Boundary layer theory is without doubt one of the most successful approximations in the history of fluid mechanics. This is certainly true for Newtonian fluids but for non-Newtonian fluids, the theory is still regarded as incomplete. A major obstacle in extending the theory to non-Newtonian fluids is in the diversity of their constitutive behavior meaning that each fluid model should be treated separately. Furthermore, the nonlinearity introduced by their shear-dependent viscosity and/or elasticity often gives rise to a formidable mathematical task which cannot be solved, at times, even numerically. Understandably, the situation becomes much more complicated when the viscosity of the fluid is time-dependent (e.g., when the fluid is thixotropic). Such fluid systems are quite frequent in industrial applications (e.g., drilling muds) with the common effect being that their viscosity drops with the progress of time at any given shear rate. Due to the complexity of their rheological behavior, working with thixotropic fluids is not an easy task. A major problem is the lack of a robust and easy-to-use rheological model which can describe such behavior. Among different rheological models available to represent such fluid systems Harris model is without doubt one of the simplest ones, albeit admittedly not the best one. Interestingly, the model developed by Harris can also represent purely-viscous shearthinning fluids for certain set of parameter values. Harris tried this version of his rheological model to study Blasius flow. He relied on the technique of similarity solution and reduced the boundary layer equations into a single ODE. But, the equation so obtained was realized to be too formidable to render itself to an analytical or even numerical solution so that it remained unsolved until recently. As a matter of fact, in a recent work Sadeqi et al relied on a robust numerical method to tackle Blasius flow of shear-thinning fluids obeying Harris model. They also showed that Harris model can represent thixotropic fluids only for certain values of the model parameters. In the present work we would like to extend the work carried out in Ref. 15 to Sakiadis flow. Due to the strong nonlinearity of the governing equation, we have decided to rely on the homotopy analysis method (HAM) in the present work. Unlike perturbation techniques, HAM is independent of the smallness/largeness of any parameter involved in the problem. In addition, it provides a simple way to ensure the convergence of the series-solution so that one can always come up with a sufficiently accurate approximation to the solution (even for strongly non-linear problems). Furthermore, unlike all other analytical techniques, the homotopy analysis method provides great freedom in choosing the so-called Sakiadis Flow of Harris Fluids: a Series-Solution
{"title":"Sakiadis Flow of Harris Fluids: a Series-Solution","authors":"N. Khabazi, M. Aryan, Jalil Jamali, K. Sadeghy","doi":"10.1678/RHEOLOGY.42.245","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.245","url":null,"abstract":"Boundary layer theory is without doubt one of the most successful approximations in the history of fluid mechanics. This is certainly true for Newtonian fluids but for non-Newtonian fluids, the theory is still regarded as incomplete. A major obstacle in extending the theory to non-Newtonian fluids is in the diversity of their constitutive behavior meaning that each fluid model should be treated separately. Furthermore, the nonlinearity introduced by their shear-dependent viscosity and/or elasticity often gives rise to a formidable mathematical task which cannot be solved, at times, even numerically. Understandably, the situation becomes much more complicated when the viscosity of the fluid is time-dependent (e.g., when the fluid is thixotropic). Such fluid systems are quite frequent in industrial applications (e.g., drilling muds) with the common effect being that their viscosity drops with the progress of time at any given shear rate. Due to the complexity of their rheological behavior, working with thixotropic fluids is not an easy task. A major problem is the lack of a robust and easy-to-use rheological model which can describe such behavior. Among different rheological models available to represent such fluid systems Harris model is without doubt one of the simplest ones, albeit admittedly not the best one. Interestingly, the model developed by Harris can also represent purely-viscous shearthinning fluids for certain set of parameter values. Harris tried this version of his rheological model to study Blasius flow. He relied on the technique of similarity solution and reduced the boundary layer equations into a single ODE. But, the equation so obtained was realized to be too formidable to render itself to an analytical or even numerical solution so that it remained unsolved until recently. As a matter of fact, in a recent work Sadeqi et al relied on a robust numerical method to tackle Blasius flow of shear-thinning fluids obeying Harris model. They also showed that Harris model can represent thixotropic fluids only for certain values of the model parameters. In the present work we would like to extend the work carried out in Ref. 15 to Sakiadis flow. Due to the strong nonlinearity of the governing equation, we have decided to rely on the homotopy analysis method (HAM) in the present work. Unlike perturbation techniques, HAM is independent of the smallness/largeness of any parameter involved in the problem. In addition, it provides a simple way to ensure the convergence of the series-solution so that one can always come up with a sufficiently accurate approximation to the solution (even for strongly non-linear problems). Furthermore, unlike all other analytical techniques, the homotopy analysis method provides great freedom in choosing the so-called Sakiadis Flow of Harris Fluids: a Series-Solution","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"1 1","pages":"245-253"},"PeriodicalIF":0.0,"publicationDate":"2014-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86629468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
k’ is typically 1/3 for good solvents, and as temperature approaches θ or as M decreases, k’ tends to 1/2. Measurement of [h ] based on the extrapolation to zero concentration is one of the most precise measurements in polymer science although it is also the simplest and cheapest method. However, the extrapolation method cannot be applied to some cases. For example, some polymers can associate and form molecular assemblies. Since [h ] can be related with hydrodynamic volume of solute, we can define [h] of these molecular assemblies hypothetically to represent the size of assemblies. The size of assemblies will vary with concentration as well as [h] of assemblies. In principle, the extrapolation to zero concentration corresponds to [h ] of the molecularly dispersed single chain, and therefore we cannot use the extrapolation method to determine [h ] of assemblies. Alternative methods are desired to determine [h] of the assembly. In this context, the length (molar mass) of thread-like micelles in aqueous solution also varies with concentration. Einaga et al. estimated intrinsic viscosity of thread-like micelles formed by polyoxyethylene alkyl ether, CiEj in the finite concentration regime with the following equation. [ ] [ ] c k c sp 2 η η η ′ + = (1)
对于好的溶剂，k′通常是1/3，当温度接近θ或M减小时，k′趋于1/2。基于外推至零浓度的[h]测量是聚合物科学中最精确的测量方法之一，尽管它也是最简单和最便宜的方法。但是，外推法不能适用于某些情况。例如，一些聚合物可以结合并形成分子组合。由于[h]可以与溶质的水动力体积有关，我们可以假设定义这些分子组合的[h]来表示组合的大小。组件的大小将随浓度以及组件的[h]而变化。原则上，外推到零浓度对应于分子分散单链的[h]，因此我们不能使用外推法来确定组装体的[h]。需要替代方法来确定装配的[h]。在这种情况下，水溶液中线状胶束的长度(摩尔质量)也随浓度的变化而变化。Einaga等人用下式估算了聚氧乙烯烷基醚(CiEj)在有限浓度下形成的丝状胶束的固有粘度。[] [] c k c sp 2 η η η ' + = (1)
{"title":"Reliability of Intrinsic Viscosity Estimated by Single Point Procedure at High Concentrations","authors":"Tadashi Inoue, Naoto Oba, O. Urakawa","doi":"10.1678/RHEOLOGY.42.261","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.261","url":null,"abstract":"k’ is typically 1/3 for good solvents, and as temperature approaches θ or as M decreases, k’ tends to 1/2. Measurement of [h ] based on the extrapolation to zero concentration is one of the most precise measurements in polymer science although it is also the simplest and cheapest method. However, the extrapolation method cannot be applied to some cases. For example, some polymers can associate and form molecular assemblies. Since [h ] can be related with hydrodynamic volume of solute, we can define [h] of these molecular assemblies hypothetically to represent the size of assemblies. The size of assemblies will vary with concentration as well as [h] of assemblies. In principle, the extrapolation to zero concentration corresponds to [h ] of the molecularly dispersed single chain, and therefore we cannot use the extrapolation method to determine [h ] of assemblies. Alternative methods are desired to determine [h] of the assembly. In this context, the length (molar mass) of thread-like micelles in aqueous solution also varies with concentration. Einaga et al. estimated intrinsic viscosity of thread-like micelles formed by polyoxyethylene alkyl ether, CiEj in the finite concentration regime with the following equation. [ ] [ ] c k c sp 2 η η η ′ + = (1)","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"174 1","pages":"261-264"},"PeriodicalIF":0.0,"publicationDate":"2014-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74773225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Long polymer chains in concentrated systems deeply overlap/penetrate with each other to mutually constrain their large-scale (global) motion over the end-to-end distance. This constraint, referred to as the entanglement, has been one of central subjects in polymer physics. The tube model has been frequently utilized to describe such entanglement effects on the chain motion/relaxation. In this model, a focused chain is confined in a uncrossable tube that represents the constraint from the surrounding chains. The relaxation of the focused chain occurs through its own motion along the tube axis and also through the motion of the tube. The latter type of relaxation, reflecting the motional correlation of chains in concentrated systems, is referred to as the constraint release (CR) relaxation. The CR process has been modeled as Rouse-like motion of the tube and the chain therein. This Rouse-like motion results in mutual equilibration of the entanglement segments of the chain, and the equilibrated segments as a whole behave as an enlarged stress-sustaining unit (dilated segment). Thus, in a coarse-grained molecular view, the CR process is described as a dynamic tube dilation (DTD) process where a ratio of the effective tube diameter a'(t) (identical to the size of this dilated segment) to the diameter a of the undilated tube increases with increasing time scale t. In fact, most of current tube models adopt this DTD molecular picture to describe rheological behavior of entangled polymers considerably well, although the consistency in the coarse-graining of the length and time scales is to be carefully examined and the basic parameters of the model are desired to be tested with molecular dynamic simulations. In relation to this consistency of coarse-graining, our previous studies focused on dielectric and viscoelastic properties of linear cis-polyisoprene (PI): PI chains have the type-A dipole parallel along the chain backbone, so that their viscoelastic and dielectric properties in long time scales commonly reflect the global chain motion. Nevertheless, the global motion is averaged differently in these properties. Namely, the dielectric relaxation function F(t ) of linear PI, detecting the end-to-end vector fluctuation, is rather insensitive to the DTD process and almost coincides with the survival fraction of the dilated tube, φ '(t ), whereas the viscoelastic relaxation function m(t ) is quite sensitive to the DTD process and is different from φ '(t ) in general. This difference between F(t ) and m(t ) is very useful for testing the molecular picture of full-DTD in which the relaxed portion of the chains is regarded as a solvent and the dilated tube diameter a'(t ) is related to φ '(t ) as a'(t ) = a{φ '(t )} (d @1.3 for PI). In fact, for monodisperse linear PI, experiments showed that the Dielectric and Viscoelastic Behavior of Low-M Linear Polyisoprene Blended in Long Matrix
{"title":"Dielectric and Viscoelastic Behavior of Low-M Linear Polyisoprene Blended in Long Matrix","authors":"Yumi Matsumiya, H. Watanabe","doi":"10.1678/RHEOLOGY.42.235","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.235","url":null,"abstract":"Long polymer chains in concentrated systems deeply overlap/penetrate with each other to mutually constrain their large-scale (global) motion over the end-to-end distance. This constraint, referred to as the entanglement, has been one of central subjects in polymer physics. The tube model has been frequently utilized to describe such entanglement effects on the chain motion/relaxation. In this model, a focused chain is confined in a uncrossable tube that represents the constraint from the surrounding chains. The relaxation of the focused chain occurs through its own motion along the tube axis and also through the motion of the tube. The latter type of relaxation, reflecting the motional correlation of chains in concentrated systems, is referred to as the constraint release (CR) relaxation. The CR process has been modeled as Rouse-like motion of the tube and the chain therein. This Rouse-like motion results in mutual equilibration of the entanglement segments of the chain, and the equilibrated segments as a whole behave as an enlarged stress-sustaining unit (dilated segment). Thus, in a coarse-grained molecular view, the CR process is described as a dynamic tube dilation (DTD) process where a ratio of the effective tube diameter a'(t) (identical to the size of this dilated segment) to the diameter a of the undilated tube increases with increasing time scale t. In fact, most of current tube models adopt this DTD molecular picture to describe rheological behavior of entangled polymers considerably well, although the consistency in the coarse-graining of the length and time scales is to be carefully examined and the basic parameters of the model are desired to be tested with molecular dynamic simulations. In relation to this consistency of coarse-graining, our previous studies focused on dielectric and viscoelastic properties of linear cis-polyisoprene (PI): PI chains have the type-A dipole parallel along the chain backbone, so that their viscoelastic and dielectric properties in long time scales commonly reflect the global chain motion. Nevertheless, the global motion is averaged differently in these properties. Namely, the dielectric relaxation function F(t ) of linear PI, detecting the end-to-end vector fluctuation, is rather insensitive to the DTD process and almost coincides with the survival fraction of the dilated tube, φ '(t ), whereas the viscoelastic relaxation function m(t ) is quite sensitive to the DTD process and is different from φ '(t ) in general. This difference between F(t ) and m(t ) is very useful for testing the molecular picture of full-DTD in which the relaxed portion of the chains is regarded as a solvent and the dilated tube diameter a'(t ) is related to φ '(t ) as a'(t ) = a{φ '(t )} (d @1.3 for PI). In fact, for monodisperse linear PI, experiments showed that the Dielectric and Viscoelastic Behavior of Low-M Linear Polyisoprene Blended in Long Matrix","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"10 1","pages":"235-244"},"PeriodicalIF":0.0,"publicationDate":"2014-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86537115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Takafumi Toyoda, R. Hidema, Hiroshi Suzuki, Y. Komoda
Latent heat transportation systems are operated by the circulation of phase change slurries, which consist of fluids containing fine particles that have high latent heat capacities. Such fine particles are called phase change materials. Since the phase change material sustains a temperature at its fusion temperature, the phase change slurries can transfer high amounts of heat. Therefore, the flow rate of the heat media is reduced, which minifies industrial systems and reduces the energy required for operation. Latent heat transportation systems using phase change slurries have great potential for various applications; however, the slurries have some disadvantages. One significant disadvantage is their low fluidities; due to the presence of particles, phase change materials have higher viscosities compared with solutions without particles. In addition, the particles agglomerate and disperse in the slurry, imparting non-Newtonian characteristics to the slurry. To increase slurry fluidity, the addition of surfactants that form drag-reducing rod-like micelles, polymers, and some types of brines have been tested to prevent particle agglomeration. These additives also enhance the non-Newtonian behavior of the slurries. The elucidation of the rheological properties of slurries is important to achieve effective control of fluid flows in industrial latent heat transportation systems. Different types of latent heat slurries are used in industry depending on a particular situation and the temperature of the process (Table I). For example, ice/water slurries have been previously employed in lower temperature applications. Since ice has a large latent heat of 334 kJ kg at 0 oC, the ice slurries are used for food cold chains. Much research has been performed on the heat transfer characteristics of ice slurries, on techniques for preventing the agglomeration of ice particles, and on techniques to increase fluidity. In these studies, surfactants, some types of brines, and poly vinyl alcohol (PVA) have been tested to prevent agglomeration. Surfactants and PVA are effective as stabilizers for preventing crystal agglomeration and growth even with the PVA concentrations of only several thousand ppm. Phase change materials whose fusion Crystal Growth and Viscosity Behaviors of Ammonium Alum Hydrate Solution with PVA in Shear Flow
{"title":"Crystal Growth and Viscosity Behaviors of Ammonium Alum Hydrate Solution with PVA in Shear Flow","authors":"Takafumi Toyoda, R. Hidema, Hiroshi Suzuki, Y. Komoda","doi":"10.1678/RHEOLOGY.42.219","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.219","url":null,"abstract":"Latent heat transportation systems are operated by the circulation of phase change slurries, which consist of fluids containing fine particles that have high latent heat capacities. Such fine particles are called phase change materials. Since the phase change material sustains a temperature at its fusion temperature, the phase change slurries can transfer high amounts of heat. Therefore, the flow rate of the heat media is reduced, which minifies industrial systems and reduces the energy required for operation. Latent heat transportation systems using phase change slurries have great potential for various applications; however, the slurries have some disadvantages. One significant disadvantage is their low fluidities; due to the presence of particles, phase change materials have higher viscosities compared with solutions without particles. In addition, the particles agglomerate and disperse in the slurry, imparting non-Newtonian characteristics to the slurry. To increase slurry fluidity, the addition of surfactants that form drag-reducing rod-like micelles, polymers, and some types of brines have been tested to prevent particle agglomeration. These additives also enhance the non-Newtonian behavior of the slurries. The elucidation of the rheological properties of slurries is important to achieve effective control of fluid flows in industrial latent heat transportation systems. Different types of latent heat slurries are used in industry depending on a particular situation and the temperature of the process (Table I). For example, ice/water slurries have been previously employed in lower temperature applications. Since ice has a large latent heat of 334 kJ kg at 0 oC, the ice slurries are used for food cold chains. Much research has been performed on the heat transfer characteristics of ice slurries, on techniques for preventing the agglomeration of ice particles, and on techniques to increase fluidity. In these studies, surfactants, some types of brines, and poly vinyl alcohol (PVA) have been tested to prevent agglomeration. Surfactants and PVA are effective as stabilizers for preventing crystal agglomeration and growth even with the PVA concentrations of only several thousand ppm. Phase change materials whose fusion Crystal Growth and Viscosity Behaviors of Ammonium Alum Hydrate Solution with PVA in Shear Flow","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"26 1","pages":"219-226"},"PeriodicalIF":0.0,"publicationDate":"2014-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77577361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Because of its excellent transparency, mechanical toughness and high heat-distortion temperature, polycarbonate (PC) is widely employed in optical applications such as plastic glasses, optical disks, and optical films. A lightweight replacement for an inorganic glass is being developed due to strong demand in the automobile industry to reduce the weight of electric vehicles. In order to serve as a replacement for an inorganic glass, however, rigidity and the dimensional stability under temperature change need to be improved. The role of a conventional plasticizer is, in general, to increase the flexibility in the solid state and flowability in the molten state. A plasticizer weakens the intermolecular topological interaction between neighbor polymer chains, leading to low viscosity in the flow region. Furthermore, the glass-to-rubber transition occurs at low temperature because the relaxation time of the segmental motion is shortened. Even in the glassy state, a plasticizer usually enlarges the free volume fraction, which has been revealed by the positron annihilation lifetime spectroscopy, proton spin-lattice relaxation at nuclear magnetic resonance and pressurevolume-temperature diagram. Because of the enlarged free volume, the modulus decreases and the thermal expansion increases. To counter this normal behavior of plasticization, additives known to enhance the modulus are used, which is called antiplasticization. According to previous studies, the decrease in the free volume is believed to be the origin of the modulus enhancement. Therefore, β -relaxation of an amorphous polymer, i.e., local relaxation mode, is strongly affected by an antiplasticizer, because the mobility in a local mode is suppressed by loss of the free volume. This anomalous but well-known behavior has been reported for various polymers including poly(vinyl chloride), poly(methyl methacrylate), and cellulose esters. PC is also known to show antiplasticization when combined with various materials. The addition of an antiplasticizer enhances the modulus and reduces the β -relaxation mode located around at -100 oC, which is attributed to mechanisms such as ring-flip process of phenyl groups and rotation of the phenylene rings. Although numerous researches have been carried out on antiplasticization, to the best of our knowledge, the thermal expansion behavior of an antiplasticized glass has not yet been reported; this phenomenon should be clarified to improve our understanding of antiplasticization. Considering the mechanism of antiplasticization, it can be predicted that Thermal Expansion Behavior of Antiplasticized Polycarbonate
{"title":"Thermal Expansion Behavior of Antiplasticized Polycarbonate","authors":"Azusa Miyagawa, S. Nobukawa, M. Yamaguchi","doi":"10.1678/RHEOLOGY.42.255","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.255","url":null,"abstract":"Because of its excellent transparency, mechanical toughness and high heat-distortion temperature, polycarbonate (PC) is widely employed in optical applications such as plastic glasses, optical disks, and optical films. A lightweight replacement for an inorganic glass is being developed due to strong demand in the automobile industry to reduce the weight of electric vehicles. In order to serve as a replacement for an inorganic glass, however, rigidity and the dimensional stability under temperature change need to be improved. The role of a conventional plasticizer is, in general, to increase the flexibility in the solid state and flowability in the molten state. A plasticizer weakens the intermolecular topological interaction between neighbor polymer chains, leading to low viscosity in the flow region. Furthermore, the glass-to-rubber transition occurs at low temperature because the relaxation time of the segmental motion is shortened. Even in the glassy state, a plasticizer usually enlarges the free volume fraction, which has been revealed by the positron annihilation lifetime spectroscopy, proton spin-lattice relaxation at nuclear magnetic resonance and pressurevolume-temperature diagram. Because of the enlarged free volume, the modulus decreases and the thermal expansion increases. To counter this normal behavior of plasticization, additives known to enhance the modulus are used, which is called antiplasticization. According to previous studies, the decrease in the free volume is believed to be the origin of the modulus enhancement. Therefore, β -relaxation of an amorphous polymer, i.e., local relaxation mode, is strongly affected by an antiplasticizer, because the mobility in a local mode is suppressed by loss of the free volume. This anomalous but well-known behavior has been reported for various polymers including poly(vinyl chloride), poly(methyl methacrylate), and cellulose esters. PC is also known to show antiplasticization when combined with various materials. The addition of an antiplasticizer enhances the modulus and reduces the β -relaxation mode located around at -100 oC, which is attributed to mechanisms such as ring-flip process of phenyl groups and rotation of the phenylene rings. Although numerous researches have been carried out on antiplasticization, to the best of our knowledge, the thermal expansion behavior of an antiplasticized glass has not yet been reported; this phenomenon should be clarified to improve our understanding of antiplasticization. Considering the mechanism of antiplasticization, it can be predicted that Thermal Expansion Behavior of Antiplasticized Polycarbonate","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"1 1","pages":"255-260"},"PeriodicalIF":0.0,"publicationDate":"2014-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78736812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Y. Sakanishi, Yusuke Narusaka, M. Itoh, Takashi Saeki
Rheology control for hydrophobic fluids is frequently needed in a wide range of industrial and commercial applications, such as inks, paints, food, cosmetics, pharmaceutical products, petroleum products, and so on. Recently, the field of hydrophobic-supramolecular polymeric materials including self-assembly technology has grown rapidly over the past decade. One of the methods to obtain a self-assembly structure is to use low-molecular-weight compounds as hydrophobic solvents. A number of such chemical reagents, which can transform low-viscosity organic liquids into gels and/or gel-like substances, have been synthesized as organogelators. For suitable molecular design of organogelators, both self-assembly of molecules into nanofibers via hydrogen bonding and formation of a threedimensional network structure due to van der Waals interaction might be important. Low-molecular-weight organogelators constructed from many aromatic rings have been reported; e.g., with biphenyl structure, bisurea compounds, and so on. Skeleton structures of benzene or cyclohexane with chemical side chains have also been reported as organogelators. Within these compounds, benzene-1,3,5-tricarboxamide is well known as an effective organogelator for various oils, the thickening property of which may be related to the hydrogen bonds of amide groups. Shikata, et al. investigated both the supramolecular structure and dynamics of benzene-1,3,5tricarboxamide in hydrophobic fluid. The hydrogen bonds of three amide group quickly formed a coordinate structure like a polymer molecule, which entangled and showed remarkable viscoelastic property. However, unlike the case in a polymer, relaxation of the entanglement occurred by the rearrangement of two supramolecular structures, following the Phantom Crossing Model. The effects of introducing chirality chains and polymer chains have previously been reported. Webb, et al. and Tong, et al. examined N,N’,N’’,N’’’-1,2,4,5tetra alkyl pyromellitamide. This organogelator showed a similar thickening effect as that of tricarboxamide, in which four amide groups of chemical side chains were expected to increase the intermolecular force. In these above-mentioned studies, the target oils were general organic solvents like Rheology Control of Isododecane with Newly Synthesized Organogelators; 3,3',4,4'-Benzophenone Tetracarboxamide
{"title":"Rheology Control of Isododecane with Newly Synthesized Organogelators; 3,3,4,4-Benzophenone Tetracarboxamide","authors":"Y. Sakanishi, Yusuke Narusaka, M. Itoh, Takashi Saeki","doi":"10.1678/RHEOLOGY.42.185","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.185","url":null,"abstract":"Rheology control for hydrophobic fluids is frequently needed in a wide range of industrial and commercial applications, such as inks, paints, food, cosmetics, pharmaceutical products, petroleum products, and so on. Recently, the field of hydrophobic-supramolecular polymeric materials including self-assembly technology has grown rapidly over the past decade. One of the methods to obtain a self-assembly structure is to use low-molecular-weight compounds as hydrophobic solvents. A number of such chemical reagents, which can transform low-viscosity organic liquids into gels and/or gel-like substances, have been synthesized as organogelators. For suitable molecular design of organogelators, both self-assembly of molecules into nanofibers via hydrogen bonding and formation of a threedimensional network structure due to van der Waals interaction might be important. Low-molecular-weight organogelators constructed from many aromatic rings have been reported; e.g., with biphenyl structure, bisurea compounds, and so on. Skeleton structures of benzene or cyclohexane with chemical side chains have also been reported as organogelators. Within these compounds, benzene-1,3,5-tricarboxamide is well known as an effective organogelator for various oils, the thickening property of which may be related to the hydrogen bonds of amide groups. Shikata, et al. investigated both the supramolecular structure and dynamics of benzene-1,3,5tricarboxamide in hydrophobic fluid. The hydrogen bonds of three amide group quickly formed a coordinate structure like a polymer molecule, which entangled and showed remarkable viscoelastic property. However, unlike the case in a polymer, relaxation of the entanglement occurred by the rearrangement of two supramolecular structures, following the Phantom Crossing Model. The effects of introducing chirality chains and polymer chains have previously been reported. Webb, et al. and Tong, et al. examined N,N’,N’’,N’’’-1,2,4,5tetra alkyl pyromellitamide. This organogelator showed a similar thickening effect as that of tricarboxamide, in which four amide groups of chemical side chains were expected to increase the intermolecular force. In these above-mentioned studies, the target oils were general organic solvents like Rheology Control of Isododecane with Newly Synthesized Organogelators; 3,3',4,4'-Benzophenone Tetracarboxamide","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"67 1","pages":"185-190"},"PeriodicalIF":0.0,"publicationDate":"2014-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73585288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We do not have to explain the importance of liquid crystalline (LC) materials in our daily life. Especially, without the application of liquid crystalline materials to display technologies in many practical tools such as television sets, personal computers, mobile phones, and so on, ubiquitous information technologies sustaining our convenient network societies are not considered. 4-cyano-4’-alkyl biphenyls (nCBs), such as 4-cyano-4’-pentyl biphenyl (5CB) and 4-cyano-4’-octyl biphenyl (8CB), have been well known as LC substances widely used in LC displays. Pure 5CB is thermo-tropic LC substance, and demonstrates isotropic to nematic LC phase transition at TI-N = 35 oC and nematic LC phase to solid phase transition (melting point) at TM = 22.5 oC. On the other hand, pure 8CB possesses TI-N = 40 oC, nematic LC to smectic LC phase transition at TN-S = 32.5 oC and TM = 22 oC. 7) In the case of a smectic LC phase formed by 8CB in a temperature range between TN-S and TM, it has been revealed via several scattering experiments and scanning tunneling microscopic (STM) observation on a graphite surface that 8CB molecules form anti-parallel dimers and the formed dimers arranged in a direction (uniaxial director) and also form periodically well-defined layers that can slide over one another. The reason for the anti-parallel dimer formation should be the strong dipole-dipole interaction between cyano groups. Moreover, Smith et al. reported that a solid phase structure of some longer nCBs (n ≥ 8) deposited on flat graphite surfaces showed two-dimensional molecular arrangements constructed by the anti-parallel dimers. Consequently, an anti-parallel dimer, (8CB)2, is an intrinsic Anti-Parallel Dimer Formation of 4-Cyano-4’-Alkyl Biphenyls in Isotropic Benzene Solution Seeds of Liquid Crystalline Phases -
{"title":"Anti-Parallel Dimer Formation of 4-Cyano-4’-Alkyl Biphenyls in Isotropic Benzene Solution - Seeds of Liquid Crystalline Phases -","authors":"T. Shikata, Megumi Minamoto","doi":"10.1678/RHEOLOGY.42.197","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.197","url":null,"abstract":"We do not have to explain the importance of liquid crystalline (LC) materials in our daily life. Especially, without the application of liquid crystalline materials to display technologies in many practical tools such as television sets, personal computers, mobile phones, and so on, ubiquitous information technologies sustaining our convenient network societies are not considered. 4-cyano-4’-alkyl biphenyls (nCBs), such as 4-cyano-4’-pentyl biphenyl (5CB) and 4-cyano-4’-octyl biphenyl (8CB), have been well known as LC substances widely used in LC displays. Pure 5CB is thermo-tropic LC substance, and demonstrates isotropic to nematic LC phase transition at TI-N = 35 oC and nematic LC phase to solid phase transition (melting point) at TM = 22.5 oC. On the other hand, pure 8CB possesses TI-N = 40 oC, nematic LC to smectic LC phase transition at TN-S = 32.5 oC and TM = 22 oC. 7) In the case of a smectic LC phase formed by 8CB in a temperature range between TN-S and TM, it has been revealed via several scattering experiments and scanning tunneling microscopic (STM) observation on a graphite surface that 8CB molecules form anti-parallel dimers and the formed dimers arranged in a direction (uniaxial director) and also form periodically well-defined layers that can slide over one another. The reason for the anti-parallel dimer formation should be the strong dipole-dipole interaction between cyano groups. Moreover, Smith et al. reported that a solid phase structure of some longer nCBs (n ≥ 8) deposited on flat graphite surfaces showed two-dimensional molecular arrangements constructed by the anti-parallel dimers. Consequently, an anti-parallel dimer, (8CB)2, is an intrinsic Anti-Parallel Dimer Formation of 4-Cyano-4’-Alkyl Biphenyls in Isotropic Benzene Solution Seeds of Liquid Crystalline Phases -","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"69 1","pages":"197-206"},"PeriodicalIF":0.0,"publicationDate":"2014-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83394534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T. Yaoita, T. Yaoita, Yuichi Masubuchi, H. Watanabe
Recent experiments have established the thinning feature of the uniaxial steady state elongational viscosity η E for entangled monodisperse linear polystyrene (PS) melts and the thickening feature for equally entangled PS solutions, both occurring in the same range of strain rate ε4 higher than the equilibrium Rouse relaxation frequency, wR. The classical Doi-Edwards tube theory (DE theory) assuming a constant chain length cannot describe the thickening of the solutions, whereas the extended tube theory of Marrucci and Grizzuti considering the chain stretch does not reproduce the monotonic thinning for the melts. Thus, several molecular mechanisms have been proposed for consistent description of the behavior of the melts and solutions, as explained below. One of the important molecular mechanisms under elongational flow is the finite extensible nonlinear elasticity (FENE). Ye et al. investigated the elongational behavior of PS solutions using a modified Mead-Larson-Doi (MLD) model that incorporates reptation, contour length fluctuation, thermal constraint release (TCR), convective constraint release (CCR) and chain stretch associated with FENE. They showed quantitative agreement of the model with the solution data and reported that η E is sensitive to the maximum stretch ratio. Leygue et al. have developed another tube model to show that the magnitude of elongational thickening decreases with a decrease of the maximum stretch ratio. From this result, one may expect that the difference of the maximum stretch ratio between melts and solutions results in the difference of their elongational behavior. However, the reported value of the maximum stretch ratio to attain the thinning was unrealistically small. Yaoita et al. performed multi-chain slip-link (PCN) simulations with reasonable maximum stretch ratios for polystyrene melts and solutions. They showed quantitative agreement of the simulation with the solution data and confirmed the importance of the maximum stretch ratio for thinning/thickening of η E. However, they also found that a reasonable value of this ratio for melts still leads to the thickening and thus tuning of the FENE factor alone cannot reproduce the difference between the melts and solutions. Marrucci and Ianniruberto focused on the interchain Concept of Stretch/Orientation-Induced Friction Reduction Tested with a Simple Molecular Constitutive Equation
{"title":"Concept of Stretch/Orientation-Induced Friction Reduction Tested with a Simple Molecular Constitutive Equation","authors":"T. Yaoita, T. Yaoita, Yuichi Masubuchi, H. Watanabe","doi":"10.1678/RHEOLOGY.42.207","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.207","url":null,"abstract":"Recent experiments have established the thinning feature of the uniaxial steady state elongational viscosity η E for entangled monodisperse linear polystyrene (PS) melts and the thickening feature for equally entangled PS solutions, both occurring in the same range of strain rate ε4 higher than the equilibrium Rouse relaxation frequency, wR. The classical Doi-Edwards tube theory (DE theory) assuming a constant chain length cannot describe the thickening of the solutions, whereas the extended tube theory of Marrucci and Grizzuti considering the chain stretch does not reproduce the monotonic thinning for the melts. Thus, several molecular mechanisms have been proposed for consistent description of the behavior of the melts and solutions, as explained below. One of the important molecular mechanisms under elongational flow is the finite extensible nonlinear elasticity (FENE). Ye et al. investigated the elongational behavior of PS solutions using a modified Mead-Larson-Doi (MLD) model that incorporates reptation, contour length fluctuation, thermal constraint release (TCR), convective constraint release (CCR) and chain stretch associated with FENE. They showed quantitative agreement of the model with the solution data and reported that η E is sensitive to the maximum stretch ratio. Leygue et al. have developed another tube model to show that the magnitude of elongational thickening decreases with a decrease of the maximum stretch ratio. From this result, one may expect that the difference of the maximum stretch ratio between melts and solutions results in the difference of their elongational behavior. However, the reported value of the maximum stretch ratio to attain the thinning was unrealistically small. Yaoita et al. performed multi-chain slip-link (PCN) simulations with reasonable maximum stretch ratios for polystyrene melts and solutions. They showed quantitative agreement of the simulation with the solution data and confirmed the importance of the maximum stretch ratio for thinning/thickening of η E. However, they also found that a reasonable value of this ratio for melts still leads to the thickening and thus tuning of the FENE factor alone cannot reproduce the difference between the melts and solutions. Marrucci and Ianniruberto focused on the interchain Concept of Stretch/Orientation-Induced Friction Reduction Tested with a Simple Molecular Constitutive Equation","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"44 1","pages":"207-213"},"PeriodicalIF":0.0,"publicationDate":"2014-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82332141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In medical facilities, thickening agents are used to avoid the risk of aspiration. However it is problematic that clinical staff is often unsure how to adjust the liquid consistency for each individual dysphagic patient. We need to determine a common index of consistency when we use thickening agents. In Japan, the value of viscosity for patients with difficulties in masticating and swallowing had been measured using a B-type viscometer at a rotor rotation rate of 12 rpm and 20 oC as decided by the Ministry of Health , Labor and Welfare. This rotor rotation rate, calculated as an approximate shear rate of 2-3 s , is a much lower shear rate than that stated for liquid flows through the pharynx. Recently the Japanese Society of Dysphagia Rehabilitation proposed a new criterion for thickened solutions for elderly patients with swallowing difficulties measured by using a cone-and-plate viscometer at a shear rate of 50 s. The rate of 50 s had been adopted as the criterion on the grounds that Wood found that a power function described the relationship between shear stress measured at 50 s and the oral perception of viscosity, so that a shear rate of 50 s was related to the oral perception of viscosity. Other studies of oral shear rates of thickened liquid samples 15-18) have been reported, showing that the correlation between the shear rate of oral perception and the shear rate of objective viscosity is a matter of opinion. In a previous study, we reported a measurement for evaluating the physical properties of thickened solutions and liquid food to examine the correlation with non-oral sensory properties (by tilting the containers, stirring the contents with a spoon, or dripping the thickened solution from a spoon) to establish an index (model foods) of thickened solutions such as honey-like solutions. However, this suggested that the food was not appropriate for the index. The reason was most thickened solutions contain thickening agents that are non-Newtonian liquids, their apparent viscosity varies with shear rate, while other liquid foods, like honey and syrup, are Newtonian. Therefore, flow properties and non-oral sensory properties, e.g., dripping from a spoon, indicated difference between Newtonian and non-Newtonian flow. Recently many kinds of commercial thickening agents have been developed using major ingredients of xanthan gum, guargum, modified starch, etc. Thickened solutions with these ingredients are nonNewtonian; thus, their apparent viscosity varies with shear rate, and they show different dependence on the shear rate of the solution due to the added thickening Relationship between Non-Oral Sensory Evaluations, Oral Sensory Evaluations, and Viscosity of Commercial Thickening Agents –Consideration to the Difference of Shear Rate Dependence–
{"title":"Relationship between Non-Oral Sensory Evaluations, Oral Sensory Evaluations, and Viscosity of Commercial Thickening Agents -Consideration to the Difference of Shear Rate Dependence-","authors":"Y. Iwasaki, H. Ogoshi","doi":"10.1678/RHEOLOGY.42.169","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.169","url":null,"abstract":"In medical facilities, thickening agents are used to avoid the risk of aspiration. However it is problematic that clinical staff is often unsure how to adjust the liquid consistency for each individual dysphagic patient. We need to determine a common index of consistency when we use thickening agents. In Japan, the value of viscosity for patients with difficulties in masticating and swallowing had been measured using a B-type viscometer at a rotor rotation rate of 12 rpm and 20 oC as decided by the Ministry of Health , Labor and Welfare. This rotor rotation rate, calculated as an approximate shear rate of 2-3 s , is a much lower shear rate than that stated for liquid flows through the pharynx. Recently the Japanese Society of Dysphagia Rehabilitation proposed a new criterion for thickened solutions for elderly patients with swallowing difficulties measured by using a cone-and-plate viscometer at a shear rate of 50 s. The rate of 50 s had been adopted as the criterion on the grounds that Wood found that a power function described the relationship between shear stress measured at 50 s and the oral perception of viscosity, so that a shear rate of 50 s was related to the oral perception of viscosity. Other studies of oral shear rates of thickened liquid samples 15-18) have been reported, showing that the correlation between the shear rate of oral perception and the shear rate of objective viscosity is a matter of opinion. In a previous study, we reported a measurement for evaluating the physical properties of thickened solutions and liquid food to examine the correlation with non-oral sensory properties (by tilting the containers, stirring the contents with a spoon, or dripping the thickened solution from a spoon) to establish an index (model foods) of thickened solutions such as honey-like solutions. However, this suggested that the food was not appropriate for the index. The reason was most thickened solutions contain thickening agents that are non-Newtonian liquids, their apparent viscosity varies with shear rate, while other liquid foods, like honey and syrup, are Newtonian. Therefore, flow properties and non-oral sensory properties, e.g., dripping from a spoon, indicated difference between Newtonian and non-Newtonian flow. Recently many kinds of commercial thickening agents have been developed using major ingredients of xanthan gum, guargum, modified starch, etc. Thickened solutions with these ingredients are nonNewtonian; thus, their apparent viscosity varies with shear rate, and they show different dependence on the shear rate of the solution due to the added thickening Relationship between Non-Oral Sensory Evaluations, Oral Sensory Evaluations, and Viscosity of Commercial Thickening Agents –Consideration to the Difference of Shear Rate Dependence–","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"24 1","pages":"169-175"},"PeriodicalIF":0.0,"publicationDate":"2014-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86229206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Ahmadpour, M. Ghasemi, Jalil Jamali, K. Sadeghy
Exact solutions are rather rare in fluid mechanics, and this is particularly so for non-Newtonian fluids. This is perhaps why the field of non-Newtonian fluid mechanics relies so heavily on approximate theories such as boundary layer theory. Having said this, it should be conceded that while this theory has been very successful for Newtonian fluids, for nonNewtonian fluids its validity, in general, is in doubt. That is to say, there is always the danger that by dropping certain non-Newtonian terms from the governing equations, the nonNewtonian flavor of the flow is tarnished thereby affecting the physics of the problem. Also, it is by no means certain that the potential flow outside the boundary remains uninfluenced by the non-Newtonian behavior of the fluid―a point missed in virtually all boundary layer studies carried out in the past in relation to non-Newtonian fluids. Ironically, an exact solution is needed at the first place to assess the validity of boundary layer approximation for any given non-Newtonian fluid. In a recent work Ahmadpour and Sadeghy have shown that for Bingham fluids, an exact solution can be found in von Karman flow (i.e., the swirling flow generated by a rotating disk in an otherwise quiescent fluid). This exact solution provides us with a perfect tool to investigate the validity of boundary theory for Bingham fluids. With this in mind, it is the main objective of the present work to show that for Bingham fluids, the boundary layer theory is valid over a broad range of parameters. To achieve this goal, we will rely on the idea that a suitable similarity variable can be found [see Ref. 1] which transforms the governing partial differential equations into ordinary differential equations. (The idea, which was first introduced by von Karman while obtaining a self-similar exact solution for Newtonian fluids above a rotating disk [see, also, Refs. 3-5], has been shown to be valid for a variety of non-Newtonian fluids comprising shear-thinning fluid, viscoelastic fluids and viscoplastic fluids.) The work is organized as follows: we start with presenting the governing equations in its most general form before simplifying them using the boundary layer approximation. The Bingham model will be introduced next as the rheological model of interest. We will then proceed with transforming the set of governing PDEs into ODEs using an appropriate similarity variable. The numerical method of solution used to solve the governing ODEs will be described next. Numerical results are presented showing the validity of boundary layer approximation in von Karman flow of Bingham fluids. The work is concluded by highlighting its major findings. On the Validity of Boundary Layer Theory for Simulating von Karman Flows of Bingham Fluids
{"title":"On the Validity of Boundary Layer Theory for Simulating von Karman Flows of Bingham Fluids","authors":"A. Ahmadpour, M. Ghasemi, Jalil Jamali, K. Sadeghy","doi":"10.1678/RHEOLOGY.42.161","DOIUrl":"https://doi.org/10.1678/RHEOLOGY.42.161","url":null,"abstract":"Exact solutions are rather rare in fluid mechanics, and this is particularly so for non-Newtonian fluids. This is perhaps why the field of non-Newtonian fluid mechanics relies so heavily on approximate theories such as boundary layer theory. Having said this, it should be conceded that while this theory has been very successful for Newtonian fluids, for nonNewtonian fluids its validity, in general, is in doubt. That is to say, there is always the danger that by dropping certain non-Newtonian terms from the governing equations, the nonNewtonian flavor of the flow is tarnished thereby affecting the physics of the problem. Also, it is by no means certain that the potential flow outside the boundary remains uninfluenced by the non-Newtonian behavior of the fluid―a point missed in virtually all boundary layer studies carried out in the past in relation to non-Newtonian fluids. Ironically, an exact solution is needed at the first place to assess the validity of boundary layer approximation for any given non-Newtonian fluid. In a recent work Ahmadpour and Sadeghy have shown that for Bingham fluids, an exact solution can be found in von Karman flow (i.e., the swirling flow generated by a rotating disk in an otherwise quiescent fluid). This exact solution provides us with a perfect tool to investigate the validity of boundary theory for Bingham fluids. With this in mind, it is the main objective of the present work to show that for Bingham fluids, the boundary layer theory is valid over a broad range of parameters. To achieve this goal, we will rely on the idea that a suitable similarity variable can be found [see Ref. 1] which transforms the governing partial differential equations into ordinary differential equations. (The idea, which was first introduced by von Karman while obtaining a self-similar exact solution for Newtonian fluids above a rotating disk [see, also, Refs. 3-5], has been shown to be valid for a variety of non-Newtonian fluids comprising shear-thinning fluid, viscoelastic fluids and viscoplastic fluids.) The work is organized as follows: we start with presenting the governing equations in its most general form before simplifying them using the boundary layer approximation. The Bingham model will be introduced next as the rheological model of interest. We will then proceed with transforming the set of governing PDEs into ODEs using an appropriate similarity variable. The numerical method of solution used to solve the governing ODEs will be described next. Numerical results are presented showing the validity of boundary layer approximation in von Karman flow of Bingham fluids. The work is concluded by highlighting its major findings. On the Validity of Boundary Layer Theory for Simulating von Karman Flows of Bingham Fluids","PeriodicalId":17434,"journal":{"name":"Journal of the Society of Rheology, Japan","volume":"22 1","pages":"161-167"},"PeriodicalIF":0.0,"publicationDate":"2014-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86441634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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