Viscosity Model Research Articles

Postglacial relative sea-level changes in the Gulf of Maine, USA: Database compilation, assessment and modelling

Relative sea level (RSL) reconstructions from paleo records are often the most valuable data set for testing and constraining glacial isostatic adjustment (GIA) models. In some regions, the amplitude and rate of the reconstructed RSL changes are large making the data difficult to fit. Arguably, the reconstructed RSL curve from Maine, USA, is the classic example of such a data set with peak values at about 120 m dropping to a low stand of around −40 m within a few thousand years. To our knowledge, no GIA model has captured these extreme variations and the record has been somewhat neglected by the GIA modelling community. Here we critically assess and present a revised pre-10 ka RSL data base for this region and combine it with two recent Holocene compilations. Based on our assessment, we conclude that the large and rapid changes, inferred in previous studies, are robust. To determine if a successful model fit can be found, we consider a GIA parameter set comprising five ice models and 440 spherically-symmetric, Earth viscosity models assuming a Maxwell rheology. Results show that none of the model parameter sets produce a good fit to the data set. The rapid RSL fall and lowstand can be simulated by Earth models with low values of upper mantle viscosity (∼5 × 1019 Pas). However, such low viscosity values result in a large mid-Holocene highstand (order 10 m) while the observations indicate a monotonic RSL rise throughout this interval. Our results indicate that Earth models able to simulate time-dependent viscosity (i.e., those that include transient and/or non-Newtonian deformation) might be required to fit the Maine RSL data set.

Enhancing partial least squares modeling of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry data by tile-based variance ranking

Chemometric methods like partial least squares (PLS) regression are valuable for correlating sample-based differences hidden in comprehensive two-dimensional gas chromatography (GC × GC) data to independently measured physicochemical properties. Herein, this work establishes the first implementation of tile-based variance ranking as a selective data reduction methodology to improve PLS modeling performance of 58 diverse aerospace fuels. Tile-based variance ranking discovered a total of 521 analytes with a square of the relative standard deviation (RSD2) in signal between 0.07 to 22.84. The goodness-of-fit for the models were determined by their normalized root-mean-square error of cross-validation (NRMSECV) and normalized root-mean-square error of prediction (NRMSEP). PLS models developed for viscosity, hydrogen content, and heat of combustion using all 521 features discovered by tile-based variance ranking had a respective NRMSECV (NRMSEP) equal to 10.5 % (10.2 %), 8.3 % (7.6 %), and 13.1 % (13.5 %). In contrast, use of a single-grid binning scheme, a common data reduction strategy for PLS analysis, resulted in less accurate models for viscosity (NRMSECV = 14.2 %; NRMSEP = 14.3 %), hydrogen content (NRMSECV = 12.1 %; NRMSEP = 11.0 %), and heat of combustion (NRMSECV = 14.4 %; NRMSEP = 13.6 %). Further, the features discovered by tile-based variance ranking can be optimized for each PLS model with RReliefF analysis, a machine learning algorithm. RReliefF feature optimization selected 48, 125, and 172 analytes out of the original 521 discovered by tile-based variance ranking to model viscosity, hydrogen content, and heat of combustion, respectively. The RReliefF optimized features developed highly accurate property-composition models for viscosity (NRMSECV = 7.9 %; NRMSEP = 5.8 %), hydrogen content (NRMSECV = 7.0 %; NRMSEP = 4.9 %), heat of combustion (NRMSECV = 7.9 %; NRMSEP = 8.4 %). This work also demonstrates that processing the chromatograms with a tile-based approach allows the analyst to directly identify the analytes of importance in a PLS model. Coupling tile-based feature selection with PLS analysis allows for deeper understanding in any property-composition study.

Thermodynamic properties, viscosity modelling and FTIR studies of binary liquid mixtures of 2-isopropoxy ethanol with amines at different temperatures

Thermodynamic and spectral analysis for binary liquid mixtures of 2-isoporopxy ethanol with diisopropylamine, di-n-butylamine and tri-n-butylamine has been carried out in the present discussion. For this purpose, measurements of density, speed of sound and viscosity for binary mixtures were carried out over the entire composition range and at temperatures (298.15, 303.15 and 308.15) K. Various excess and deviation parameters were evaluated using the measured properties. Behaviour of calculated parameters was found quite sensitive towards the intermolecular interactions. Change in behaviour of these parameters with composition and temperature has been discussed in terms of intermolecular interactions due to physical and chemical effects among unlike molecules. Excess parameters were correlated with composition using Redlich-Kister polynomial. Existing theories and semi-empirical relations for viscosity were tested. Spectroscopic methods were also utilized to support the results obtained from above calculated parameters qualitatively.

The SquAd derivation: A Square Additive approach to the turbulent Prandtl number.

Liquid metals have been chosen as primary coolant of innovative nuclear systems under current development. They present a very high thermal conductivity and hence a very low molecular Prandtl number. This feature challenges the modeling of turbulent thermal flows applying the Reynolds analogy. This paper addresses this challenge. A new formula for the turbulent Prandtl number is derived in terms of local variables available from two-equations turbulence models. The derivation is a direct consequence of the expected square additivity of the molecular and flow parameters defining the effective viscosity and the effective conductivity. The formula does not degenerate and leads to a Kays like formulation if approximated. While constrained by the quality of the turbulent viscosity modeling, it has the potential to improve the numerical simulation of turbulent thermal flows.

On the mathematical theory of plumes

ABSTRACT We reconsider the theory of turbulent plume formation provided by Schmidt (1941a,b) and its integral formulation, particularly that of Morton et al. (1956). A particular issue for the correct formulation of a mathematical theory is whether the plume is taken to have finite or infinite width, and whether the entrainment rate is prescribed or deduced. Fox (1970) showed that the entrainment rate for a plume can be deduced from the governing partial differential equations by the use of integral moment theory, providing one assumes expressions for the velocity and buoyancy profiles, but it is less clear if entrainment needs to be prescribed if the plume is taken to be of infinite width (as might be appropriate for a laminar plume). Here we choose an eddy viscosity model of a plume which differs from those previously used by allowing the eddy viscosity to vanish with the vertical velocity. We then show that for the ordinary differential equations describing the similarity solution for such a plume rising in an unstratified medium, their solution implies that the plume is finite, and that the entrainment rate at the plume edge is a consequence of the model formulation, and does not need to be hypothesised; and we also show that the entrainment coefficient which is thus determined is consistent with values obtained by experiment. We also show that the resulting velocity profiles differ from those found experimentally by their omission of the Gaussian tail, and we suggest that this discrepancy may be resolved in the model by the inclusion of the small molecular kinematic viscosity.

Cosmology with viscous generalized Chaplygin gas in [formula omitted] gravity

We use the hybrid model of bulk viscosity and generalized chaplygin gas (GCG), named the viscous generalized chaplygin gas (VGCG) model, which is thought to be an alternate dark fluid of the universe. We explore the dynamics of the VGCG model in the framework of the non-metricity f(Q) gravity using the functional form f(Q)=βQn, where β and n are arbitrary constants. For the purpose of constraining model parameters, we use recent observational datasets such as Observational Hubble data, Baryon Acoustic Oscillations, and Type Ia supernovae data. According to our study, the evolution of the deceleration parameter q and the equation of state (EoS) parameter w shows a transition from deceleration to an acceleration phase and its deviation from the ΛCDM model.

An Effect of a Porous Structure, Slip Velocity and Rosensweig’s Viscosity on the Ferrofluid Based Squeeze Film in Porous Curved Annular Plates

An endeavor has been made to analyze porous squeeze film performance in curved annular plates considering slip velocity, Kozeny-Carman’s porous structure and Rosensweig’s viscosity in Shliomis model-based magnetic fluid lubrication. The globular sphere model of Kozeny-Carman for porous facing is adopted here. An extension of the Einstein’s viscosity for ferrofluid proposed by Rosensweig is considered here to improve the viscosity of ferrofluid for the Shliomis model, while Beavers and Joseph’s slip model is used for evaluating the slip effect. The pressure and load lifting capacity in dimensionless form is obtained by modifying the Reynolds equation incorporating the Rosensweig’s viscosity, Kozeny-Carman’s model-based porosity, slip and Shliomis model-based ferofluid lubrication. The graphical representation reveals that load carrying capacity (LCC) can be increased by increasing the curvature of upper plates, volume concentration and magnetization parameter but decrease with the slip velocity, porous structure parameter and porosity parameter. This study indicates that the load-bearing capacity remains higher as compared to the case of Einstein’s viscosity model. However, this investigation conclusively establishes that the Shliomis model goes ahead of the other two magnetic fluid flow models in overall improvement of bearing performance characteristics. Interestingly, even considerable amount of slip may not pose a serious problem when Kozeny-Carman’s model is resorted to. This investigation reveals that this type of bearing system sustains good amount of load even in the absence of flow which does not happen in the case of conventional bearing system.

Injection molding of semi‐crystalline polymers in a space‐time framework

AbstractThe challenges in the numerical simulation of the polymer injection molding process are manifold. Such simulation involves a two‐phase flow formulation and the physical modeling of complex material, i.e., molten polymer. This paper presents a complete macroscale simulation approach for the filling stage of injection molding with semi‐crystalline polymers, applied on polypropylene as example. Accurate and efficient results are obtained using a space‐time finite‐element discretization. Heading towards more efficient computations, we search for a reduction of the polymer's physical model, which includes variable viscosity, density, and several crystallization models. The final contribution of the present work is a model sensitivity analysis, which evaluates the relevance of each material model during the filling stage of injection molding.

Kinetic stability and rheological properties of photosensitive zirconia suspensions for DLP printing

Digital light processing (DLP) is a rapidly developing technology accessing the opportunity to print complex ceramics objects. The main prerequisite for successful printing is the preparation of kinetically stable suspension with low viscosity and homogenous distribution of perfectly dispersed particles. All three mentioned assumptions could be fulfilled by a selection of a suitable dispersant and starting zirconia powder. In this paper, a commercial agent Disperbyk-103 was used to create a highly stable suspension with 30 vol% of zirconia powder with appropriate viscosity (0.93 Pa s at a shear rate of 10 s−1). The optimal concentration of the agent was set not only by rheological measurements but also with the help of measurement of the kinetic stability over time using an analytical centrifuge. Stability measurement was evaluated as an appropriate supplementary analysis to the conventional viscosimetric analysis. Furthermore, the predictive viscosity models were tested either as a tool how to estimate the maximum solid volume fraction for the ceramic suspensions as well as for the prediction of suspension dynamic viscosity according to the used solid content in the prepared suspension. Finally, the suspension with the most suitable physicochemical properties was printed, sintered, and subsequently characterized using the analysis of mechanical properties by the Vickers hardness (1315 HV), relative density (98.2%) and shrinkage. The presented work points to the excellent possibility of using stability analysis as a complementary ceramic suspension analysis.

Soret and Dufour effects on MHD nanofluid flow of blood through a stenosed artery with variable viscosity

This study deals with the effects of Soret and Dufour on MHD nanofluid flow through a composite stenosed artery having temperature-dependent viscosity. To determine the radiation effect in the energy equation, the Rosseland approximation has been considered in this study. The Reynolds viscosity model has been considered to describe the influence of temperature dependent viscosity. The governing equations of the model are solved numerically by applying “Finite Difference Method”. The effects of the above-mentioned parameters on the velocity, temperature and concentration along the radial axis have been studied and are physically interpreted for medical applications. Shear stress, heat transfer and mass transfer effects have been examined. The heat and mass transfer effects are studied using the Nusselt number and Sherwood number, respectively. Shear stress, Sherwood number and Nusselt number are analyzed with the help of graphs for different physical parameters along with the height of stenosis. Temperature increases with the Soret number as thermophoretic diffusion increases due to temperature gradient and decreases with the Dufour number as concentration gradient causes a decrease in energy flux. In this paper, we studied the CuNPs with blood as a base fluid under an external magnetic field. CuNPs are of great interest for many reasons, including low cost and easy availability and their similar properties to those of noble metals like silver, gold, etc. Recently, biological applications of CuNPs have been considered for several usages, such as drug delivery, antibacterial, antifungal, antiviral, anticancer, and novel therapeutic agents for combating other diseases. Enhancement in the copper nanoparticle volume fraction resulted in an increase in the thermal conductivity and dissipation of heat throughout the stenosed artery resulted in a decline of the temperature profile. This study contributes to the understanding of the nonsurgical treatment of stenosis and other anomalies, as well as the minimization of post-operative complications. Further, these studies may be helpful in the biomedical field such as magnetic resonance angiography (MRA) to take the image of an artery to locate the abnormalities in the artery.

Variable fluid properties analysis for thermally laminated 3-dimensional magnetohydrodynamic non-Newtonian nanofluid over a stretching sheet

This article is mainly focused on the viscous flow of cu-water/Methanol suspended nanofluids towards a three-dimensional stretching sheet reformed by magnetohydrodynamic phenomenon. The viscous effect is considered as temperature dependent with water treated as a base fluid. Similarity conversions are employed to set forth the non-linear equations of this physical problem. An innovative model for 3D analysis for cu-water/Methanol nanofluid with an irregular viscosity is presented in the present study. Reynold’s model of viscosity is considered in the present study. Moreover, shooting technique is employed to elaborate the non-linear coupled governing equations with the relevant boundary conditions. The physical interpretation of these numerical calculations is presented through a graphical specimen of velocity, Nusselt number, temperature, and skin friction etc. The results of present model are showing quality harmony with the results of existing model. This model is being used for manipulating and designing the surfaces such as stretching/shrinking wrapping and panting devices in nanotechnology. The results also show the significant changes in flow characteristics with changing the value of stretching parameter. It is observed that with an increasing in nanoparticles volume fraction boundary layer thickness decreases. Further, it is also observed that with an increase in viscosity parameter, temperature increases because here we are considering temperature dependent viscosity.

Mathematical modeling for experimental data to investigate the convective heat transfer in non‐Newtonian nanofluid's flow over a thin needle

AbstractThe flow of homogeneous non‐Newtonian nanofluid over a horizontal moving thin needle is studied through experimental data‐based mathematical approach. Experimental data is collected for nanofluids which are prepared by spreading the SiO2, MgO, and TiO2 nanoparticles with correspondingly diameters (20–30 nm, 60–70 nm), (20, 40 nm), and (30, 50 nm) at volume fractions (5%–20%) in ethylene glycol (EG). The rheological power‐law model of viscosity is employed on the current experimental data to govern the co‐relation expression and is further used in heat and mass flow equations. The problem is reduced to ordinary differential equations by employing similarity conversion and then numerically solved. The influence of various volume fractions and diameter of nanoparticles on the distribution of velocity and temperature are discussed through the graphical results. Moreover, velocity and thermal boundary layer thicknesses, momentum and displacement thickness, skin friction coefficient, and Nusselt number are also studied in detail and displayed graphically. The results indicate that enhancing nanoparticle volume fraction causes the decline in velocity profile and rise in temperature profiles. On the contrary, the velocity is amplified and temperature is reduced with enhancing the diameter of the nanoparticle. Newtonian model for nanofluid is not valid in all cases. So, a non‐Newtonian model is applied for nanofluid flow that follows the experimental behavior in the current study. This experimental based model has not investigated before.

Integrated modeling of heat transfer, shear rate, and viscosity for simulation-based characterization of polymer coalescence during material extrusion

The material extrusion process (MEX), also known as the fused filament fabrication process, has attracted attention in the manufacturing industry. A major obstacle to further application of the technology is the lack of mechanical strength due to the weak interlayer strength and poor coalescence between the adjacent beads. Understanding the effect of printing parameters on the coalescence of the adjacent beads is a step toward the improvement of the process. In this study, a novel two-phase flow numerical simulation approach coupled with heat transfer simulation has been applied to the high-viscosity polymers to determine the coalescence in the MEX process. The influence of printing temperature, substrate temperature, and the temperature of the printing chamber, as well as material deposition strategy (unidirectional and bidirectional) on the coalescence of the beads, has been investigated by numerical simulation and validated by experimental study. The modeling approach is applied to Glycerol, Polyether ether ketone (PEEK) and Polylactic acid (PLA). The results show that increasing temperature points (substrate temperature, chamber temperature, and printing temperature), increase the coalescence between the beads in the MEX process. The heat transfer model reveals that the cooling rate of the deposited bead in the MEX process is relatively high, and hence, the time window for reaching the coalescence between beads/layers is short. The heat transfer model also indicates that deposition of the further layers and beads does not influence the coalescence. The coalescence in the bidirectional deposition is higher compared to the unidirectional all conditions remaining similar. Unidirectional deposition leads to a uniform coalescence between the beads. However, the coalescence is not uniform for bidirectional deposition. The main novelty of this research is to simultaneously model heat transfer, shear rate and coalescence for numerical simulation to study the effect of printing parameters on the coalescence in the MEX process. Since the modeling of coalescence is time-consuming, two empirical equations based on obtained results have been proposed to predict the coalescence for PLA and PEEK separately.

Wall Layer Formation in Continuously Operated Tubular Reactors for Free‐Radical Polymerizations

AbstractPolymer fouling is a major problem for the operation of continuous reactors. Therefore, it is important to understand and quantitatively describe the mechanisms leading to formation of fouling deposits. In this work, a CFD model for the radical polymerization of N‐vinylpyrrolidone is presented, where the reaction kinetics, a viscosity model, and a transport model for polymer moments are determined from independent experiments. The model is compared to experimental obtained residence time distributions in capillary reactors over a wide range of concentrations. Model predictions are in good agreement with experimental findings.

Assessment of Irregular Biomass Particles Fluidization in Bubbling Fluidized Beds

Biomass as a clean and renewable source of energy has immense potential to aid in solving the energy crisis in the world. In order to accurately predict the fluidization behavior of biomass particles using the Eulerian–Eulerian approach and the kinetic theory for granular flows (KTGF), employing appropriate models that adapt to irregularly shaped particles and can precisely predict the interaction between particles is crucial. In this study, the effects of varying radial distribution functions (RDF), frictional viscosity models (FVM), angles of internal friction (ϕ), and stress blending functions (SBF) on the performance of two-fluid models (TFM) were investigated. Simulation predictions were compared and validated with the previous experiments in the literature on Geldart B biomass particles of walnut shells. When applying sphericity to account for size irregularities of biomass particles, the results of this study demonstrated that predictions of both the Ma–Ahmadi and the Carnahan–Starling RDFs along with the Schaeffer FVM agree with experimental data. More specifically, the bubbling behavior prediction slightly favored the use of the Ma–Ahmadi RDF for biomass particles. The results also revealed the importance of using FVM regardless of the initial void fraction. The use of the Schaeffer FVM became more important as time proceeded and particle bulk density decreased. With the change of ϕ and the application of SBF, no significant differences in the time-averaged results were observed. However, when ϕ ranges were between 30 and 40, the predictions of bubbling behavior became more greatly aligned with experimental results.

Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.

Active flow control of the airflow of a ship at yaw

This paper implements the steady Coanda effect active flow control (AFC) on the Chalmers ship model (CSM) to study its influence on the ship’s side force and airwake under the yaw effect. The study is conducted numerically using Large Eddy Simulation (LES) with Wall-Adapting Local-Eddy Viscosity (WALE) model. Numerical methods are validated by the experimental data acquired from the baseline CSM under 10∘ port-side wind. The model with AFC is created by modifying the square-shaped hanger base to the Coanda surface and added with injection slots along the base’s roof edge and two side edges. The results show that the base-shape modification significantly alters the vortex structure on deck from z-direction vortex (ZV) to streamwise vortex (SV), and the steady Coanda effect with a momentum coefficient (Cμ) of 0.02 further enhances the SV with the removal of port-side vortex (PV). The side force and yaw moment are reduced by 5.27% and 7.97%, respectively in the AFC case due to the reduction of port-side (windward) ship-surface pressure. Furthermore, the current AFC can suppress the low-speed region and alleviate the velocity gradient in the lateral direction, which mitigates the regions of high TKE (turbulent kinetic energy) and high shear stress along the port-side deck.

Infinite shear rate viscosity of cross model over Riga plate with entropy generation and melting process: A numerical Keller box approach

This paper presents the effects of cross fluid model associated with entropy generation and melt process. The Cross-fluid viscosity model based on the infinite shear rate effect is taken with attaching Riga plate. Physical interpretation generates a system of partial differential equations (PDEs), and further, these are processed with similarity variables to attain a system of ordinary differential equations (ODEs). The numerical experiments are presented compared and discussed. Here, the numerical Keller Box approach is utilized. The obtained results indicate that the melt process loses the temperature and entropy generation enlarges the temperature visibility.

A new group contribution model for prediction liquid hydrocarbon viscosity based on free-volume theory

In this paper a group contribution model for predicting the viscosity values of n-alkanes and iso-alkanes in the liquid phase based on Free-Volume Theory was developed. A database with 2129 experimental data with a temperature range up to 573.15 K and a pressure range up to 4000 bar was used to develop the model. The total weighted average percentage error is 4.894%. The model was tested on the next 472 experimental data with a temperature range up to 564.15 K and a pressure range up to 2019 bar and a mean percentage error that was obtained is 5.155%.

Reynolds nano fluid model for Casson fluid flow conveying exponential nanoparticles through a slandering sheet

Nanofluids with their augmented thermal characteristics exhibit numerous implementations in engineering and industrial fields such as heat exchangers, microelectronics, chiller, pharmaceutical procedures, etc. Due to such properties of nanofluids, a mathematical model of non-Newtonian Casson nanofluid is analyzed in this current study to explore the steady flow mechanism with the contribution of water-based Aluminum oxide nanoparticles. A stretchable surface incorporating variable thickness is considered to be the source of the concerning fluid flow in two-dimension. An exponential viscosity of the nanofluid is proposed to observe the fluid flow phenomenon. Different models of viscosity including Brinkman and Einstein are also incorporated in the flow analysis and compared with the present exponential model. The physical flow problem is organized in the boundary layer equations which are further tackled by the execution of the relevant similarity transformations and appear in the form of ordinary nonlinear differential equations. The different three models of nanofluid viscosity exhibit strong graphical and tabulated relations with each other relative to the various aspects of the flow problem. In all concerned models of the viscosity, the deteriorating nature of the velocity field corresponding to the Casson fluid and surface thickness parameters is observed.