Pub Date : 2024-09-21DOI: 10.1016/j.jnnfm.2024.105326
A. Gharagozlou , M. Pourjafar-Chelikdani , K. Sadeghy
The classic Richards equation is a good model for predicting imbibition of viscous fluids in porous materials such as dry soils or filter papers. It cannot, in principle, be used for physiological fluids such as blood simply because such fluids often exhibit a variety of non-Newtonian behavior such as a yield stress. In the present work, we have theoretically extended the classic Richards equation to viscoplastic fluids obeying the Bingham model using the concept of the effective viscosity together with the bundle-of-tube model. The new imbibition model could partly resolve the discrepancy reported in the literature between the predictions of the classic Richards equation for the stain growth of sessile blood droplets in a typical filter paper. A better fit, however, requires considering other non-Newtonian effects of the blood such as its viscoelasticity. Using the Bingham-modified Richards equation, it is demonstrated that yield stress in a test fluid has a retarding effect on the imbibition phenomenon, so that such fluids may not necessarily reach the test line of a paper-based diagnostic kit. But yield stress is predicted to extend the duration of the quasi-steady regime on the test line of diagnostic kits, which is a desirable effect. The results suggest that inducing (or elevating) the level of yield stress in a test liquid such as blood can be used as a passive means to control imbibition characteristics in paper-based systems.
{"title":"Yield-stress effects on spontaneous imbibition in paper-based kits","authors":"A. Gharagozlou , M. Pourjafar-Chelikdani , K. Sadeghy","doi":"10.1016/j.jnnfm.2024.105326","DOIUrl":"10.1016/j.jnnfm.2024.105326","url":null,"abstract":"<div><div>The classic Richards equation is a good model for predicting imbibition of viscous fluids in porous materials such as dry soils or filter papers. It cannot, in principle, be used for physiological fluids such as blood simply because such fluids often exhibit a variety of non-Newtonian behavior such as a yield stress. In the present work, we have theoretically extended the classic Richards equation to viscoplastic fluids obeying the Bingham model using the concept of the effective viscosity together with the bundle-of-tube model. The new imbibition model could partly resolve the discrepancy reported in the literature between the predictions of the classic Richards equation for the stain growth of sessile blood droplets in a typical filter paper. A better fit, however, requires considering other non-Newtonian effects of the blood such as its viscoelasticity. Using the Bingham-modified Richards equation, it is demonstrated that yield stress in a test fluid has a retarding effect on the imbibition phenomenon, so that such fluids may not necessarily reach the test line of a paper-based diagnostic kit. But yield stress is predicted to extend the duration of the quasi-steady regime on the test line of diagnostic kits, which is a desirable effect. The results suggest that inducing (or elevating) the level of yield stress in a test liquid such as blood can be used as a passive means to control imbibition characteristics in paper-based systems.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105326"},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.jnnfm.2024.105324
Kai Tian , Chundong Xue , Jifeng Cui , Kai-Rong Qin , Zhaodong Ding
This study conducts a comprehensive exploration of the elasticity and Marangoni instability exhibited by a non-Newtonian polymer film flow down an inclined plane within the context of an upper-convected Maxwell (UCM) model. The asymptotic solutions are derived utilizing the stream function and perturbation method based on the long-wave assumption. The numerical solutions are effectively solved at arbitrary wavelengths through the implementation of the Chebyshev spectral collocation technique. The results show that the presence of elastic stress renders the film more susceptible to destabilization. The underlying mechanisms that instigate the instability are examined from an energy balance perspective. It is determined that the instability of the film is predominantly governed by shear stress (SHE) and elastic stress (DIP) effects. Shear stress increases the perturbation kinetic energy to promote instability, while elastic stress decreases the perturbation kinetic energy to enhance stability. However, for the Weissenberg number , the shear stress changes from an unstable to a stabilizing factor, and the elastic stress changes from stable to unstable when the wave number . This intriguing inversion is attributed to the dual nature of elasticity, possessing both stabilizing and destabilizing tendencies. Despite the work of Marangoni stress (MAT) magnitude remaining within the order of , the Marangoni effect indirectly contributes to instability enhancement.
{"title":"Instabilities of Marangoni and elasticity in a molten polymer film","authors":"Kai Tian , Chundong Xue , Jifeng Cui , Kai-Rong Qin , Zhaodong Ding","doi":"10.1016/j.jnnfm.2024.105324","DOIUrl":"10.1016/j.jnnfm.2024.105324","url":null,"abstract":"<div><div>This study conducts a comprehensive exploration of the elasticity and Marangoni instability exhibited by a non-Newtonian polymer film flow down an inclined plane within the context of an upper-convected Maxwell (UCM) model. The asymptotic solutions are derived utilizing the stream function and perturbation method based on the long-wave assumption. The numerical solutions are effectively solved at arbitrary wavelengths through the implementation of the Chebyshev spectral collocation technique. The results show that the presence of elastic stress renders the film more susceptible to destabilization. The underlying mechanisms that instigate the instability are examined from an energy balance perspective. It is determined that the instability of the film is predominantly governed by shear stress (SHE) and elastic stress (DIP) effects. Shear stress increases the perturbation kinetic energy to promote instability, while elastic stress decreases the perturbation kinetic energy to enhance stability. However, for the Weissenberg number <span><math><mrow><mi>W</mi><mi>i</mi><mo>=</mo><mn>1</mn></mrow></math></span>, the shear stress changes from an unstable to a stabilizing factor, and the elastic stress changes from stable to unstable when the wave number <span><math><mrow><mi>k</mi><mo>></mo><mn>1</mn></mrow></math></span>. This intriguing inversion is attributed to the dual nature of elasticity, possessing both stabilizing and destabilizing tendencies. Despite the work of Marangoni stress (MAT) magnitude remaining within the order of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math></span>, the Marangoni effect indirectly contributes to instability enhancement.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105324"},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-19DOI: 10.1016/j.jnnfm.2024.105323
Xiang Qiu , Xu Ding , Yizhou Tao , Junwang Qu , Jiahua Li , Yulu Liu
In this study, direct numerical simulations (DNS) was used to investigate the flow behavior of power-law fluids flow around a circular cylinder near a wall at the Reynolds number of 200. The power-law index represents the typical situation of shear-thinning fluids ( to 1.0), whereas the gap ratio ranges from 0.2 to 1.0 (where represents the gap between the cylinder and the plane wall and represents the diameter of the cylinder). This study aimed to analyze the influence of the power-law index and gap ratio on the time-averaged flow, vortex dynamics, and the force exerted on the cylinder. The results indicate that for and , two secondary vortex structures form behind the cylinder because of the induction of the primary vortices, and they are in reverse rotation. An analysis of the signed enstrophy revealed a positive correlation between the strengths of the primary and secondary vortices, both of which diminished as the gap ratio decreased and increased as the power-law index decreased. Notably, vortex shedding was observed at when , which is absent in Newtonian fluids. Through the analysis of vorticity transport equation, the development of vorticity is attributed to changes in the convection term, viscosity diffusion term and viscosity gradient term. By examining the key points, the formation of secondary vortex structure and the reason of vortex shedding at in power-law fluids are explained. Furthermore, the time-averaged drag coefficient initially decreases and then increases with decreasing , and decreases with decreasing . The time-averaged lift coefficient exhibits a typical L-type curve with increasing gap ratios, where initially decreases and then increases.
本研究采用直接数值模拟（DNS）方法研究了雷诺数为 200 时，幂律流体在靠近壁面的圆柱体周围的流动行为。幂律指数 n 代表剪切稀化流体的典型情况（n=0.2 至 1.0），而间隙比 G/D 的范围为 0.2 至 1.0（其中 G 代表圆柱体与平面壁之间的间隙，D 代表圆柱体的直径）。本研究旨在分析幂律指数和间隙比对时均流动、涡旋动力学和气缸受力的影响。结果表明，当 G/D≥0.5 和 n≤0.5 时，由于主涡旋的诱导，在圆柱体后方形成了两个次级涡旋结构，它们处于反向旋转状态。对符号漩涡的分析表明，主漩涡和副漩涡的强度呈正相关，两者都随着间隙比的减小而减小，随着幂律指数的减小而增大。值得注意的是，当 n≤0.3 时，在 G/D=0.3 处观察到涡流脱落，而这在牛顿流体中是不存在的。通过对涡度传输方程的分析，涡度的发展归因于对流项、粘度扩散项和粘度梯度项的变化。通过对关键点的研究，解释了幂律流体在 G/D=0.3 时次级涡旋结构的形成和涡旋脱落的原因。此外，时均阻力系数 C¯D 随 n 的减小先减小后增大，并随 G/D 的减小而减小。时均升力系数 C¯L 随着间隙比的增大呈现典型的 L 型曲线，即 C¯L 先减小后增大。
{"title":"Research on the flow around a circular cylinder near a wall for shear-thinning power-law fluids","authors":"Xiang Qiu , Xu Ding , Yizhou Tao , Junwang Qu , Jiahua Li , Yulu Liu","doi":"10.1016/j.jnnfm.2024.105323","DOIUrl":"10.1016/j.jnnfm.2024.105323","url":null,"abstract":"<div><div>In this study, direct numerical simulations (DNS) was used to investigate the flow behavior of power-law fluids flow around a circular cylinder near a wall at the Reynolds number of 200. The power-law index <span><math><mi>n</mi></math></span> represents the typical situation of shear-thinning fluids (<span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mrow></math></span> to 1.0), whereas the gap ratio <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi></mrow></math></span> ranges from 0.2 to 1.0 (where <span><math><mi>G</mi></math></span> represents the gap between the cylinder and the plane wall and <span><math><mi>D</mi></math></span> represents the diameter of the cylinder). This study aimed to analyze the influence of the power-law index and gap ratio on the time-averaged flow, vortex dynamics, and the force exerted on the cylinder. The results indicate that for <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi><mo>≥</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span> and <span><math><mrow><mi>n</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span>, two secondary vortex structures form behind the cylinder because of the induction of the primary vortices, and they are in reverse rotation. An analysis of the signed enstrophy revealed a positive correlation between the strengths of the primary and secondary vortices, both of which diminished as the gap ratio decreased and increased as the power-law index decreased. Notably, vortex shedding was observed at <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></math></span> when <span><math><mrow><mi>n</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></math></span>, which is absent in Newtonian fluids. Through the analysis of vorticity transport equation, the development of vorticity is attributed to changes in the convection term, viscosity diffusion term and viscosity gradient term. By examining the key points, the formation of secondary vortex structure and the reason of vortex shedding at <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></math></span> in power-law fluids are explained. Furthermore, the time-averaged drag coefficient <span><math><msub><mrow><mover><mrow><mi>C</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>D</mi></mrow></msub></math></span> initially decreases and then increases with decreasing <span><math><mi>n</mi></math></span>, and decreases with decreasing <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi></mrow></math></span>. The time-averaged lift coefficient <span><math><msub><mrow><mover><mrow><mi>C</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>L</mi></mrow></msub></math></span> exhibits a typical L-type curve with increasing gap ratios, where <span><math><msub><mrow><mover><mrow><mi>C</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>L</mi></mrow></msub></math></span> initially decreases and then increases.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105323"},"PeriodicalIF":2.7,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-18DOI: 10.1016/j.jnnfm.2024.105321
Ann Aisling, Renee Saraka, Nicolas J. Alvarez
This work focuses on inferring the molecular state of the polymer chain required to induce stress relaxation and the accurate measure of the polymer’s longest relaxation time in uniaxial stretching of dilute polymer solutions. This work is facilitated by the discovery that constant velocity applied at early times leads to initial constant extension rate before reaching the Rayleigh–Plateau instability. Such constant rate experiments are used to correlate initial stretching kinematics with the thinning dynamics in the final thinning regime. We show that there is a minimum initial strain-rate required to induce rate independent elastic effects, and measure the longest relaxation time of the material. Below the minimum extension rate, insufficient stretching of the chain is observed before capillary instability, such that the polymer stress is comparable to the capillary stress at long times and stress relaxation is not achieved. Above the minimum strain-rate, the chain reaches a critical stretch before instability, such that during the unstable filament thinning the polymer stress is significantly larger than the capillary stress and rate-independent stress relaxation is observed. Using a single relaxation mode FENE model, we show that the minimum strain rate leads to a required initial stretch of the chain before reaching the Rayleigh–Plateau limit. These results indicate that the chain conformation before entering the Rayleigh Instability Regime, and the stretching induced during the instability, determines the elastic behavior of the filament. Lastly, this work introduces a characteristic dimensionless group, called the stretchability factor, that can be used to quantitatively compare different materials based on the overall material deformation/kinematic behavior, not just the relaxation time. Overall, these results demonstrate a useful methodology to study the stretching of dilute solutions using a constant velocity stretching scheme.
{"title":"The importance of initial extension rate on elasto-capillary thinning of dilute polymer solutions","authors":"Ann Aisling, Renee Saraka, Nicolas J. Alvarez","doi":"10.1016/j.jnnfm.2024.105321","DOIUrl":"10.1016/j.jnnfm.2024.105321","url":null,"abstract":"<div><div>This work focuses on inferring the molecular state of the polymer chain required to induce stress relaxation and the accurate measure of the polymer’s longest relaxation time in uniaxial stretching of dilute polymer solutions. This work is facilitated by the discovery that constant velocity applied at early times leads to initial constant extension rate before reaching the Rayleigh–Plateau instability. Such constant rate experiments are used to correlate initial stretching kinematics with the thinning dynamics in the final thinning regime. We show that there is a minimum initial strain-rate required to induce rate independent elastic effects, and measure the longest relaxation time of the material. Below the minimum extension rate, insufficient stretching of the chain is observed before capillary instability, such that the polymer stress is comparable to the capillary stress at long times and stress relaxation is not achieved. Above the minimum strain-rate, the chain reaches a critical stretch before instability, such that during the unstable filament thinning the polymer stress is significantly larger than the capillary stress and rate-independent stress relaxation is observed. Using a single relaxation mode FENE model, we show that the minimum strain rate leads to a required initial stretch of the chain before reaching the Rayleigh–Plateau limit. These results indicate that the chain conformation before entering the Rayleigh Instability Regime, and the stretching induced during the instability, determines the elastic behavior of the filament. Lastly, this work introduces a characteristic dimensionless group, called the stretchability factor, that can be used to quantitatively compare different materials based on the overall material deformation/kinematic behavior, not just the relaxation time. Overall, these results demonstrate a useful methodology to study the stretching of dilute solutions using a constant velocity stretching scheme.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105321"},"PeriodicalIF":2.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S037702572400137X/pdfft?md5=d1f32f9cee619f02d115117fa2418228&pid=1-s2.0-S037702572400137X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-18DOI: 10.1016/j.jnnfm.2024.105325
Banashree Samanta , Manish Kaushal , Gargi Das , Subhabrata Ray
Laminar planar hydraulic jump during viscoplastic liquid flow in a horizontal channel is investigated through experiments and numerical simulation using Herschel-Bulkley (HB) model. The simulations are performed using the phase-field method with Papanastasiou regularization parameter and validated against experimental results. Both experiments and simulations show the free surface height to gradually increase upstream of jump and recede after the jump with a remarkable increase in free surface height and surface waviness at the jump. The model further reveals that an increase in any of the rheological parameters [yield stress () flow behaviour index (n) and flow consistency index (k)] keeping the other properties constant increases film thickness. This increases jump strength and shifts jump towards the entry. However, each parameter influences free surface profile and jump characteristics in a different way. While a higher τo suppresses the development of the shear zone and results in a thicker plug zone, a higher n increases shear zone thickness and decreases the plug zone thickness. On the other hand, a higher k increases both shear and plug zone thickness. The steady state fully developed self-similar velocity profile is independent of k and depends on and n. Different jump types, obtained from simulations, are presented as phase diagrams in non-dimensional coordinates for a generalised approach.
{"title":"A numerical investigation of laminar planar hydraulic jump in Herschel-Bulkley fluid","authors":"Banashree Samanta , Manish Kaushal , Gargi Das , Subhabrata Ray","doi":"10.1016/j.jnnfm.2024.105325","DOIUrl":"10.1016/j.jnnfm.2024.105325","url":null,"abstract":"<div><div>Laminar planar hydraulic jump during viscoplastic liquid flow in a horizontal channel is investigated through experiments and numerical simulation using Herschel-Bulkley (HB) model. The simulations are performed using the phase-field method with Papanastasiou regularization parameter and validated against experimental results. Both experiments and simulations show the free surface height to gradually increase upstream of jump and recede after the jump with a remarkable increase in free surface height and surface waviness at the jump. The model further reveals that an increase in any of the rheological parameters [yield stress (<span><math><msub><mi>τ</mi><mi>o</mi></msub></math></span>) flow behaviour index (<em>n</em>) and flow consistency index (<em>k</em>)] keeping the other properties constant increases film thickness. This increases jump strength and shifts jump towards the entry. However, each parameter influences free surface profile and jump characteristics in a different way. While a higher τ<em><sub>o</sub></em> suppresses the development of the shear zone and results in a thicker plug zone, a higher <em>n</em> increases shear zone thickness and decreases the plug zone thickness. On the other hand, a higher <em>k</em> increases both shear and plug zone thickness. The steady state fully developed self-similar velocity profile is independent of <em>k</em> and depends on <span><math><msub><mi>τ</mi><mi>o</mi></msub></math></span> and <em>n</em>. Different jump types, obtained from simulations, are presented as phase diagrams in non-dimensional coordinates for a generalised approach.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105325"},"PeriodicalIF":2.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-16DOI: 10.1016/j.jnnfm.2024.105322
Giovanni Soligo, Marco Edoardo Rosti
We perform numerical simulations of planar jets of elastoviscoplastic (EVP) fluid (Saramito (2007) model) at low Reynolds number. Three different configurations are considered: EVP jet in EVP ambient fluid, EVP jet in Newtonian ambient fluid (miscible), and EVP jet in Newtonian ambient fluid (immiscible). We investigate the effect of the Bingham number, i.e. of the dimensionless yield stress of the EVP fluid, on the jet dynamics, and find a good agreement with the scaling for laminar, Newtonian jets for the centerline velocity and for the jet thickness at small Bingham number. This is lost once substantial regions of the fluid become unyielded, where we find that the spreading rate of the jet and the decay rate of the centerline velocity increase with the Bingham number, due to the regions of unyielded fluid inducing a blockage effect on the jet. The most striking difference among the three configurations we considered is the extent and position of the regions of unyielded fluid: large portions of ambient and jet fluids (in particular, away from the inlet) are unyielded for the EVP jet in EVP ambient fluid, whereas for the other two configurations, the regions of unyielded fluid are limited to the jet, as expected. We derive a power law scaling for the centerline yield variable and confirm it with the results from our numerical simulations. The yield variable determines the transition from the viscoelastic Oldroyd-B fluid (yielded) to the viscoelastic Kelvin–Voigt material (unyielded).
{"title":"Laminar planar jets of elastoviscoplastic fluids","authors":"Giovanni Soligo, Marco Edoardo Rosti","doi":"10.1016/j.jnnfm.2024.105322","DOIUrl":"10.1016/j.jnnfm.2024.105322","url":null,"abstract":"<div><div>We perform numerical simulations of planar jets of elastoviscoplastic (EVP) fluid (Saramito (2007) model) at low Reynolds number. Three different configurations are considered: <span><math><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></math></span> EVP jet in EVP ambient fluid, <span><math><mrow><mo>(</mo><mi>i</mi><mi>i</mi><mo>)</mo></mrow></math></span> EVP jet in Newtonian ambient fluid (miscible), and <span><math><mrow><mo>(</mo><mi>i</mi><mi>i</mi><mi>i</mi><mo>)</mo></mrow></math></span> EVP jet in Newtonian ambient fluid (immiscible). We investigate the effect of the Bingham number, <em>i.e.</em> of the dimensionless yield stress of the EVP fluid, on the jet dynamics, and find a good agreement with the scaling for laminar, Newtonian jets for the centerline velocity <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>/</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∝</mo><msup><mrow><mrow><mo>(</mo><mi>x</mi><mo>/</mo><mi>h</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span> and for the jet thickness <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mi>m</mi><mi>o</mi><mi>m</mi></mrow></msub><mo>/</mo><mi>h</mi><mo>∝</mo><msup><mrow><mrow><mo>(</mo><mi>x</mi><mo>/</mo><mi>h</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span> at small Bingham number. This is lost once substantial regions of the fluid become unyielded, where we find that the spreading rate of the jet and the decay rate of the centerline velocity increase with the Bingham number, due to the regions of unyielded fluid inducing a blockage effect on the jet. The most striking difference among the three configurations we considered is the extent and position of the regions of unyielded fluid: large portions of ambient and jet fluids (in particular, away from the inlet) are unyielded for the EVP jet in EVP ambient fluid, whereas for the other two configurations, the regions of unyielded fluid are limited to the jet, as expected. We derive a power law scaling for the centerline yield variable and confirm it with the results from our numerical simulations. The yield variable determines the transition from the viscoelastic Oldroyd-B fluid (yielded) to the viscoelastic Kelvin–Voigt material (unyielded).</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105322"},"PeriodicalIF":2.7,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1016/j.jnnfm.2024.105320
Donggang Yao , Martin Zatloukal
This paper presents an extension to the Generalized Newtonian Fluid (GNF) model, where the effects of different flow modes can be discerned. While existing GNF models have proven valuable in simulating processes like molding and extrusion, they often struggle to differentiate between distinct flow modes such as planar extension and simple shear. To address this challenge, we propose a modified GNF model that integrates an objective flow-type parameter, aiming to refine flow characterization. Emphasis is placed on defining the flow-type parameter to be able to transcend viscometric flows, remain frame-indifferent, quantify deformation magnitude, and differentiate between diverse flow modes. Inspired by the new advances in vortex identification in turbulent flow, we introduce a new stretch rate tensor and a new stretch rate parameter that are derived from the real Schur form of the objective velocity gradient tensor. These elements are embedded into the constitutive modeling of non-Newtonian fluid flow. The resulting model is employed to fit polymer melt data from the literature, demonstrating excellent fitting to combined shear and extension data. The basic model uses 5 to 6 parameters for data fitting, and further enhancement may be achieved by incorporating other extracted information of the stretch rate tensor.
{"title":"Inelastic fluid models with an objective stretch rate parameter","authors":"Donggang Yao , Martin Zatloukal","doi":"10.1016/j.jnnfm.2024.105320","DOIUrl":"10.1016/j.jnnfm.2024.105320","url":null,"abstract":"<div><div>This paper presents an extension to the Generalized Newtonian Fluid (GNF) model, where the effects of different flow modes can be discerned. While existing GNF models have proven valuable in simulating processes like molding and extrusion, they often struggle to differentiate between distinct flow modes such as planar extension and simple shear. To address this challenge, we propose a modified GNF model that integrates an objective flow-type parameter, aiming to refine flow characterization. Emphasis is placed on defining the flow-type parameter to be able to transcend viscometric flows, remain frame-indifferent, quantify deformation magnitude, and differentiate between diverse flow modes. Inspired by the new advances in vortex identification in turbulent flow, we introduce a new stretch rate tensor and a new stretch rate parameter that are derived from the real Schur form of the objective velocity gradient tensor. These elements are embedded into the constitutive modeling of non-Newtonian fluid flow. The resulting model is employed to fit polymer melt data from the literature, demonstrating excellent fitting to combined shear and extension data. The basic model uses 5 to 6 parameters for data fitting, and further enhancement may be achieved by incorporating other extracted information of the stretch rate tensor.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105320"},"PeriodicalIF":2.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-11DOI: 10.1016/j.jnnfm.2024.105319
Alexander Kubinski , Fahed Albreiki , Jelena Dinic, Prerana Rathore, Vivek Sharma
Boger fluids that exhibit a rate-independent shear viscosity (typically ∼ 1 Pa∙s = 1000x water viscosity) and elasticity measurable using torsional rheometers (modulus, relaxation time, or first normal stress difference) are considered as the realization of viscoelastic fluids described by the Oldroyd-B model. However, Boger fluids, conventionally formulated as dilute solutions of high molecular weight (Mw) polymers in relatively high viscosity solvents (or solutions of oligomers or lower Mw polymer), are unsuitable for emulating polymeric fluids used in coating formulations that are lower in viscosity, appear inelastic in torsional shear rheometry, and yet appear prone to viscoelastic instabilities. Therefore, Dontula, Macosko, and Scriven (DMS) (AIChE J, 1998) chose to create an alternative model of elastic fluids by dissolving ultrahigh molecular weight (UHMw) poly(ethylene oxide) (PEO) in an aqueous solution of its lower Mw analog, often referred to as poly(ethylene glycol) or PEG. Even though numerous studies of printing and coating flow instabilities use this aqueous PEO/PEG or DMS Boger fluids as model viscoelastic fluids, only a few explicitly measured elastic properties, especially using relaxation time, and hardly any characterized extensional rheology. In this contribution, we recreate the DMS Boger fluids to examine their elasticity and extensional rheology response using dripping-onto-substrate (DoS) rheometry that relies on an analysis of capillarity-driven pinching dynamics. Though the aqueous PEG solution is often treated as a viscous and Newtonian solvent, we discover that in DoS rheometry, both the PEG solution and the DMS Boger fluid display power law response followed by elastocapillary, in contradiction with the assumptions and the response expected of the Oldroyd-B model. Furthermore, the solution of entangled PEG chains influences specific viscosity, pinching dynamics, and measured extensional rheology response in striking contrast with Newtonian solvents of the same viscosity. Lastly, we describe the possibility of using dilute, aqueous solutions of UHMw PEO as model viscoelastic fluids for coating flows, for both elasticity and extensional viscosity can be determined using DoS rheometry. Due to their water-like viscosity, the aqueous PEO solutions appeal as model fluids that have elasticity, emulate Newtonian fluids in the early stages of pinching, and have a relaxation time tunable by changing polymer Mw or concentration.
{"title":"Extensional rheology of elastoviscous aqueous PEO/PEG or DMS Boger fluids and weakly elastic alternatives for investigating viscoelastic flows and instabilities","authors":"Alexander Kubinski , Fahed Albreiki , Jelena Dinic, Prerana Rathore, Vivek Sharma","doi":"10.1016/j.jnnfm.2024.105319","DOIUrl":"10.1016/j.jnnfm.2024.105319","url":null,"abstract":"<div><div>Boger fluids that exhibit a rate-independent shear viscosity (typically ∼ 1 Pa∙s = 1000x water viscosity) and elasticity measurable using torsional rheometers (modulus, relaxation time, or first normal stress difference) are considered as the realization of viscoelastic fluids described by the Oldroyd-B model. However, Boger fluids, conventionally formulated as dilute solutions of high molecular weight (M<sub>w</sub>) polymers in relatively high viscosity solvents (or solutions of oligomers or lower M<sub>w</sub> polymer), are unsuitable for emulating polymeric fluids used in coating formulations that are lower in viscosity, appear inelastic in torsional shear rheometry, and yet appear prone to viscoelastic instabilities. Therefore, Dontula, Macosko, and Scriven (DMS) (AIChE J, 1998) chose to create an alternative model of elastic fluids by dissolving ultrahigh molecular weight (UHM<sub>w</sub>) poly(ethylene oxide) (PEO) in an aqueous solution of its lower M<sub>w</sub> analog, often referred to as poly(ethylene glycol) or PEG. Even though numerous studies of printing and coating flow instabilities use this aqueous PEO/PEG or DMS Boger fluids as model viscoelastic fluids, only a few explicitly measured elastic properties, especially using relaxation time, and hardly any characterized extensional rheology. In this contribution, we recreate the DMS Boger fluids to examine their elasticity and extensional rheology response using dripping-onto-substrate (DoS) rheometry that relies on an analysis of capillarity-driven pinching dynamics. Though the aqueous PEG solution is often treated as a viscous and Newtonian solvent, we discover that in DoS rheometry, both the PEG solution and the DMS Boger fluid display power law response followed by elastocapillary, in contradiction with the assumptions and the response expected of the Oldroyd-B model. Furthermore, the solution of entangled PEG chains influences specific viscosity, pinching dynamics, and measured extensional rheology response in striking contrast with Newtonian solvents of the same viscosity. Lastly, we describe the possibility of using dilute, aqueous solutions of UHM<sub>w</sub> PEO as model viscoelastic fluids for coating flows, for both elasticity and extensional viscosity can be determined using DoS rheometry. Due to their water-like viscosity, the aqueous PEO solutions appeal as model fluids that have elasticity, emulate Newtonian fluids in the early stages of pinching, and have a relaxation time tunable by changing polymer M<sub>w</sub> or concentration.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105319"},"PeriodicalIF":2.7,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-02DOI: 10.1016/j.jnnfm.2024.105309
Sai Peng , Xiang Li , Li Yu , Xiaoyang Xu , Peng Yu
This study aims to investigate the impact of fluid shear-thinning on the Magnus forces acting on a rotating cylinder or a sphere immersed in an unbounded flow using direct numerical simulation. The Carreau model is employed to represent the shear-thinning fluid, with the considered Reynolds number (Re) ranging from 0.01 to 100, Carreau number (Cu) from 0 to 100, power-law index (n) from 0.1 to 1, and viscosity ratio (β) from 0.001 to 0.5. The rotation rate (α) is fixed at 6. A characteristic Reynolds number, Rec, based on a viscosity evaluated at the characteristic shear rate, , is introduced. It is found that, at a constant Rec, compared to that in a Newtonian fluid, the Magnus force exerted on the rotating cylinder or sphere in the shear-thinning fluid is reduced. This reduction results from the difference in viscosity distribution between the upper and lower sides of the cylinder or sphere. Furthermore, our analysis demonstrates that the logarithmic reduction in the Magnus force coefficient can be expressed as a linear combination of the logarithm of the strain rate difference and the logarithm of the shear strain rate sensitive function at two limit states, Cu→0 or Cu→∞. This work may be helpful to deepen the understanding of complex rheological behavior encountered in swirling flow hydrodynamics.
{"title":"Magnus force reduction in a shear-thinning fluid","authors":"Sai Peng , Xiang Li , Li Yu , Xiaoyang Xu , Peng Yu","doi":"10.1016/j.jnnfm.2024.105309","DOIUrl":"10.1016/j.jnnfm.2024.105309","url":null,"abstract":"<div><p>This study aims to investigate the impact of fluid shear-thinning on the Magnus forces acting on a rotating cylinder or a sphere immersed in an unbounded flow using direct numerical simulation. The Carreau model is employed to represent the shear-thinning fluid, with the considered Reynolds number (<em>Re</em>) ranging from 0.01 to 100, Carreau number (<em>Cu</em>) from 0 to 100, power-law index (<em>n</em>) from 0.1 to 1, and viscosity ratio (<em>β</em>) from 0.001 to 0.5. The rotation rate (<em>α</em>) is fixed at 6. A characteristic Reynolds number, <em>Re</em><sub>c</sub>, based on a viscosity evaluated at the characteristic shear rate, <span><math><mrow><msub><mover><mi>γ</mi><mo>˙</mo></mover><mi>α</mi></msub><mspace></mspace><mo>=</mo><mspace></mspace><mi>α</mi><msub><mi>U</mi><mi>∞</mi></msub><mo>/</mo><mn>2</mn><mi>a</mi></mrow></math></span>, is introduced. It is found that, at a constant <em>Re</em><sub>c</sub>, compared to that in a Newtonian fluid, the Magnus force exerted on the rotating cylinder or sphere in the shear-thinning fluid is reduced. This reduction results from the difference in viscosity distribution between the upper and lower sides of the cylinder or sphere. Furthermore, our analysis demonstrates that the logarithmic reduction in the Magnus force coefficient can be expressed as a linear combination of the logarithm of the strain rate difference and the logarithm of the shear strain rate sensitive function at two limit states, <em>Cu</em>→0 or <em>Cu</em>→∞. This work may be helpful to deepen the understanding of complex rheological behavior encountered in swirling flow hydrodynamics.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105309"},"PeriodicalIF":2.7,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142149200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we present a numerical model to analyse particle migration and its impact on local rheological properties when a high-yield stress suspension like 3D printable concrete is transported through a narrow circular pipe. The particle migration is studied through the lens of suspension rheology, where the effect of local particle concentration on rheological properties is accounted for using Krieger–Dougherty-type models. 3D printable mixtures with different aggregate-to-binder (a/b) ratios and flows at various discharge rates are evaluated. It is observed that, depending on the discharge rate and a/b ratio, the flow behaviour could deviate from that expected in a Poiseuille flow of Bingham fluid owing to shear-induced particle migration. Interestingly, as a consequence of particle migration, the formation of a local unsheared region close to the pipe wall is observed, apart from the plug zone at the pipe centre in the partially unsheared pipe flow of Bingham fluids. Often, for concrete pipe flow simulation, the particle size is not small enough to warrant local treatment since the finite size of the particle is not fully reflected in the flow domain. In this work, the developed numerical model is also extended to account for the finite particle size to study the transition between the sheared and unsheared regions and assess the effect of considering finite size in our simulation. Finally, the model’s capability to predict global pressure loss in pipe flow is assessed through comparisons with experimental results.
在这项工作中，我们提出了一个数值模型，用于分析三维可打印混凝土等高屈服应力悬浮液通过狭窄圆管时的颗粒迁移及其对局部流变特性的影响。我们从悬浮流变学的角度研究了颗粒迁移问题，利用克里格-道格蒂（Krieger-Dougherty）型模型考虑了局部颗粒浓度对流变特性的影响。对不同骨料与粘合剂 (a/b) 比率的 3D 可打印混合物和不同排放速率下的流动情况进行了评估。结果表明，根据排出率和 a/b 比率的不同，由于剪切力引起的颗粒迁移，流动行为可能会偏离宾汉流体的普瓦赛流的预期。有趣的是，由于颗粒迁移，在宾汉姆流体部分无剪切的管道流动中，除了管道中心的堵塞区外，还观察到靠近管壁的局部无剪切区的形成。通常情况下，在混凝土管道流动模拟中，由于颗粒的有限尺寸不能完全反映在流动域中，因此颗粒尺寸小到不足以进行局部处理。在这项工作中，还对所开发的数值模型进行了扩展，以考虑有限粒径，从而研究剪切区域和非剪切区域之间的过渡，并评估在模拟中考虑有限粒径的效果。最后，通过与实验结果进行比较，评估了该模型预测管道流动中全局压力损失的能力。
{"title":"Migration of particles suspended in yield stress fluids: Insights from numerical simulation of pipe flow of 3D printable concrete","authors":"Vishwanath Ravindran , Thiyagarajan Ranganathan , A.V. Rahul","doi":"10.1016/j.jnnfm.2024.105305","DOIUrl":"10.1016/j.jnnfm.2024.105305","url":null,"abstract":"<div><p>In this work, we present a numerical model to analyse particle migration and its impact on local rheological properties when a high-yield stress suspension like 3D printable concrete is transported through a narrow circular pipe. The particle migration is studied through the lens of suspension rheology, where the effect of local particle concentration on rheological properties is accounted for using Krieger–Dougherty-type models. 3D printable mixtures with different aggregate-to-binder (a/b) ratios and flows at various discharge rates are evaluated. It is observed that, depending on the discharge rate and a/b ratio, the flow behaviour could deviate from that expected in a Poiseuille flow of Bingham fluid owing to shear-induced particle migration. Interestingly, as a consequence of particle migration, the formation of a local unsheared region close to the pipe wall is observed, apart from the plug zone at the pipe centre in the partially unsheared pipe flow of Bingham fluids. Often, for concrete pipe flow simulation, the particle size is not small enough to warrant local treatment since the finite size of the particle is not fully reflected in the flow domain. In this work, the developed numerical model is also extended to account for the finite particle size to study the transition between the sheared and unsheared regions and assess the effect of considering finite size in our simulation. Finally, the model’s capability to predict global pressure loss in pipe flow is assessed through comparisons with experimental results.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"332 ","pages":"Article 105305"},"PeriodicalIF":2.7,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142095342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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