume of the packed bed is reduced. A correlation which takes end effects into consideration for kLa in a rotating packed bed was proposed and is valid for different sizes of the rotating packed bed and for viscous Newtonian and non-Newtonian liquid systems. In addition, it was also found that the correlation could reasonably estimate most of the kLa data in the Higee literature.

Soft lubrication of model hydrocolloids

Many food products are highly structured, complex hydrocolloids that are characterized by either a gel-like or shear thinning behaviour and are thus strongly non-Newtonian systems. Their sensory perception during use is dependent on their behaviour in very thin film conditions at high shear rates. In order to better understand their behaviour in thin films, we have formulated two kinds of solution which are typically present in real systems. We examine the lubricating properties (i.e. tribology) of thin films of structured and non-structured fluids between a hard and soft surface (‘soft-EHL’ lubrication), when the film thickness is of a similar size to the microstructural elements. The present work involves relating the tribology of both shear thinning polymer solutions and swollen microgel suspensions to their rheological and microstructural properties in thin films and at high shear rates in the boundary, mixed and fluid film lubrication regimes. We show that the polymer solutions are typically entrained into rubbing contacts to form mixed fluid/boundary lubricating films while model yield stress fluids generate only boundary lubricating films. Soft-EHL theory satisfactorily predicts friction measurements at high entrainment speeds in full film lubrication. The microgels are found to form a confined film which minimizes contact between the surfaces, causing a lowering of the friction coefficient in the boundary-regime, while the friction in the mixed-regime is also dependent on the high-shear viscosity.

Wall Heat Transfer in Stirred Tank Reactors

Local wall heat-transfer coefficients have been measured for water and for the non-Newtonian systems consisting of 0.3, 0.6, and 1.0 wt % carboxymethylcellulose in water. The results were compared to existing correlations, and good agreement was found for the water system outside the impeller region. In the impeller region, deviations were large. For the non-Newtonian systems, a functional dependence between the Reynolds number and the heat-transfer coefficient, given by Nu/(Pr0.33Vi0.14) ∝ Re0.8, was found to fit the data well. Support for this was found by a closer examination of the existing literature. This is in contrast to the currently accepted dependence on a Reynolds number exponent of 0.67−0.68. On the basis of the data, a new correlation for non-Newtonian fluids has been suggested. Radial temperature profiles for the wall region were also measured and presented.

Deformation of a non-Newtonian ellipsoidal drop in a non-Newtonian matrix: extension of Maffettone–Minale model

A phenomenological model for the dynamics of a buoyancy free non-Newtonian drop immersed in a non-Newtonian fluid subjected to a flow field with an arbitrary uniform velocity gradient is presented. The model is based on the assumption that the drop deforms while remaining ellipsoidal and the volume is preserved. The analytical limits of Taylor for both small deformations and high viscosity ratios are exactly recovered. Also, the affine deformation limit is recovered under the appropriate conditions. In addition, the second-order theory for non-Newtonian systems [F. Greco, J. Non-Newtonian Fluid Mech. 107 (2002) 111–131] is also recovered to within a minor term. As a consequence, the major and minor drop semiaxes, together with the drop angle, properly degenerate into the analytical limits, while the third semiaxis differs only slightly from the exact theory. Model predictions are compared with experimental data for both Newtonian and non-Newtonian systems, throughout a significant range of parameters values.

Minimum Fluidization Velocity in a Three Phase Inverse Fluidized Bed Reactor with Newtonian and Non-Newtonian Fluids

The influence of operational parameters and the effect of viscosity on minimum fluidization velocity, Ulmf (minimum fluidization liquid velocity) and Ugmf (minimum fluidization gas velocity) were investigated in a three-phase inverse fluidized bed reactor using low-density polyethylene (LDPE) and polypropylene (PP) particles. The Ulmf showed an increasing trend with an increase in particle diameter. The effect of superficial gas velocity, Ug on Ulmf and the effect of superficial liquid velocity, Ul on Ugmf for water, glycerol and carboxy methyl cellulose (CMC) as the liquid phase were studied. With an increase in Ug, the Ulmf decreased and with an increase in Ul, the Ugmf also decreased. With an increase in the viscosity (concentration) of glycerol and CMC, Ulmf decreased. Correlations for the prediction of Ulmf in Newtonian and non-Newtonian systems are proposed.

Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a non-Newtonian filtration system

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for a differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reaction-diffusion (Fujita type) systems.

Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a quasilinear reaction–diffusion system

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–diffusion systems (non-Newtonian filtration systems) are established to extend the result for semilinear reaction–diffusion systems (Fujita type).

Non-existence of positive solution to a quasilinear elliptic system and blow-up estimates for a reaction-diffusion system

The non-existence result for radially nonincreasing positive solutions of the system is implied. By using this non-existence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result for semilinear reaction-diffusion systems (Fujita type).

Hydrodynamic characteristics and mixing behaviour of Sclerotium glucanicum culture fluids in an airlift reactor with an internal loop used for scleroglucan production.

The filamentous fungus, Sclerotium glucanicum NRRL 3006, was cultivated in a 0.008 m(3) airlift bioreactor with internal recirculation loop (ARL-IL) for production of the biopolymer, scleroglucan. The rheological behaviour of the culture fluid was characterised by measurement of the fluid consistency coefficient (K) and the flow behaviour index (n). Based on these measurements, the culture fluid changed from a low viscosity Newtonian system early in the process, to a viscous non-Newtonian (pseudoplastic) system. In addition, reactor hydrodynamics and mixing behaviour were characterised by measurement of whole mean gas hold-up (epsilon(g)), liquid re-circulation velocity (U(ld)) and mixing time (t(m)). Under identical process conditions, the effects of the viscosity of the culture fluid and air flow rate on epsilon(g), U(ld) and t(m) were examined and empirical correlations for epsilon(g), U(ld) and t(m) with both superficial velocity U(g) and consistency coefficient K were obtained and expressed separately. The correlations obtained are likely to describe the behaviour of real fungal culture fluids more accurately than previous correlations based on Newtonian or simulated non-Newtonian systems.

Blow-up estimates for a non-newtonian filtration system

The prior estimate and decay property of positive solutions are derived for a system of quasi-linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this non-existence result, blow-up estimates for a class quasi-linear reaction-diffusion systems (non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction-diffusion (Fujita type) systems.

Gas Holdup in Circulating Bubble Columns with Pseudoplastic Liquids

The contributions of pressure drop due to wall frictional losses to the total gas holdup of two-phase viscous non-Newtonian systems were experimentally investigated using a 150 dm3 circulating bubble column. The column had a downcomer-to-riser cross-sectional area ratio of 0.54 and a dispersion height of 2.5 m. Aqueous solutions of xanthan gum and carboxymethyl cellulose were used to simulate a wide range of rheological properties. The average wall shear stress was estimated from Al-Masry's (1999) correlation for the average wall shear rate in external loop airlift reactors. Pressure drop due to wall shear stress was found significantly contributed by 10–70 % to the total gas holdup. This contribution has always been ignored in the data presented in the literature due to the absence of reliable and simple correlations for the average shear rate and shear stress. Corrections to gas holdup were found necessary for non-Newtonian solutions with concentrations of ≥ 0.5 wt/wt.-%.