Pub Date : 2024-10-19DOI: 10.1016/j.jnnfm.2024.105343
Vickie Chen , Charles T. Drucker , Claire Love , Jonathon Peterson , Joseph D. Peterson
It is often said that well-entangled and fast-breaking living polymers (such as wormlike micelles) exhibit a single relaxation time in their reptation dynamics, but the full story is somewhat more complicated. Understanding departures from single-Maxwell behavior is crucial for fitting and interpreting experimental data, but in some limiting cases numerical methods for solving living polymer models can struggle to produce reliable predictions/interpretations. In this work, we develop an analytic solution for the shuffling model of living polymers. The analytic solution is a converging infinite series, and it converges fastest in the fast-breaking limit where other methods can struggle.
{"title":"Analytic solution for the linear rheology of living polymers","authors":"Vickie Chen , Charles T. Drucker , Claire Love , Jonathon Peterson , Joseph D. Peterson","doi":"10.1016/j.jnnfm.2024.105343","DOIUrl":"10.1016/j.jnnfm.2024.105343","url":null,"abstract":"<div><div>It is often said that well-entangled and fast-breaking living polymers (such as wormlike micelles) exhibit a single relaxation time in their reptation dynamics, but the full story is somewhat more complicated. Understanding departures from single-Maxwell behavior is crucial for fitting and interpreting experimental data, but in some limiting cases numerical methods for solving living polymer models can struggle to produce reliable predictions/interpretations. In this work, we develop an analytic solution for the shuffling model of living polymers. The analytic solution is a converging infinite series, and it converges fastest in the fast-breaking limit where other methods can struggle.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105343"},"PeriodicalIF":2.7,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142526219","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 : 2024-10-15DOI: 10.1016/j.jnnfm.2024.105330
Mary Agnes Joens , Patrick S. Doyle , Gareth H. McKinley
We study analytically the propulsion of a force- and torque-free swimmer composed of two counterrotating spheres of differing radii through a viscoelastic fluid described by the Giesekus constitutive model. Our analysis includes both swimmers composed of directly touching spheres and those composed of spheres separated by some finite distance. The propulsion speed of the swimmer is calculated by first expanding the equations of motion and the Giesekus constitutive model as a power series in the Weissenberg number, and then using the Lorentz reciprocal theorem to determine the first-order propulsion speed using the known flow fields for rotating and translating two-sphere geometries at zeroth order. We calculate the relative rotation speeds of the two spheres necessary to maintain the torque-free condition, including an approximate correction for fluid elasticity. The impact of the separation distance between the two spheres, the ratio of their radii, and the value of the Giesekus mobility parameter on the propulsion speed are all examined; we find that the propulsion speed of the swimmer is maximized for two touching spheres with a radius ratio of approximately 0.7, with a Giesekus mobility parameter of , corresponding to an Oldroyd-B fluid. We also quantify how increased shear-thinning in the fluid, represented by increasing values of , results in a significant decrease in the swimmer speed. Finally, through calculations of the fluid stresses around the two-sphere swimmer, we demonstrate the development of enhanced hoop stresses around the smaller sphere, which drive the expulsion of stretched fluid behind the smaller sphere and induce motion of the swimmer in the direction of the larger sphere.
{"title":"The motion of a self-propelling two-sphere swimmer in a weakly viscoelastic fluid","authors":"Mary Agnes Joens , Patrick S. Doyle , Gareth H. McKinley","doi":"10.1016/j.jnnfm.2024.105330","DOIUrl":"10.1016/j.jnnfm.2024.105330","url":null,"abstract":"<div><div>We study analytically the propulsion of a force- and torque-free swimmer composed of two counterrotating spheres of differing radii through a viscoelastic fluid described by the Giesekus constitutive model. Our analysis includes both swimmers composed of directly touching spheres and those composed of spheres separated by some finite distance. The propulsion speed of the swimmer is calculated by first expanding the equations of motion and the Giesekus constitutive model as a power series in the Weissenberg number, and then using the Lorentz reciprocal theorem to determine the first-order propulsion speed using the known flow fields for rotating and translating two-sphere geometries at zeroth order. We calculate the relative rotation speeds of the two spheres necessary to maintain the torque-free condition, including an approximate correction for fluid elasticity. The impact of the separation distance between the two spheres, the ratio of their radii, and the value of the Giesekus mobility parameter <span><math><mi>α</mi></math></span> on the propulsion speed are all examined; we find that the propulsion speed of the swimmer is maximized for two touching spheres with a radius ratio of approximately 0.7, with a Giesekus mobility parameter of <span><math><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow></math></span>, corresponding to an Oldroyd-B fluid. We also quantify how increased shear-thinning in the fluid, represented by increasing values of <span><math><mi>α</mi></math></span>, results in a significant decrease in the swimmer speed. Finally, through calculations of the fluid stresses around the two-sphere swimmer, we demonstrate the development of enhanced hoop stresses around the smaller sphere, which drive the expulsion of stretched fluid behind the smaller sphere and induce motion of the swimmer in the direction of the larger sphere.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105330"},"PeriodicalIF":2.7,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551992","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 : 2024-10-10DOI: 10.1016/j.jnnfm.2024.105341
Alexandros Syrakos , Evgenios Gryparis , Georgios C. Georgiou
This study revisits the development of viscoplastic flow in pipes and channels, focusing on the flow of a Bingham plastic. Using finite element simulations and the Papanastasiou regularisation, results are obtained across a range of Reynolds and Bingham numbers. The novel contributions of this work include: (a) investigating a definition of the development length based on wall shear stress, a critical parameter in numerous applications; (b) considering alternative definitions of the Reynolds number in an effort to collapse the development length curves onto a single master curve, independent of the Bingham number; (c) examining the patterns of yielded and unyielded regions within the flow domain; and (d) assessing the impact of the regularisation parameter on the accuracy of the results. The findings enhance the existing literature, providing a more comprehensive understanding of this classic flow problem.
{"title":"A revisit of the development of viscoplastic flow in pipes and channels","authors":"Alexandros Syrakos , Evgenios Gryparis , Georgios C. Georgiou","doi":"10.1016/j.jnnfm.2024.105341","DOIUrl":"10.1016/j.jnnfm.2024.105341","url":null,"abstract":"<div><div>This study revisits the development of viscoplastic flow in pipes and channels, focusing on the flow of a Bingham plastic. Using finite element simulations and the Papanastasiou regularisation, results are obtained across a range of Reynolds and Bingham numbers. The novel contributions of this work include: (a) investigating a definition of the development length based on wall shear stress, a critical parameter in numerous applications; (b) considering alternative definitions of the Reynolds number in an effort to collapse the development length curves onto a single master curve, independent of the Bingham number; (c) examining the patterns of yielded and unyielded regions within the flow domain; and (d) assessing the impact of the regularisation parameter on the accuracy of the results. The findings enhance the existing literature, providing a more comprehensive understanding of this classic flow problem.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105341"},"PeriodicalIF":2.7,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437779","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 : 2024-10-09DOI: 10.1016/j.jnnfm.2024.105331
Panagiotis Sialmas, Kostas D. Housiadas
An exact analytical solution of the lubrication equations for the steady, isothermal, incompressible flow of a viscoelastic Oldroyd-B fluid in a hyperbolic cylindrical contracting pipe is derived. The solution is valid for values of the Deborah number, De, up to order unity (De is defined as the ratio of the longest relaxation time of the polymer to the characteristic residence time of the fluid in the pipe), all values of the ratio of the polymer viscosity to the total viscosity of the fluid, η, and typical values of the contraction ratio, Λ, encountered in experiments and practical applications. It is provided in terms of the streamfunction only and is used in the momentum balance to derive a strongly non-linear ordinary differential equation of second order with unknown a function which corresponds to a modified fluid velocity along the main flow direction. The final equation is solved semi-numerically using a fully spectral (Legendre)-Galerkin approach to resolve the unknown function almost down to machine accuracy. The exact solution for the polymer extra-stresses, which is emphasized is not the full solution of the complete lubrication equations, allows for the derivation of a variety of theoretical expressions for the average pressure-drop along the pipe. In all cases, a decrease in the pressure drop compared to the Newtonian value with increasing De, η and/or Λ is predicted. The differences between the corresponding analytical solution for the planar geometrical configuration are also identified and discussed.
{"title":"An exact solution of the lubrication equations for the Oldroyd-B model in a hyperbolic pipe","authors":"Panagiotis Sialmas, Kostas D. Housiadas","doi":"10.1016/j.jnnfm.2024.105331","DOIUrl":"10.1016/j.jnnfm.2024.105331","url":null,"abstract":"<div><div>An exact analytical solution of the lubrication equations for the steady, isothermal, incompressible flow of a viscoelastic Oldroyd-B fluid in a hyperbolic cylindrical contracting pipe is derived. The solution is valid for values of the Deborah number, De, up to order unity (De is defined as the ratio of the longest relaxation time of the polymer to the characteristic residence time of the fluid in the pipe), all values of the ratio of the polymer viscosity to the total viscosity of the fluid, η, and typical values of the contraction ratio, Λ, encountered in experiments and practical applications. It is provided in terms of the streamfunction only and is used in the momentum balance to derive a strongly non-linear ordinary differential equation of second order with unknown a function which corresponds to a modified fluid velocity along the main flow direction. The final equation is solved semi-numerically using a fully spectral (Legendre)-Galerkin approach to resolve the unknown function almost down to machine accuracy. The exact solution for the polymer extra-stresses, which is emphasized is not the full solution of the complete lubrication equations, allows for the derivation of a variety of theoretical expressions for the average pressure-drop along the pipe. In all cases, a decrease in the pressure drop compared to the Newtonian value with increasing De, η and/or Λ is predicted. The differences between the corresponding analytical solution for the planar geometrical configuration are also identified and discussed.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"335 ","pages":"Article 105331"},"PeriodicalIF":2.7,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744984","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 : 2024-10-05DOI: 10.1016/j.jnnfm.2024.105332
P.S.D. Surya Phani Tej , Pratyush Kumar Mohanty , V. Shankar
We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio , for a fixed solvent to solution viscosity parameter . Here, is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of , that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the regime, for all the flows considered, the limit of zero solvent () is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for and .
{"title":"Master curves for unidirectional flows of FENE-P fluids in rectilinear and curvilinear geometries","authors":"P.S.D. Surya Phani Tej , Pratyush Kumar Mohanty , V. Shankar","doi":"10.1016/j.jnnfm.2024.105332","DOIUrl":"10.1016/j.jnnfm.2024.105332","url":null,"abstract":"<div><div>We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi></mrow></math></span> , for a fixed solvent to solution viscosity parameter <span><math><mi>β</mi></math></span>. Here, <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi></mrow></math></span> is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while <span><math><mi>L</mi></math></span> is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi><mo>≫</mo><mn>1</mn></mrow></math></span>, that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi><mo>≫</mo><mn>1</mn></mrow></math></span> regime, for all the flows considered, the limit of zero solvent (<span><math><mrow><mi>β</mi><mo>=</mo><mn>0</mn></mrow></math></span>) is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for <span><math><mrow><mi>β</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>→</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105332"},"PeriodicalIF":2.7,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417119","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 : 2024-10-03DOI: 10.1016/j.jnnfm.2024.105328
D.R. Hewitt , N.J. Balmforth
Stokes’s second problem is reconsidered for three models of complex fluids: an elasto-viscoplastic fluid, a thixotropic viscoplastic fluid and a discontinuously shear-thickening fluid. In each case, the Stokes-layer dynamics is interrogated with a view to examining the signatures of the detailed rheology. Significant deformations are possible below the yield stress for elasto-viscoplastic fluids as a result of the excitation of elastic waves, particularly near resonances. Thixotropic fluids with viscosity bifurcations layer internally, but surface-speed signatures mostly appear similar to those for simple yield-stress fluids. Stokes-layer oscillations of discontinuous shear thickening fluids can prompt abrupt increases in viscosity, introducing sudden jumps in surface speed. Pre-existing experimental results for layers of kaolin slurries in a motorized, oscillating tray are reconsidered and compared with the results for elasto-viscoplastic and thixotropic fluids.
{"title":"Stokes layers in complex fluids","authors":"D.R. Hewitt , N.J. Balmforth","doi":"10.1016/j.jnnfm.2024.105328","DOIUrl":"10.1016/j.jnnfm.2024.105328","url":null,"abstract":"<div><div>Stokes’s second problem is reconsidered for three models of complex fluids: an elasto-viscoplastic fluid, a thixotropic viscoplastic fluid and a discontinuously shear-thickening fluid. In each case, the Stokes-layer dynamics is interrogated with a view to examining the signatures of the detailed rheology. Significant deformations are possible below the yield stress for elasto-viscoplastic fluids as a result of the excitation of elastic waves, particularly near resonances. Thixotropic fluids with viscosity bifurcations layer internally, but surface-speed signatures mostly appear similar to those for simple yield-stress fluids. Stokes-layer oscillations of discontinuous shear thickening fluids can prompt abrupt increases in viscosity, introducing sudden jumps in surface speed. Pre-existing experimental results for layers of kaolin slurries in a motorized, oscillating tray are reconsidered and compared with the results for elasto-viscoplastic and thixotropic fluids.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105328"},"PeriodicalIF":2.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417121","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 : 2024-10-01DOI: 10.1016/j.jnnfm.2024.105329
Maksim A. Pakhomov , Uzak K. Zhapbasbayev
A transition of Newtonian turbulent fluid to viscoplastic non-Newtonian fluid by cooling in a pipe with a sudden expansion is numerically studied. A recirculation region with negative velocities appears for fluid velocity profiles corresponding to the zone of flow recirculation. A small corner eddy disappears for a non-Newtonian fluid. Significant anisotropy between axial and radial components of Reynolds stresses is numerically shown. The heat transfer distributions along the pipe surface for turbulent non- and Newtonian fluids are qualitatively similar. The peak of heat transfer is shifted upstream in the Schwedoff-Bingham fluid in comparison with the Newtonian one. Authors’ numerical predictions are compared with numerical simulations by other authors for turbulent Schwedoff-Bingham fluids.
{"title":"RANS predictions of turbulent non-isothermal viscoplastic fluid in pipe with sudden expansion","authors":"Maksim A. Pakhomov , Uzak K. Zhapbasbayev","doi":"10.1016/j.jnnfm.2024.105329","DOIUrl":"10.1016/j.jnnfm.2024.105329","url":null,"abstract":"<div><div>A transition of Newtonian turbulent fluid to viscoplastic non-Newtonian fluid by cooling in a pipe with a sudden expansion is numerically studied. A recirculation region with negative velocities appears for fluid velocity profiles corresponding to the zone of flow recirculation. A small corner eddy disappears for a non-Newtonian fluid. Significant anisotropy between axial and radial components of Reynolds stresses is numerically shown. The heat transfer distributions along the pipe surface for turbulent non- and Newtonian fluids are qualitatively similar. The peak of heat transfer is shifted upstream in the Schwedoff-Bingham fluid in comparison with the Newtonian one. Authors’ numerical predictions are compared with numerical simulations by other authors for turbulent Schwedoff-Bingham fluids.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105329"},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417120","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 : 2024-09-23DOI: 10.1016/j.jnnfm.2024.105327
Zhen Liu , Shuai Dong , He Yang , Wenzhi Yang , Muyao Zhu
Coal seam water injection technology is adopted by many mines as an effective means of dust reduction in coal mines. There is a threshold pressure gradient phenomenon in the process of water injection in low permeability coal seam, which makes the flow of pressure water in the fracture structure of coal body present nonlinear seepage characteristics. To reveal the theoretical relationship between the structural parameters of coal and the nonlinear seepage characteristics, firstly, the Bingham fluid constitutive equation is used to describe the non-Newtonian behavior in low-permeability coal. Combined with the fractal tree-like bifurcation fracture network model, a mathematical analytical model of threshold pressure gradient is established. Secondly, the model was verified by high-pressure water invasion and radial seepage experiments, and the sensitivity of the model was analyzed. The results show that the error between the theoretical calculation value and the experimental measurement value is between 8.65 % and 42.4 %, which verifies the validity of the model. The above research results can provide a theoretical basis for improving the water injection effect of low permeability coal seam.
{"title":"Theoretical study on nonlinear seepage mechanism in fractal dendritic fracture network of low permeability coal with water injection","authors":"Zhen Liu , Shuai Dong , He Yang , Wenzhi Yang , Muyao Zhu","doi":"10.1016/j.jnnfm.2024.105327","DOIUrl":"10.1016/j.jnnfm.2024.105327","url":null,"abstract":"<div><div>Coal seam water injection technology is adopted by many mines as an effective means of dust reduction in coal mines. There is a threshold pressure gradient phenomenon in the process of water injection in low permeability coal seam, which makes the flow of pressure water in the fracture structure of coal body present nonlinear seepage characteristics. To reveal the theoretical relationship between the structural parameters of coal and the nonlinear seepage characteristics, firstly, the Bingham fluid constitutive equation is used to describe the non-Newtonian behavior in low-permeability coal. Combined with the fractal tree-like bifurcation fracture network model, a mathematical analytical model of threshold pressure gradient is established. Secondly, the model was verified by high-pressure water invasion and radial seepage experiments, and the sensitivity of the model was analyzed. The results show that the error between the theoretical calculation value and the experimental measurement value is between 8.65 % and 42.4 %, which verifies the validity of the model. The above research results can provide a theoretical basis for improving the water injection effect of low permeability coal seam.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105327"},"PeriodicalIF":2.7,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357221","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.2024.105326
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.
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