Fluids

2024

Jump to: 2022, 2021

26 pages, 7430 KiB

Open AccessArticle

Rheological Characterization of a Thixotropic Semisolid Slurry by Means of Numerical Simulations of Squeeze-Flow Experiments

by Georgios C. Florides, Georgios C. Georgiou, Michael Modigell and Eugenio José Zoqui

Fluids 2024, 9(2), 36; https://doi.org/10.3390/fluids9020036 - 31 Jan 2024

Viewed by 1399

Abstract

We propose a methodology for the rheological characterization of a semisolid metal slurry using experimental squeeze-flow data. The slurry is modeled as a structural thixotropic viscoplastic material, obeying the regularized Herschel–Bulkley constitutive equation. All rheological parameters are assumed to vary with the structure [...] Read more.

We propose a methodology for the rheological characterization of a semisolid metal slurry using experimental squeeze-flow data. The slurry is modeled as a structural thixotropic viscoplastic material, obeying the regularized Herschel–Bulkley constitutive equation. All rheological parameters are assumed to vary with the structure parameter that is governed by first-order kinetics accounting for the material structure breakdown and build-up. The squeeze flow is simulated using finite elements in a Lagrangian framework. The evolution of the sample height has been studied for wide ranges of the Bingham and Reynolds numbers, the power-law exponent as well as the kinetics parameters of the structure parameter. Systematic comparisons have been carried out with available experimental data on a semisolid aluminum alloy (A356), where the sample is compressed from its top side under a specified strain of 80% at a temperature of 582 °C, while the bottom side remains fixed. Excellent agreement with the experimental data could be achieved provided that at the initial instances (up to 0.01 s) of the experiment, the applied load is much higher than the nominal experimental load and that the yield stress and the power-law exponent vary linearly with the structure parameter. The first assumption implies that a different model, such as an elastoviscoplastic one, needs to be employed during the initial stages of the experiment. As for the second one, the evolution of the sample height can be reproduced allowing the yield stress to vary from 0 (no structure) to a maximum nominal value (full structure) and the power-law exponent from 0.2 to 1.4, i.e., from the shear-thinning to the shear-thickening regime. These variations are consistent with the internal microstructure variation pattern known to be exhibited by semisolid slurries. Full article

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16 pages, 1488 KiB

Open AccessArticle

Calibration of Thixotropic and Viscoelastic Shear-Thinning Fluids Using Pipe Rheometer Measurements

by Eric Cayeux

Fluids 2024, 9(1), 23; https://doi.org/10.3390/fluids9010023 - 10 Jan 2024

Viewed by 1733

Abstract

Some non-Newtonian fluids have time-dependent rheological properties like a shear stress that depends on the shear history or a stress overshoot that is a function of the resting time, when fluid movement is started. The rheological properties of such complex fluids may not [...] Read more.

Some non-Newtonian fluids have time-dependent rheological properties like a shear stress that depends on the shear history or a stress overshoot that is a function of the resting time, when fluid movement is started. The rheological properties of such complex fluids may not stay constant while they are used in an industrial process, and it is therefore desirable to measure these properties frequently and with a simple and robust device like a pipe rheometer. This paper investigated how the time-dependent rheological properties of a thixotropic and viscoelastic shear-thinning fluid can be extracted from differential pressure measurements obtained at different flowrates along a circular pipe section. The method consists in modeling the flow of a thixotropic version of a Quemada fluid and solving the inverse problem in order to find the model parameters using the measurements made in steady-state conditions. Also, a Maxwell linear viscoelastic model was used to reproduce the stress overshoot observed when starting circulation after a resting period. The pipe rheometer was designed to have the proper features necessary to exhibit the thixotropic and viscoelastic effects that were needed to calibrate the rheological model parameters. The accuracy of rheological measurements depends on understanding the effects that can influence the observations and on a proper design that takes advantage of these side effects instead of attempting to eliminate them. Full article

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2022

Jump to: 2024, 2021

10 pages, 671 KiB

Open AccessArticle

Effects of Numerical Forcing on the Two-Time Correlation of Fluid Velocity Differences in Stationary Isotropic Turbulence

by Rohit Dhariwal and Sarma L. Rani

Fluids 2022, 7(3), 115; https://doi.org/10.3390/fluids7030115 - 18 Mar 2022

Viewed by 2121

Abstract

In direct numerical simulations (DNS) of homogeneous isotropic turbulence, numerical forcing is needed to achieve statistically stationary velocity fields. The Eulerian two-time correlation tensor of the fluid velocity difference field, [...] Read more.

In direct numerical simulations (DNS) of homogeneous isotropic turbulence, numerical forcing is needed to achieve statistically stationary velocity fields. The Eulerian two-time correlation tensor of the fluid velocity difference field,

Δ u (r, t) = u (x + r, t) - u (x, t)

, characterizes the temporal evolution of turbulent eddies whose sizes scale with separation

r = | r |

. In this study, we investigate the effects of two spectral forcing schemes on the temporal decay of the Eulerian two-time correlation of fluid velocity differences

⟨ Δ u (r, t^{'}) Δ u (r, t) ⟩

. Accordingly, DNS of homogeneous isotropic turbulence were performed for two grid sizes,

128^{3}

and

512^{3}

, corresponding to the Taylor micro-scale Reynolds numbers

R e_{λ}

\approx 80

and 210, respectively. Statistical stationarity was achieved by employing deterministic and stochastic spectral forcing schemes. In the stochastic scheme, one needs to specify the time scale,

T_{f}

, of the Uhlenbeck–Ornstein (UO) processes that constitute the forcing. We considered four values of the UO time scale (

T_{f} = T_{E} / 4, T_{E}, 2 T_{E}

, and

4 T_{E}

) for each

R e_{λ}

, where

T_{E}

is the large-eddy time scale obtained from the DNS run with deterministic forcing at the same

R e_{λ}

. It is seen that the correlations

⟨ Δ u (r, t^{'}) Δ u (r, t) ⟩

obtained from the deterministic-forcing DNS runs decay more slowly than those from stochastic-forcing DNS runs of all four

T_{f}

values. The slower decay of correlations in deterministic DNS runs is more pronounced at larger separations and for higher

R e_{λ}

. Full article

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18 pages, 2706 KiB

Open AccessArticle

The Functional Relationship of Sediment Transport under Various Simulated Rainfall Conditions

by Hanna Mariana Henorman, Duratul Ain Tholibon, Masyitah Md Nujid, Hamizah Mokhtar, Jamilah Abd Rahim and Azlinda Saadon

Fluids 2022, 7(3), 107; https://doi.org/10.3390/fluids7030107 - 15 Mar 2022

Cited by 1 | Viewed by 2252

Abstract

Sediment removed in the detachment process is transported by overland flow. Previous experimental and field works studied that sediment transport is influenced by hydraulic properties of flow, physical properties of soil, and surface characteristics. Several equations in predicting sediment transport have been developed [...] Read more.

Sediment removed in the detachment process is transported by overland flow. Previous experimental and field works studied that sediment transport is influenced by hydraulic properties of flow, physical properties of soil, and surface characteristics. Several equations in predicting sediment transport have been developed from previous research. The objective of this paper was to establish the selected parameters that contribute to the sediment transport capacity in overland flow conditions under different rainfall pattern conditions and to evaluate their significance. The establishment of independent variables was performed using the dimensional analysis approach that is Buckingham’s π theorem. The final results obtained are a series of independent parameters; the Reynolds number (

R e)

, dimensionless rainfall parameter

(\frac{i L}{ν})

, hydraulic characteristics

(\frac{Q}{L ν})

that related to the dependent parameters; and dimensionless sediment transport

(\frac{q_{s}}{ρ v})

. The relationship indicates that 63.6% to 72.44% of the variance in the independent parameters is in relation to the dependent parameter. From the iteration method, the estimation of constant and regression coefficient values is presented in the form of the general formula for linear and nonlinear model equations. The linear and nonlinear model equations have the highest model accuracy of 93.1% and 81.5%, respectively. However, the nonlinear model equation has the higher discrepancy ratio of 54.9%. Full article

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16 pages, 3217 KiB

Open AccessArticle

Simulations of Graphene Oxide Dispersions as Discotic Nematic Liquid Crystals in Couette Flow Using Ericksen-Leslie (EL) Theory

by Arash Nikzad, Somesh Bhatia and Dana Grecov

Fluids 2022, 7(3), 103; https://doi.org/10.3390/fluids7030103 - 10 Mar 2022

Cited by 1 | Viewed by 2420

Abstract

The objective of this study was to simulate the flow of graphene oxide (GO) dispersions, a discotic nematic liquid crystal (DNLC), using the Ericksen-Leslie (EL) theory. GO aqueous suspension, as a lubricant, effectively reduces the friction between solid surfaces. The geometry considered in [...] Read more.

The objective of this study was to simulate the flow of graphene oxide (GO) dispersions, a discotic nematic liquid crystal (DNLC), using the Ericksen-Leslie (EL) theory. GO aqueous suspension, as a lubricant, effectively reduces the friction between solid surfaces. The geometry considered in this study was two cylinders with a small gap size, which is the preliminary geometry for journal bearings. The Leslie viscosity coefficients calculated in our previous study were used to calculate the stress tensor in the EL theory. The behavior of GO dispersions in the concentration range of 15 mg/mL to 30 mg/mL, shown in our recent experiments to be in the nematic phase, was investigated to obtain the orientation and the viscosity profile. The viscosities of GO dispersions obtained from numerical simulations were compared with those from our recent experimental study, and we observed that the values are within the range of experimental uncertainty. In addition, the alignment angles of GO dispersions at different concentrations were calculated numerically using EL theory and compared with the respective theoretical values, which were within 1% error. The anchoring angles corresponding to viscosity values closest to the experimental results were between 114 and 118 degrees. Moreover, a sensitivity analysis was performed to determine the effects of different ratios of the elasticity coefficients in EL theory. Using this procedure, the same study could be extended for other DNLCs in different geometries. Full article

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12 pages, 3622 KiB

Open AccessArticle

Viscoelastic Representation of the Operation of Sucker Rod Pumps

by Sheldon Wang, Lynn Rowlan, Abbey Henderson, Sean T. Aleman, Trent Creacy and Carrie Anne Taylor

Fluids 2022, 7(2), 70; https://doi.org/10.3390/fluids7020070 - 8 Feb 2022

Cited by 3 | Viewed by 2626

Abstract

The issues of leakage with respect to the clearance between the pump plunger outer surface and the pump barrel inner surface and other operational conditions have been revisited in this paper. Both Poiseuille flow rate due to the pressure difference and Couette flow [...] Read more.

The issues of leakage with respect to the clearance between the pump plunger outer surface and the pump barrel inner surface and other operational conditions have been revisited in this paper. Both Poiseuille flow rate due to the pressure difference and Couette flow rate due to the plunger motion have been considered. The purpose of this study is to explore the possibility of representing the entire downhole pump system with a simple viscoelastic model. We have explored both Kelvin and Maxwell viscoelastic models along with the dynamic behaviors of a mass point attached to the viscoelastic model. By using the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic models, we have obtained the displacement responses, which match closely with the actual measurements in experiments and operations. Further study and experiments have been planned and partially implemented in the McCoy School of Engineering at Midwestern State University, a member of the Texas Tech University System. Full article

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2021

Jump to: 2024, 2022

12 pages, 1542 KiB

Open AccessArticle

Strong Viscosity Increase in Aqueous Solutions of Cationic C22-Tailed Surfactant Wormlike Micelles

by Vyacheslav S. Molchanov, Andrei V. Rostovtsev, Kamilla B. Shishkhanova, Alexander I. Kuklin and Olga E. Philippova

Fluids 2022, 7(1), 8; https://doi.org/10.3390/fluids7010008 - 27 Dec 2021

Cited by 6 | Viewed by 2872

Abstract

The viscoelastic properties and structure parameters have been investigated for aqueous solutions of wormlike micelles of cationic surfactant erucyl bis(hydroxyethyl) methylammonium chloride with long C22 tail in the presence inorganic salt KCl. The salt content has been varied to estimate linear to branched [...] Read more.

The viscoelastic properties and structure parameters have been investigated for aqueous solutions of wormlike micelles of cationic surfactant erucyl bis(hydroxyethyl) methylammonium chloride with long C22 tail in the presence inorganic salt KCl. The salt content has been varied to estimate linear to branched transition conditions due to screening of the electrostatic interaction in the networks. The local cylindrical structure and low electrostatic repulsion was obtained by SANS data. The drastic power law dependencies of rheological properties on surfactant concentrations were obtained at intermediate salt content. Two power law regions of viscosity dependence were detected in semi-dilute solutions related to “unbreakable” and “living” micellar chains. The fast contour length growth with surfactant concentration demonstrated that is in good agreement with theoretical predictions. Full article

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21 pages, 8035 KiB

Open AccessArticle

Using Computational Modelling to Study Extensional Rheometry Tests for Inelastic Fluids

by Mohammadreza Aali, Célio Fernandes, Olga Sousa Carneiro and João Miguel Nóbrega

Fluids 2021, 6(12), 464; https://doi.org/10.3390/fluids6120464 - 19 Dec 2021

Viewed by 2934

Abstract

The present work focuses on the extensional rheometry test, performed with the Sentmanat extensional rheometer (SER) device, and its main objectives are: (i) to establish the modelling requirements, such as the geometry of the computational domain, initial and boundary conditions, appropriate case setup, [...] Read more.

The present work focuses on the extensional rheometry test, performed with the Sentmanat extensional rheometer (SER) device, and its main objectives are: (i) to establish the modelling requirements, such as the geometry of the computational domain, initial and boundary conditions, appropriate case setup, and (ii) to investigate the effect of self-induced errors, namely on the sample dimensions and test temperature, on the extensional viscosity obtained through the extensional rheometry tests. The definition of the modelling setup also comprised the selection of the appropriate mesh refinement level to model the process and the conclusion that gravity can be neglected without affecting the numerical predictions. The subsequent study allowed us to conclude that the errors on the sample dimensions have similar effects, originating differences on the extensional viscosity proportional to the induced variations. On the other hand, errors of a similar order of magnitude on the test temperature promote a significant difference in the predicted extensional viscosity. Full article

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15 pages, 13602 KiB

Open AccessArticle

Spin-Up from Rest of a Liquid Metal with Deformable Free Surface in a Cylinder under the Influence of a Uniform Axial Magnetic Field

by Toshio Tagawa and Kewei Song

Fluids 2021, 6(12), 438; https://doi.org/10.3390/fluids6120438 - 2 Dec 2021

Viewed by 2902

Abstract

Spin-up from rest of a liquid metal having deformable free surface in the presence of a uniform axial magnetic field is numerically studied. Both liquid and gas phases in a vertically mounted cylinder are assumed to be an incompressible, immiscible, Newtonian fluid. Since [...] Read more.

Spin-up from rest of a liquid metal having deformable free surface in the presence of a uniform axial magnetic field is numerically studied. Both liquid and gas phases in a vertically mounted cylinder are assumed to be an incompressible, immiscible, Newtonian fluid. Since the viscous dissipation and the Joule heating are neglected, thermal convection due to buoyancy and thermocapillary effects is not taken into account. The effects of Ekman number and Hartmann number were computed with fixing the Froude number of 1.5, the density ratio of 800, and the viscosity ratio of 50. The evolutions of the free surface, three-component velocity field, and electric current density are portrayed using the level-set method and HSMAC method. When a uniform axial magnetic field is imposed, the azimuthal momentum is transferred from the rotating bottom wall to the core region directly through the Hartmann layer. This is the most striking difference from spin-up of the nonmagnetic case. Full article

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12 pages, 27072 KiB

Open AccessFeature PaperArticle

Effect of Surfactant Concentration on the Long-Term Properties of a Colloidal Chemical, Biological and Radiological (CBR) Decontamination Gel

by Alban Gossard, Fabien Frances, Camille Aloin, Clara Penavayre, Nicolas Fabrègue and Célia Lepeytre

Fluids 2021, 6(11), 410; https://doi.org/10.3390/fluids6110410 - 12 Nov 2021

Cited by 2 | Viewed by 1988

Abstract

Chemically, biologically, or radiologically contaminated surfaces can be treated using colloidal “vacuumable” gels containing alumina particles as a thickening agent, decontaminating solutions to inhibit/eliminate biological and chemical contaminants, and Pluronic PE 6200 as a surfactant to adjust the gel’s physicochemical properties. These gels [...] Read more.

Chemically, biologically, or radiologically contaminated surfaces can be treated using colloidal “vacuumable” gels containing alumina particles as a thickening agent, decontaminating solutions to inhibit/eliminate biological and chemical contaminants, and Pluronic PE 6200 as a surfactant to adjust the gel’s physicochemical properties. These gels have been shown to remain efficient even after prolonged storage. In the present study, the properties of gels with different surfactant concentrations were monitored over several months using rheological analyses, contact angle measurements, and ion chromatography. Results show that the surfactant reacts with the hypochlorite ions in the decontaminating solution. This leads to sedimentation, which modifies the rheological properties of the gel. Increasing the surfactant concentration ensures the physicochemical properties of the gel are preserved for longer, but because the surfactant reacts with the hypochlorite ions, the concentration of the latter decreases drastically and thus so do the decontamination properties of the gel. There is therefore a trade-off between the efficiency of the gel against chemical and biological contamination at a given time and how long its physicochemical properties are preserved, with the optimal balance depending on its intended use. Full article

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22 pages, 915 KiB

Open AccessArticle

On a Casson Fluid Motion: Nonuniform Width Symmetric Channel and Peristaltic Flows

by Simone Guadagni, Liviu Iulian Palade, Lorenzo Fusi and Angiolo Farina

Fluids 2021, 6(10), 356; https://doi.org/10.3390/fluids6100356 - 8 Oct 2021

Cited by 7 | Viewed by 2134

Abstract

Widely used for modeling biological fluids flows—in particular, blood vessel flows—a Casson flow is studied in a symmetric channel for which the aspect ratio enables one to use the lubrication approximation. Two flow driving conditions are prescribed: inlet–outlet pressure difference and peristaltic oscillations [...] Read more.

Widely used for modeling biological fluids flows—in particular, blood vessel flows—a Casson flow is studied in a symmetric channel for which the aspect ratio enables one to use the lubrication approximation. Two flow driving conditions are prescribed: inlet–outlet pressure difference and peristaltic oscillations of the vessel walls. In both cases, starting from mass and momentum balance and using lubrication approximation, we investigate the conditions to be imposed on the driving mechanisms so that the inner plug does not come in touch with the walls. The study of the peristaltic flow is of great importance in view of its applications in physiology (including microcirculation applications). Full article

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11 pages, 1168 KiB

Open AccessArticle

Rheological and Functional Properties of Hydrocolloids from Pereskia bleo Leaves

by Diana López-Barraza, Andres Ortega-Ramos, Edilbert Torregroza-Fuentes, Somaris E. Quintana and Luis A. García-Zapateiro

Fluids 2021, 6(10), 349; https://doi.org/10.3390/fluids6100349 - 2 Oct 2021

Cited by 8 | Viewed by 2942

Abstract

The food industry has increased its interest in using natural and consumer-friendly ingredients to produce food products. In the case of hydrocolloids of natural origin, the materials are biodegradable and environmentally friendly. This study aimed to isolate hydrocolloids from Pereskia bleo leaves and [...] Read more.

The food industry has increased its interest in using natural and consumer-friendly ingredients to produce food products. In the case of hydrocolloids of natural origin, the materials are biodegradable and environmentally friendly. This study aimed to isolate hydrocolloids from Pereskia bleo leaves and evaluate their proximal composition, technological and rheological properties. High-carbohydrate Pereskia bleo with high water holding capacity and emulsifying stability were obtained. The samples showed a shear-thinning behavior adjusted to the Cross model (R² > 0.93) and a high dependence on temperature corroborating with the higher activation energy value (11.78 kJ/mol, R² = 0.99) as an indicator of a rapid change in viscosity and microstructure. The viscoelastic properties are shown with a storage modulus higher than the loss modulus, presenting a gel structure. The isolation of hydrocolloids from leaves is a major challenge for commercializing natural ingredients with technological properties. Therefore, this study suggests that these hydrocolloids from Pereskia bleo leaves can be good ingredients in microstructure and texturizing products, improving the stability as thickener agents. Full article

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18 pages, 4020 KiB

Open AccessArticle

Rheological and Microstructural Properties of Oil-in-Water Emulsion Gels Containing Natural Plant Extracts Stabilized with Carboxymethyl Cellulose/Mango (Mangiferaindica) Starch

by Luis Mieles-Gómez, Santander E. Lastra-Ripoll, Edilbert Torregroza-Fuentes, Somaris E. Quintana and Luis A. García-Zapateiro

Fluids 2021, 6(9), 312; https://doi.org/10.3390/fluids6090312 - 1 Sep 2021

Cited by 10 | Viewed by 3965

Abstract

Emulsion gels are an alternative to developing food products and adding bioactive compounds; however, different stabilizers have been employed considering natural ingredients. In this work, stabilization of emulsion gels with blends of carboxymethylcellulose and kernel mango starch was performed with the addition of [...] Read more.

Emulsion gels are an alternative to developing food products and adding bioactive compounds; however, different stabilizers have been employed considering natural ingredients. In this work, stabilization of emulsion gels with blends of carboxymethylcellulose and kernel mango starch was performed with the addition of mango peel extracts, evaluating their physical, rheological and microstructural properties. Phenolic extract from mango peels (yields = 11.35 ± 2.05% w/w), with 294.60 ± 0.03 mg GAE/100 g of extract and 436.77 ± 5.30 µMol Trolox/g of the extract, was obtained by ultrasound-assisted extraction (1:10 peel: Ethanol w/v, 200 W, 30 min), containing pyrogallol, melezitose, succinic acid, γ-tocopherol, campesterol, stigmasterol, lupeol, vitamin A and vitamin E. In addition, mango kernel starch (yields = 59.51 ± 1.35% w/w) with 27.28 ± 0.05% of amylose was obtained, being the by-product of mango (Mangiferaindica var fachir) an alternative to producing natural food ingredients. After that, stable emulsions gels were prepared to stabilize with carboxy methylcellulose–kernel mango starch blends and mango peel extracts. These results provide an ingredient as an alternative to the development of gelled systems. They offer an alternative to elaborating a new multifunctional food system with bioactive properties with potential application as a fat replacement or delivery system in the food industry. Full article

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17 pages, 2732 KiB

Open AccessArticle

Natural Yogurt Stabilized with Hydrocolloids from Butternut Squash (Cucurbita moschata) Seeds: Effect on Physicochemical, Rheological Properties and Sensory Perception

by Sergio A. Rojas-Torres, Somaris E. Quintana and Luis Alberto García-Zapateiro

Fluids 2021, 6(7), 251; https://doi.org/10.3390/fluids6070251 - 9 Jul 2021

Cited by 15 | Viewed by 3758

Abstract

Stabilizers are ingredients employed to improve the technological properties of products. The food industry and consumers have recently become interested in the development of natural ingredients. In this work, the effects of hydrocolloids from butternut squash (Cucurbita moschata) seeds (HBSS) [...] Read more.

Stabilizers are ingredients employed to improve the technological properties of products. The food industry and consumers have recently become interested in the development of natural ingredients. In this work, the effects of hydrocolloids from butternut squash (Cucurbita moschata) seeds (HBSS) as stabilizers on the physicochemical, rheological, and sensory properties of natural yogurt were examined. HBSS improved the yogurt’s physical stability and physicochemical properties, decreasing syneresis and modifying the samples’ rheological properties, improving the assessment of sensory characteristics. The samples presented shear thinning behavior characterized by a decrease in viscosity with the increase of the shear rate; nevertheless, the samples showed a two-step yield stress. HBSS is an alternative as a natural stabilizer for the development of microstructured products. Full article

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13 pages, 5496 KiB

Open AccessArticle

PIV-Measurements of Centrifugal Instabilities in a Rectangular Curved Duct with a Small Aspect Ratio

by Afshin Goharzadeh and Peter Rodgers

Fluids 2021, 6(5), 184; https://doi.org/10.3390/fluids6050184 - 13 May 2021

Cited by 4 | Viewed by 2757

Abstract

In this study, experimental measurements were undertaken using non-intrusive particle image velocimetry (PIV) to investigate fluid flow within a 180° rectangular, curved duct geometry of a height-to-width aspect ratio of 0.167 and a curvature of 0.54. The duct was constructed from Plexiglas to [...] Read more.

In this study, experimental measurements were undertaken using non-intrusive particle image velocimetry (PIV) to investigate fluid flow within a 180° rectangular, curved duct geometry of a height-to-width aspect ratio of 0.167 and a curvature of 0.54. The duct was constructed from Plexiglas to permit optical access to flow pattern observations and flow velocity field measurements. Silicone oil was used as working fluid because it has a similar refractive index to Plexiglas. The measured velocity fields within the Reynolds number ranged from 116 to 203 and were presented at the curved channel section inlet and outlet, as well as at the mid-channel height over the complete duct length. It was observed from spanwise measurements that the transition to unsteady secondary flows generated the creation of wavy structures linked with the formation of Dean vortices close to the outer channel wall. This flow structure became unsteady with increasing Reynolds number. Simultaneously, the presence of Dean vortices in the spanwise direction influenced the velocity distribution in the streamwise direction. Two distinct regions defined by a higher velocity distribution were observed. Fluid particles were accelerated near the inner wall of the channel bend and subsequently downstream near the outer channel wall. Full article

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39 pages, 814 KiB

Open AccessArticle

Hydrodynamics of Collapsing Glass Tubes and Measuring of Glass Viscosities: Analytic Results beyond Asymptotic Approaches for Rapidly Varying Viscosities

by Thomas Klupsch

Fluids 2021, 6(5), 179; https://doi.org/10.3390/fluids6050179 - 6 May 2021

Viewed by 2244

Abstract

We present novel analytic solutions of the axial-symmetric boundary value problem of the Stokes equation for incompressible liquids with rapidly varying viscosity, which cover the hydrodynamics of collapsing glass tubes with moving torch. We meet requirements to optimize the contactless measuring of dynamical [...] Read more.

We present novel analytic solutions of the axial-symmetric boundary value problem of the Stokes equation for incompressible liquids with rapidly varying viscosity, which cover the hydrodynamics of collapsing glass tubes with moving torch. We meet requirements to optimize the contactless measuring of dynamical viscosities and surface tensions of molten glasses through collapsing for tools working with sharply peaked axial temperature courses. We study model solutions for axial courses of the reciprocal viscosity specified as Gaussians extended on small distances compared to the outer tube radius, and we neglect the boundary inclination, corresponding to measuring conditions for large torch velocities. The surface tension is assumed to be constant across the collapsing zone. The boundary value problem becomes disentangled, changing to a gradually independent hierarchy of streaming function, vorticity, and pressure. Axial Fourier transforms are introduced to focus on solutions for infinitely extended tubes. Beyond the predictions of the asymptotic collapsing theory, a successively increasing steepness of the reciprocal viscosity induces an increasing radial pressure gradient that acts against the surface tension and diminishes the collapsing efficiency. The arising systematic error in evaluating the viscosity from experimental data in virtue of the asymptotic collapsing theory is corrected. Error estimations regarding deviations from the specified viscosity course, the neglected boundary inclination, and heat conduction within the tube wall are outlined, and preconditions to simplify the measuring of surface tensions through collapsing are discussed. Full article

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