Axial dispersion in packed bed reactors involving viscoinelastic and viscoelastic non-Newtonian fluids

Axial dispersion is an important parameter in the performance of packed bed reactors. A lot of fluids exhibit non-Newtonian behaviour but the effect of rheological parameters on axial dispersion is not available in literature. The effect of rheology on axial dispersion has been analysed for viscoinelastic and viscoelastic non-Newtonian fluids. Aqueous solutions of carboxymethyl cellulose and polyacrylamide have been chosen to represent viscoinelastic and viscoelastic liquid-phases. Axial dispersion has been measured in terms of Bo_L number. The single parameter axial dispersion model has been applied to analyse RTD response curve. The Bo_L numbers were observed to increase with increase in liquid flow rate and consistency index ‘K’ for viscoinelastic as well as viscoelastic fluids. Bodenstein correlation for Newtonian fluids proposed has been modified to account for the effect of fluid rheology. Further, Weissenberg number is introduced to quantify the effect of viscoelasticity.     

Heat Generation/Absorption Effects in a Boundary Layer Stretched Flow of Maxwell Nanofluid: Analytic and Numeric Solutions

Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM) has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion “D_b” and thermophoresis effects “D_t” occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.     

Constructal Law of Vascular Trees for Facilitation of Flow

Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.     

Absorption of oxygen in highly viscous newtonian and non-Newtonian fermentation model media in bubble column bioreactors

Summary Mean relative gas holdup, slip velocity, bubble size distribution, mean specific interfacial area, and volumetric mass transfer coefficient of oxygen were estimated in sparged columns 14 cm in diameter and 380 and/or 390 cm high with two different aerator types (porous plate and injector nozzle) in highly viscous Newtonian (glycerol solutions) and non-Newtonian (CMC solutions) fluids.For the Newtonian liquids the above properties were estimated as function of the viscosity of the liquid. For the non-Newtonian liquids they were determined as function of the fluid consistency index and flow behavior index. Significant differences between Newtonian and non-Newtonian systems appear. In Newtonian medium k_L a drops with increasing viscosity and already approaches a constant value at =40 cP. In pseudoplastic medium k_L a varies with the fluid consistency and flow behavior indexes in the entire investigated range.In both of these systems the primary bubble population changes into two or three populations along the reactor: the medium bubbles gradually disappear and small and large bubbles are formed.     

Relation between critical disk speed for foam-breaking of rotating-disk mechanical foam-breakers and foaming characteristics of solutions

For tower fermentors, i.e., bubble columns (BCs), treating various foaming liquids, the critical disk rotational speed N_c required for foam-breaking of rotating-disk mechanical foam-breakers (MFRDs) fitted to BCs was studied in relation to the foaming characteristics of the liquids. An empirical equation was presented for predicting N_c in foam-breaking regions. With this equation, it was found that prediction of N_c of MFRDs fitted to BCs treating various liquids was possible regardless of the type of foaming liquid or its concentration.     

Effect of pH on successive foam and sonic droplet fractionation of a bromelain-invertase mixture

A droplet fractionation method was previously developed to concentrate a dilute nonfoaming protein solution. In that earlier study with invertase, it was demonstrated that droplets created by ultrasonic energy waves could be enriched up to 8 times that of the initial dilute invertase solution. In this study, a mixture of bromelain (a foaming protein) and invertase (a nonfoaming protein) is investigated as a preliminary step to determine if droplet fractionation can also be used to separate a non-foaming protein from foaming proteins. The foaming mixture containing bromelain is first removed by bubbling the binary mixture with air. After the foam is removed, the protein rich air-water interfacial layer is skimmed off (prior to droplet fractionation) so as not to interfere with the subsequent droplet production from the remaining bulk liquid, rich in non-foaming protein. Finally, sonic energy waves are then applied to this residual bulk liquid to recover droplets containing the non-foaming protein, presumed to be invertase. The primary control variable used in this droplet fractionation process is the pH, which ranged for separate experiments between 2 and 9. It was observed that the maximum overall protein partition coefficients of 5 and 4 were achieved at pH 2 and 4, respectively, for the initial foaming experiment followed by the post foaming droplet fractionation experiment.     

Relation between mechanical foam-breaking difficulty and the foaming characteristics of solutions

Using a small foaming apparatus, liquid foaming characteristics such as liquid holdup in foamate flow (φ_t), rate of liquid drainage from foam (ν), foam velocity (u_f) and foam size (d_f) were examined for various liquids. A parameter φ_f, incorporating φ_t, ν and u_f, was obtained. The relationship among φ_f, d_f and the liquid holdup in foam, φ_b, in the actual gas-bubbling systems under foam control was expressed in the form of φ_b ∞ φ_fd_f^1.83, regardless of the type of foaming liquid or its concentration. This relationship was useful for the prediction of φ_b as related to mechanical foam-breaking difficulty.     

The effect of organic loading rate on foam initiation during mesophilic anaerobic digestion of municipal wastewater sludge

The impact of increasing organic load on anaerobic digestion foaming was studied at both full and bench scale. Organic loadings of 1.25, 2.5 and 5 kg VS m⁻³ were applied to bench-scale digesters. Foaming was monitored at a full scale digester operated in a comparable organic loading range over 15 months. The bench scale batch studies identified 2.5 kg VS m⁻³ as a critical threshold for foam initiation while 5 kg VS m⁻³ resulted in persistent foaming. Investigation of a full scale foaming event corroborated the laboratory observation that foaming may be initiated at a loading rate of ?2.5 kg VS m⁻³. Experimental findings on foam composition and differences in the quality characteristics between foaming and non-foaming sludges indicated that foam initiation derived from the combined effect of the liquid and gas phases inside a digester and that the solids/biomass ultimately stabilized foaming.     

Realistic non-Newtonian viscosity modelling highlights hemodynamic differences between intracranial aneurysms with and without surface blebs

Most computational fluid dynamic (CFD) simulations of aneurysm hemodynamics assume constant (Newtonian) viscosity, even though blood demonstrates shear-thinning (non-Newtonian) behavior. We sought to evaluate the effect of this simplifying assumption on hemodynamic forces within cerebral aneurysms, especially in regions of low wall shear stress, which are associated with rupture. CFD analysis was performed for both viscosity models using 3D rotational angiography volumes obtained for 26 sidewall aneurysms (12 with blebs, 12 ruptured), and parametric models incorporating blebs at different locations (inflow/outflow zone). Mean and lowest 5% values of time averaged wall shear stress (TAWSS) computed over the dome were compared using Wilcoxon rank-sum test. Newtonian modeling not only resulted in higher aneurysmal TAWSS, specifically in areas of low flow and blebs, but also showed no difference between aneurysms with or without blebs. In contrast, for non-Newtonian analysis, bleb-bearing aneurysms showed significantly lower 5% TAWSS compared to those without (p=0.005), despite no significant difference in mean dome TAWSS (p=0.32). Non-Newtonian modeling also accentuated the differences in dome TAWSS between ruptured and unruptured aneurysms (p<0.001). Parametric models further confirmed that realistic non-Newtonian viscosity resulted in lower bleb TAWSS and higher focal viscosity, especially when located in the outflow zone. The results show that adopting shear-thinning non-Newtonian blood viscosity in CFD simulations of intracranial aneurysms uncovered hemodynamic differences induced by bleb presence on aneurysmal surfaces, and significantly improved discriminant statistics used in risk stratification. These findings underline the possible implications of using a realistic model of blood viscosity in predictive computational hemodynamics.     

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.     

Rheological behaviour of some antibiotic biosynthesis liquids

This paper prsents the results of teh study of rheological behaviour of antibiotic biosynthesis liquids obtained by submerged aerobic cultivation of microorganisms belonging to the actinomycete and fungi classes, in stirred tank bioreactors with turbine impellers. These liquids have a non-Newtonian behaviour which follows the power-law rhcological model with a correlation index of over 0.95. The studied liquids are pseudoplastic, and alter their rheological properties, such as consistency index, (K), flow index, (n), apparent viscosity, (η_a), maximum Newtonian viscosity (η₀), with the culture age, microrganism strain and batch conditions. Also, these liquids are time dependent, exhibiting thixotropy. The most viscous liquids are produced by Streptomyces aureofaciens and Streptomyces rimosus cultivation, while that produced by Streptomyces griseus is the least viscous. A higher pseudoplasticity appears after 30 hours culture age. Since all these biosynthesis are aerobic, a careful observation of the rhelogical behaviour dynamics is necessary to avoid the oxygen culture supply limitation and the decrease of the bioreactor performance during biosynthesis.     

Rheology of polymers in many-body dissipative particle dynamics simulations: Schmidt number effect

The Schmidt number effect on the rheology of finitely extensible nonlinear elastic chains (FENE) in many-body dissipative particle dynamics (MDPD) is investigated in this work. We find that the Schmidt number, ranging from (10¹) to (10³), has limited influence on the polymer properties, such as its radius of gyration (R_g), diffusion coefficient (D) and relaxation time (τ). The simulation results follow Zimm model's predictions well. The hydrodynamic interaction strength parameter h* demonstrates that the full hydrodynamic interaction can be simulated for Schmidt number from (10⁰-10⁶) in MDPD. Next, the rheology of FENE polymers is studied using Lees-Edward boundary condition in shear flow. The shear-thinning and normal stress difference are measured and analysed with MDPD; meanwhile, the volume fraction, solvent quality and chain length are varied to explore their effects on the extent of the Newtonian region. Finally, the non-Newtonian droplet is firstly simulated in MDPD. Its maximum spreading diameter is measured for both Newtonian and non-Newtonian droplet with Weber number (We) ranging from 4.37 to 109.2 on hydrophilic, moderate and hydrophobic surfaces, respectively. The fluid shear-thinning property increases at high shear rate and is further enhanced on more hydrophobic surface, from the maximum spreading diameter results. The non-Newtonian (FENE) droplet can be now well simulated in MDPD and this provides additional insight to further research concerning polymer-solvent-surface interactions, which is crucial in various applications.     

A study of the rheological properties of a non-Newtonian fermentation broth

Polysaccharide was synthesized by Aureobasidium pullulans (or Pullularia pullulans) 2552 in a sucrose medium. The field apparent viscosity of the culture medium from shake flask experiments rose to 24,500 cP and then dropped toward its initial value as the fermentation progressed. The magnitude of the maximum apparent viscosity depended on the initial pH of the fermentation broth. The inoculum age influenced the cultivation period before which the maximum viscosity was reached. Rheograms of the fermentation broths showed a change in viscosity behavior from Newtonian to pseudoplastic, and then toward Newtonian characteristics during the fermentation. The calculated non-Newtonian index was found to be a sensitive factor for the indication of the non-Newtonian behavior. Such behavior could not be detected from rheograms. Viscosity profiles of polysaccharide isolated from various stages of the fermentation showed a change from Newtonian to pseudoplastic behavior depending on the concentration (0–2%) of polysaccharide.     

Comparison of the hydrodynamics and mass transfer characteristics in internal-loop airlift bioreactors utilizing either a novel membrane-tube sparger or perforated plate sparger

Two gas spargers, a novel membrane-tube sparger and a perforated plate sparger, were compared in terms of hydrodynamics and mass transfer (or oxygen transfer) performance in an internal-loop airlift bioreactor. The overall gas holdup ε _T, downcomer liquid velocity V _d, and volumetric mass transfer coefficient K _L a were examined depending on superficial gas velocity U _G increased in Newtonian and non-Newtonian fluids for the both spargers. Compared with the perforated plate sparger, the bioreactor with the membrane-tube sparger increased the values of ε _T by 4.9–48.8 % in air–water system when the U _G was from 0.004 to 0.04 m/s, and by 65.1–512.6 % in air–CMC solution system. The V _d value for the membrane-tube sparger was improved by 40.0–86.3 %. The value of K _L a was increased by 52.8–84.4 % in air–water system, and by 63.3–836.3 % in air–CMC solution system. Empirical correlations of ε _T, V _d, and K _L a were proposed, and well corresponding with the experimental data with the deviation of 10 %.     

Mass transfer in blood oxygenators using blood analogue fluids

Mass transfer correlations for hollow fiber blood oxygenators have been determined experimentally using Newtonian and non-Newtonian blood analogue fluids. The Newtonian fluids consisted of deionized water and glycerol/water mixtures. The non-Newtonian fluids were prepared by adding small amounts of xanthan gum to the Newtonian blood analogue fluids. The rheological behavior of the non-Newtonian blood analogue fluids was modeled using the power law. The diffusion of oxygen into and out of the Newtonian and non-Newtonian blood analogue fluids has been studied. The liquid stream flowed outside and across bundles of woven hollow fibers, while the gas stream flowed inside the fibers.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.     

Numerical study of the impact of non-Newtonian blood behavior on flow over a two-dimensional backward facing step

Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50-400, the flow recirculation zone downstream of the step is 22-63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.     

A modified method for determination of diffusivities of low molecular substances in non-Newtonian liquids

A modified method for determination of diffusivities of low molecular substances in non-Newtonian liquids described by the power-law model has been proposed. It is based on the dissolution of Geiss body, with a parameter m=1/3 rotating in an infinite fluid. In this case, the solution of the differential equations of motion and mass transfer is available as an analytical formula for calculating the diffusivity coefficient.The method allows the extension of the variety of media and diffusing species. It has been illustrated with dissolving of gypsum in water and five non-Newtonian liquids. The results obtained have been interpreted taking into account the interaction between calcium ions and polymer molecules of the non-Newtonian system, as well as the heterogeneity of the system near to the dissolving surface.     

Asymmetric alkene epoxidation by Mn(III)salen catalyst in ionic liquids

The enantioselective epoxidation of 6-cyano-2,2-dimethylchromene (Chrom) catalysed by the Jacobsen catalyst, using sodium hypochlorite (NaOCl) as oxygen source, at room temperature, was performed in a series of 1,3-dialkylimidazolium and tetra-alkyl-dimethylguanidium based ionic liquids. All the room temperature ionic liquids (RTILs) could be used as reaction media for the enantioselective epoxidation of the alkene giving, generally, moderate to good epoxide yields and enantiomeric excesses (ee%).For the series of ionic liquids derived from the 1,3-dialkylimidazolium cation, it was observed some relationship between the RTILs physical properties and the catalytic reaction parameters, exemplified by linear correlations between (i) the ee% and the α Kamlet-Taft parameter (hydrogen bond acidity of the solvent) for CH₂Cl₂ and [C₄m_nim][BF₄] ionic liquids (n = 1 or 2), and (ii) the ee% and the β Kamlet-Taft parameter (hydrogen bond basicity of the solvent) for CH₂Cl₂ and [C₄mim][X] ionic liquids (X = PF₆, NTf₂ or BF₄).All the RTILs could be reused in further catalytic cycles, with the exception of [C₈mim][PF₆]. The reutilisation of the Jacobsen catalyst for four times generally led to a decrease in the epoxide yield and to a slight decrease in the enantioselectivity. The recycling of the catalyst could be improved by imparting an ionic character to the complex through abstraction of the axially coordinated chloride anion (Cat 2). Other oxygen sources, such as iodosylbenzene, hydrogen peroxide and urea-hydrogen peroxide adduct, were also tested coupled with Jacobsen catalyst, but the best results were achieved with NaOCl.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.