Shear-thinning Liquids Research Articles

Numerical study on hydrodynamics of two types of unsteady bubbles in shear-thinning liquids

Numerical study on hydrodynamics of two types of unsteady bubbles in shear-thinning liquids

A design of soft computing intelligent networks for MHD Carreau nanofluid model with thermal radiation

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values’ accuracy is upto [Formula: see text] which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms.

Gels and gelled emulsions prepared by acid-induced gelation of mixtures of faba bean (Vicia faba) protein concentrate and λ-carrageenan

In this study, gels were successfully prepared at room temperature from mixtures of dry fractionated faba bean protein concentrate (FPC) and λ-carrageenan (λ-CGN), through acidification with glucono-δ-lactone (GDL). At neutral pH, the mixtures were shear thinning liquids, although the shear viscosity increased dramatically with λ-CGN addition. After adding GDL, the gelling kinetics were followed through small amplitude oscillatory rheology for 19 hours, at which point all gels had reached a gel modulus plateau. Elastic moduli for the prepared gels were in the range of 1500 – 4500 Pa, dependent on FPC:λ-CGN ratio and concentrations, and final pH (3.5 – 4). Rheological data further indicated the gels had properties typical of aggregated particle gels, e.g., low yield strains (∼1%). All gels showed some syneresis upon centrifugation (2000g), with the least amount of syneresis (15 – 20%) at the highest λ-CGN concentrations (1.5 – 2%). FPC is a good emulsifier, and gelled emulsions were successfully prepared. Inclusion of emulsion droplets had significant impact on the gel network, with ∼40% and ∼60% increased gel storage modulus at 20% and 30% oil, respectively. Preparing similar formulations using a more extensively processed commercial faba bean protein isolate was also attempted, but this resulted in poor gels with very high syneresis. This indicates that dry fractionation methods may be beneficial to preserve native protein functionality.

An investigation of a gas–liquid swirling flow with shear-thinning power-law liquids

A gas–liquid swirling flow with shear-thinning liquid rheology exhibits complex behavior. In order to investigate its flow characteristics, experiments and computational fluid dynamics (CFD) simulations are conducted based on dimensional analysis. A Malvern particle size analyzer and electrical resistance tomography are applied to obtain the bubble size distribution and section void fraction. A Coriolis mass flowmeter is applied to obtain the mixture flow rate and mixture density for an entrance gas volume fraction smaller than 7%. The CFD coupled mixture multiphase model and large eddy simulation model are applied, considering the liquid shear-thinning power-law rheology. The results show that the swirling flow can be divided into developing and decaying sections according to the swirl intensity evolution in the axial direction. A gas–liquid swirl flow with shear-thinning liquid prohibits a core-annulus flow structure. A smaller index n contributes to maintaining the development of the swirl flow field and its core-annulus flow structure so that the swirl flow can form over a shorter distance with a stronger intensity. For a more uniform distribution of the apparent viscosity, the gas column in the pipe center is thinner. On the other hand, a larger consistency k enlarges the stress tensor. The amplitude of the velocity and the pressure of the core-annulus flow structure are reduced. A weaker swirl intensity appears with a wider gas column appearing as a consequence. Furthermore, the swirl number decays with an exponential behavior with parameters sensitive to the consistency k and index n of the decaying section of the swirling flow field. These are beneficial to gas–liquid separator design and optimization when encountering the shear-thinning power-law liquid phase in the petroleum industry.

Thermocapillary patterning of non-Newtonian thin films

Deformation of thin viscous liquid films exposed to a transverse thermal gradient results in Bénard–Marangoni instability, which would lead to the formation of micro- and nano-sized features. Linear and nonlinear analyses are performed to investigate the thermally induced pattern formation in shear thinning and shear thickening liquid films. The so-called thin film (TF) equation is re-derived to include viscosity variations using the power-law (PL) model. The characteristic wavelength for the growth of instabilities is found using a linear stability analysis of the PL-TF equation. A finite-difference-based discretization scheme and adaptive time step solver are used to solve the PL-TF equation for the nonlinear numerical model. The results show that the rheological property affects the timescale of the process and the size and final shape of the formed features. The fastest growth pillar reaching the top substrate in a shear thickening fluid is shorter than both the shear thinning and the Newtonian fluid cases. Moreover, morphological changes between patterns of shear thinning and shear thickening fluids are correlated with local viscosity variations. The number of formed pillars considerably increases with the increasing flow behavior index. The existing model also predicts the formation of pillars and bicontinuous structures at very low and high filling ratios.

Bubble's rise characteristics in shear-thinning xanthan gum solution: a numerical analysis

The rise of gaseous bubbles in shear-thinning liquid is a fundamental issue in fluid physics, particularly the bubbles rise dynamics in water-soluble xanthan gum concentration have a strong link for enhancing the stability of foams that have been encountered extensively in oil recovery, methane hydrate formation processing, froth flotation, and food and beverage industries. Here, air bubble rise behavior in xanthan gum solution (XGs) was investigated by using a coupled volume of fluid with the level set approach in CFD (computational fluid dynamics) modelling. The Carreau-Yasuda rheological model was adopted to define the viscous properties of the XGs and the continuum surface force model was used to track the interface between bubble and XGs. Additionally, ANN (artificial neural network) modeling was demonstrated for estimating the outputs of CFD. Our estimated CFD results for different bubble terminal velocities in water and experimental data obtained from the literature showed that there was a maximum relative error of 4.51%. Then, the CFD setup was utilized to investigate the effect of different concentrations of XGs and liquid flow index (N) on bubble rise dynamics within the bubble Reynolds number (Reb) range up to 10.05 and Eotvos number (Eo) range up to 3.47. For a fixed bubble size, the dimensionless bubble terminal velocity decreased in increased flow index and concentration of XGs, which led to decrease Reb and increase Eo. For a given XGs, the dimensionless bubble terminal velocity significantly depends on Reb and Eo. It was found that XGs and flow index significantly affect the distribution of dimensionless liquid viscosity than that of the dimensionless liquid velocity close to the bubble's underneath region. In a comparison with the rheological power-law model, the Carreau-Yasuda model showed to predict more accurate results. The estimated drag coefficient showed a deviation from the empirical equation reported in the literature, in contrast, a more accurate estimation in drag coefficient was obtained based on modified Reynolds number and Archimedes number. ANN modelling outputs agreed with CFD results and indicated that the training and testing of ANN have great efficiency to predict unknown values.

The shape and drag coefficient for a single bubble rising in stagnant shear-thinning viscoelastic liquids

The motion of a single bubble rising in stagnant shear-thinning viscoelastic liquids was investigated using a high-speed camera. The recorded images were analyzed using MATLAB with a self-written code in order to obtain the bubble volume and velocity. Using the experimental observations, a simple shape map was proposed based on the Reynolds number and the Deborah number. The bubble velocity was also investigated, and the phenomenon of velocity jump was observed in the Polyacrylamide (PAA) solutions. Furthermore, an empirical correlation was proposed to predict the drag coefficient of bubbles rising instagnant shear-thinning viscoelasticliquids. The predicted results of the correlation showed good conformity with the experimental values corresponding to the PAA solutions of different concentrations and 95 wt% glycerin solution.

The effect of the cavity formation on the energy consumption characteristics of the agitated gas–liquid bioreactor

Detailed power consumption characteristics from experiments and simulations of gas–liquid stirred tanks with shear-thinning power-law liquids are presented. The motion of bubbles was investigated based on the Euler–Euler approach with a bubble cluster concept. The drag coefficient of bubbles with a constant bubble diameter was modeled as the Schiller and Naumann function. The predicted power consumption of a gas–liquid mixture shows reasonable agreement with experimental data with a maximum deviation of 8.9%. For the studied aerated systems, a qualitatively new power reduction correction equation was derived and demonstrated a reasonable agreement with experimental results compared with the literature-reported equations. The effect of the concentrations and gas flow rates on power consumption was presented. It was found that the power consumption of different mixtures is related to the change in the critical generalized Reynolds number, which was Reg = 440, 230, 100, 30, and 25 for 0.2%, 0.4%, 0.62%, 0.85%, and 1.25%, respectively.

Macroscopic rheology of non-Brownian suspensions at high shear rates: the influence of solid volume fraction and non-Newtonian behaviour of the liquid phase

Modelling the macroscopic rheology of non-Brownian suspensions is complicated by the non-linear behaviour that originates from the interaction between solid particles and the liquid phase. In this contribution, a model is presented that describes suspension rheology as a function of solid volume fraction and shear rate dependency of both the liquid phase, as well as the suspension as a whole. It is experimentally validated using rotational rheometry (varphi ≤ 0.40) and capillary rheometry (0.55 ≤ varphi ≤ 0.60) at shear rates > 50 s−1. A modified Krieger-Dougherty relation was used to describe the influence of solid volume fraction on the consistency coefficient, K, and was fitted to suspensions with a shear thinning liquid phase, i.e. having a flow index, n, of 0.50. With the calculated fit parameters, it was possible to predict the consistency coefficients of suspensions with a large variation in the shear rate dependency of the liquid phase (n = 0.20–1.00). With increasing solid volume fraction, the flow indices of the suspensions were found to decrease for Newtonian and mildly shear thinning liquid phases (n ≥0.50), whereas they were found to increase for strongly shear thinning liquid phases (n ≤0.27). It is hypothesized that this is related to interparticle friction and the relative contribution of friction forces to the viscosity of the suspension. The proposed model is a step towards the prediction of the flow curves of concentrated suspensions with non-Newtonian liquid phases at high shear rates.

Onset about non-isothermal flow of Williamson liquid over exponential surface by computing numerical simulation in perspective of Cattaneo Christov heat flux theory

In view of increaing significance of non-isothermal flow of non-Newtonian fluids over exponential surfaces in numerous industrial and technological procedures such as film condensation, extrusion of plastic sheets, crystal growth, cooling process of metallic sheets, design of chemical processing equipment and various heat exchangers, and glass and polymer industries current disquisition is addressed. For comprehensive examination Williamson model expressing the attributes of shear thickening and thinning liquids is taken under consideration. The physical aspects of magnetic field applied in transverse direction to flow is also accounted. Heat transfer aspects are incorporated and analyzed by employing Cattaneo-Christov heat flux model. Mathematical formulation of problem is conceded in the form of PDE’s by implementing boudary layer approach and later on converted into ODE’s with the assistance of transformation procedure. The resulting equations are solved numerically using shooting and Runge–Kutta methods. Impact of involved parameters on flow distributions is displayed through graphs. From the analysis it is inferred that Cattaneo Christov heat flux law exhibits hyperbolic equation which follows the causality principle and make the problem more compatible to real world applications. It is also deduced that magnetic field suppresses the velocity field and associated boundary layer region. Decrease in temperature profile and heat transfer coefficient is found against inciting magnitude of thermal relaxation parameter. Substantial decrease in velocity is found against increasing magnitude of Williamson fluid parameter and magnetic field parameter whereas skin friction coefficient increments. Confirmation about present findings is executed by making comparison with existing literature.

Coalescence of Microscopic Polymeric Drops: Effect of Drop Impact Velocities.

In this paper, we employ the direct numerical simulation (DNS) method for probing three-dimensional, axisymmetric coalescence of microscale, power-law-obeying, and shear-thinning polymeric liquid drops of identical sizes impacting a solid, solvophilic substrate with a finite velocity. Unlike the cases of drop coalescence of Newtonian liquid drops, coalescence of non-Newtonian polymeric drops has received very little attention. Our study bridges this gap by providing (1) the time-dependent, three-dimensional (3D) velocity field and 3D velocity vectors inside two coalescing polymeric drops in the presence of a solid substrate and (2) the effect of the drop impact velocity (on the solid substrate), quantified by the Weber number (We), on the coalescence dynamics. Our simulations reveal that the drop coalescence is qualitatively similar for different We values, although the velocity magnitudes involved, the time required to attain different stages of coalescence, and the time needed to attain equilibrium vary drastically for finitely large We values. Finally, we provide detailed simulation-based, as well as physics-based, scaling laws describing the growth of the height and the width of the bridge (formed due to coalescence) dictating the 3D coalescence event. Our analyses reveal distinct scaling laws for the growth of bridge height and width for early and late stages of coalescence as a function of We. We also provide simulation-based coalescence results for the case of two unequal sized drops impacting on a substrate (nonaxisymmetric coalescence) as well as results for axisymmetric coalescence for drops of different rheology. We anticipate that our findings will be critical in better understanding events such as inkjet or aerosol jet polymer printing, dynamics of polymer blends, and many more.

Numerical study on the influence of liquid viscosity ratio on the hydrodynamics of a single bubble in shear-thinning liquid

The volume of fluid method combined with the adaptive grid method is used to study the influence of shear-thinning liquid viscosity ratio (ε) for various values of rheological index (n) and characteristic time (λ) on bubble shape, rise velocity, and apparent viscosity around a bubble; where 1/λ represents the shear rate at which the change in the viscosity curve occurs from the low shear rate to the power-law region. The results show that, depending on the magnitudes of n and λ, the bubble shape and deformation parameter are strongly related to ε, and bubble shape can exhibit both stable and unstable states. There are two types of deformation phenomena for the unsteady deformation of bubbles. First, the aspect ratio changes with time, whereas the shape remains similar throughout. Second, the shape changes periodically with time. For the given values of n and λ, the bubble rise velocity at large time shows a nonlinear increase as ε increases from 10 to ∞. Under the conditions of n ≤ 0.3, λ* ≥ 68.6, and ε ≥ 100 (λ* is the dimensionless characteristic time), a viscosity blind region (a region of high viscosity, where ε is close to 1) appears behind the bubble. The tendency for the viscosity blind region is to reduce the bubble rise velocity at large time.

Hydrodynamic drag reduction of shear-thinning liquids in superhydrophobic textured microchannels

Super-hydrophobic textured surfaces reduce hydrodynamic drag in pressure-driven laminar flows in micro-channels. However, despite the wide usage of non-Newtonian liquids in microfluidic devices, the flow behaviour of such liquids was rarely examined so far in the context of friction reduction in textured super-hydrophobic micro-channels. Thus, we have investigated the influence of topologically different rough surfaces on friction reduction of shear-thinning liquids in micro-channels. First, the friction factor ratio (a ratio of friction factor on a textured surface to a plain surface) on generic surface textures, such as posts, holes, longitudinal and transverse ribs, was estimated numerically over a range of Carreau number as a function of microchannel constriction ratio, gas fraction and power-law exponent. Resembling the flow behaviour of Newtonian liquids, the longitudinal ribs and posts have exhibited significantly less flow friction than the transverse ribs and holes while the friction factor ratios of all textures has exhibited non-monotonic variation with the Carreau number. While the minima of the friction factor ratio were noticed at a constant Carreau number irrespective of the microchannel constriction ratio, the minima have shifted to a higher Carreau number with an increase in the power-law index and gas fraction. Experiments were also conducted with aqueous Xanthan Gum liquids in micro-channels. The flow enhancement (the flow rate with super-hydrophobic textures with respect to a smooth surface) exhibited a non-monotonic behaviour and attenuated with an increase in power-law index tantamount to simulations. The results will serve as a guide to design frictionless micro-channels when employing non-Newtonian liquids.

Motion of a confined bubble in a shear-thinning liquid

Abstract

Rheology and tribology of starch + κ-carrageenan mixtures.

In this study, we investigated the rheological and tribological properties of biopolymer mixtures of gelatinized corn starches (0.5 – 10.0 wt%) and κ‐carrageenan (κC) (0.05 – 1.0 wt%). Two different starch samples were used. The first starch (CS1), despite extensive heating and shearing contained “ghost” granules, while the second starch (CS2) had no visible ghost granules after the same gelatinization process as CS1. Apparent viscosity measurements demonstrated that κC + CS1 mixtures were shear thinning liquids, with viscosity values being lower than the corresponding weight average of the values of the individual equilibrium phases at shear rates < 50 s−1. Tribological results revealed that κC ≥ 0.5 wt% was required to observe any decrease in friction coefficients in the mixed lubrication regime. Starch (CS1) showed an unusual behavior at ≥ 5 wt%, where the friction coefficient decreased not only in the mixed regime but also in the boundary regime, probably due to the presence of the “ghost” granules, as the latter became entrained in the contact region. The CS1 + κC mixtures showed significantly lower friction coefficients than that of pure CS1 and κC in the mixed regime. However, the CS2 + κC mixture (i.e., containing no ghost granules) showed similar behavior to pure κC in the mixed regime, while lower friction coefficients than that of the pure CS2 and κC in the boundary regime. These findings illustrate new opportunities for designing biopolymer mixtures with tunable lubrication performance, via optimizing the concentrations of the individual biopolymers and the gelatinization state of the starch.

Effect of Non-Newtonian Dynamics on the Clearance of Mucus From Bifurcating Lung Airway Models.

Mucus hypersecretion is a common pathophysiological manifestation of several obstructive airway diseases in which the mucociliary clearance is impaired, and the airflow generated by a cough or a forced expiratory maneuver called the huff is primarily responsible for clearing mucus. This airflow driven clearance of mucus is a complex process that is affected by the mucus rheology, airflow rate, airway geometry, and gravity. This study examines the role of mucus rheology in the transport and distribution of mucus in idealized 3D airway geometries. The complex air-mucus interface was tracked by the volume-of-fluid (VOF) model, and the turbulence in the core airflow was modeled using the k-ω shear stress transport (SST) model. Mucus was modeled as a shear-thinning liquid by using a power-law model. The computational model was validated using in vitro experimental data available in the literature. Gravity-dominated eccentric core-annular flow was observed with the core biased toward the outer wall in the inclined daughter branches of the bifurcation models, which transitions into concentric core-annular flow in the trachea. The increase in tangential shear at the interface due to the secondary flow structures developed in the flow divider location resulted in a region of enhanced mucus clearance with reduced mucus layer thickness. Secondary flow developed due to the curvature in the airway geometry resulted in a local redistribution of mucus that reduced the eccentricity. The accumulation of mucus around the carinal ridges and the regions with reduced clearance are sites with the potential for microbial growth.

A novel gas inducing rotor-stator impeller for gas-liquid foam generation

A novel gas inducing rotor-stator impeller was used to produce foam from viscous non-Newtonian shear thinning liquid and non-ionic surfactant Tween 80. Foam produced under various experimental conditions, was characterised based on the bubble size and foam half-life. Higher impeller speed and solution viscosity, resulted in smaller size bubbles and more stable foam. Higher gas hold-up is associated with reduction in bubble size and, longer mixing times resulted in increase in bubble size because of coalescence. Empirical models were developed to predict the foam bubble size and its half-life and a good correlation between the measured data and the predicted data was obtained (R2 > 0.94). Foam bubble size was found to be a function of Reynolds number, mixing time number and Froude number. Foam half-life was found to be dependent on the same dimensionless number along with the Weber number. It is shown that, gas inducing impeller, can produce foam with similar properties at ambient conditions and with better process control, compared to foam produced by conventional agitation-based devices.

Laminar Forced Convection in Viscous Shear-Thinning Liquid Flows Inside Circular Pipes: Case for a Modified Power-Law Rheology

Abstract Laminar forced convection in viscous, non-Newtonian polymeric liquids that exhibit pseudoplastic or shear-thinning behavior is characterized. The fluid rheology is characterized by a new asymptotic power-law (APL) model, which appropriately represents extensive data for apparent viscosity variation with shear rate—from the low-shear constant-viscosity plateau to shear thinning at high shear rates. This is contrasted with the traditional Ostwald-de-Waele or power-law (PL) model that invariably over-extends the pseudoplasticity in the very low shear-rate region. The latter's limitations are demonstrated by computationally obtaining frictional loss and convective heat transfer results for fully developed laminar flows in a circular pipe maintained at uniform heat flux. The Fanning friction factor and Nusselt number, as would be anticipated from the rheology map of pseudoplastic fluids, are functions of flow rate with the APL model unlike the Newtonian-like constant value obtained with the PL model. Comparisons of the two sets of results highlight the extent of errors inherent in the PL rheology model, which range from 23% to 68% for frictional loss and 3.8% to 13.7% for heat transfer. The new APL rheology model is thus shown to be the more precise characterization of viscous shear-thinning fluids for their thermal processing applications with convective heat transfer.

Hydrodynamics of gas/shear-thinning liquid two-phase flow in a co-flow mini-channel: Flow pattern and bubble length

The flow patterns and bubble characteristics formed during gas–liquid flows in a circular co-flow mini-channel with carboxymethyl cellulose (CMC) aqueous solutions are investigated experimentally. The pattern transition and bubble length are elucidated by systematically analyzing the influences of the various factors of the ratio of gas–liquid flow rates, CMC solution mass fraction, and surfactant [sodium dodecyl sulfate (SDS)] mass fraction. Five kinds of flow regimes, namely, bubbly flow, Taylor flow, Taylor-annular flow, annular flow, and churn flow, are identified visually in the fully developed region of the inlet side of the channel, and a universal flow-regime map in terms of the gas and liquid inlet flow rates is constructed using water, CMC solution, and polyacrylamide solution to cover a broad range of material properties. It is found that the ratio of gas–liquid flow rates has a remarkable influence on the flow pattern transitions. The CMC solution mass fraction and SDS mass fraction can also affect the flow-regime map by varying the flow drag force and surface tension acting on the bubble in the mini-channel. The bubble length increases with the ratio of gas–liquid flow rates but decreases with the increase in the CMC fraction and SDS fraction. Based on consideration of the rheological properties of the liquid, a scaling law of bubble length in a co-flow mini-channel with shear-thinning liquids is developed, and the results predicted by it can agree with the measurement data very well under present conditions.

Characterization of the shear-thinning behavior of asphalt binders with consideration of yield stress

This study focused on characterizing the shear-thinning behavior of asphalt binders. The first objective was to identify the existence of yield stress behavior and to employ a rheological model to describe the flow curve of asphalt binders. The second objective was to verify the applicability of the Cox–Merz rule to asphalt binders with consideration of yield stress. A Dynamic Shear Rheometer (DSR) was employed to perform the frequency sweep test and the shear rate sweep test on three types of neat asphalt binders at 50, 60 and 70 °C. The test results of both tests confirmed the yield stress behavior of selected asphalt binders. The asphalt binders were then classified as the shear-thinning liquids with yield stress. As a result, the zero shear viscosity (ZSV), which was utilized as a rutting indicator, was not an indicator of the shear viscosity at zero shear rate but corresponded to the shear viscosity of a Newtonian plateau at low shear rates. A modified Carreau model was employed to characterize the shear-thinning behavior of asphalt binders, which demonstrated the ability to account for the yield stress behavior. The applicability of the Cox–Merz rule was examined by establishing the flow curve and the log–log plot of complex viscosity versus angular frequency in the same graph with respect to each replicate at each temperature. It was demonstrated that the Cox–Merz rule was followed in part of the ZSV region and part of the shear-thinning region but not followed in the yield stress region.