• Korea-Australia Rheology Journal
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• v.15 no.3
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• pp.131-150
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• 2003

A new numerical algorithm of finite element methods is presented to solve high Deborah number flow problems with geometric singularities. The steady inertialess planar 4 : 1 contraction flow is chosen for its test. As a viscoelastic constitutive equation, we have applied the globally stable (dissipative and Hadamard stable) Leonov model that can also properly accommodate important nonlinear viscoelastic phenomena. The streamline upwinding method with discrete elastic-viscous stress splitting is incorporated. New interpolation functions classified as rational interpolation, an alternative formalism to enhance numerical convergence at high Deborah number, are implemented not for the whole set of finite elements but for a few elements attached to the entrance comer, where stress singularity seems to exist. The rational interpolation scheme contains one arbitrary parameter b that controls the singular behavior of the rational functions, and its value is specified to yield the best stabilization effect. The new interpolation method raises the limit of Deborah number by 2∼5 times. Therefore on average, we can obtain convergent solution up to the Deborah number of 200 for which the comer vortex size reaches 1.6 times of the half width of the upstream reservoir. Examining spatial violation of the positive definiteness of the elastic strain tensor, we conjecture that the stabilization effect results from the peculiar behavior of rational functions identified as steep gradient on one domain boundary and linear slope on the other. Whereas the rational interpolation of both elastic strain and velocity distorts solutions significantly, it is shown that the variation of solutions incurred by rational interpolation only of the elastic strain is almost negligible. It is also verified that the rational interpolation deteriorates speed of convergence with respect to mesh refinement.

• Proceedings of the Korean Society of Rheology Conference
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• 2002.11a
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• pp.101-103
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• 2002

• Korea-Australia Rheology Journal
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• v.17 no.3
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• pp.99-110
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• 2005

This work presents results of finite element analysis of isothermal incompressible creeping viscoelastic flows with the tensor-logarithmic formulation of the Leonov model especially for the planar geometry with singular comers in the domain. In the case of 4:1 contraction flow, for all 5 meshes we have obtained solutions over the Deborah number of 100, even though there exists slight decrease of convergence limit as the mesh becomes finer. From this analysis, singular behavior of the comer vortex has been clearly seen and proper interpolation of variables in terms of the logarithmic transformation is demonstrated. Solutions of 4:1:4 contraction/expansion flow are also presented, where there exists 2 singular comers. 5 different types spatial resolutions are also employed, in which convergent solutions are obtained over the Deborah number of 10. Although the convergence limit is rather low in comparison with the result of the contraction flow, the results presented herein seem to be the only numerical outcome available for this flow type. As the flow rate increases, the upstream vortex increases, but the downstream vortex decreases in their size. In addition, peculiar deflection of the streamlines near the exit comer has been found. When the spatial resolution is fine enough and the Deborah number is high, small lip vortex just before the exit comer has been observed. It seems to occur due to abrupt expansion of the elastic liquid through the constriction exit that accompanies sudden relaxation of elastic deformation.

• Korea-Australia Rheology Journal
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• v.20 no.1
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• pp.15-26
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• 2008

It has been known that there is a viscoelastic instability in the channel flow past a cylinder at high Deborah (De) number. Some of our numerical simulations and a boundary layer analysis indicated that this instability is related to the shear flow in the gap between the cylinder and the channel walls in our previous work. The critical condition for instability initiation may be related to an inflection velocity profile generated by the normal stress near the cylinder surface. At high De, the elastic normal stress coupling with the streamline curvature is responsible for the shear instability, which has been recognized by the community. In this study, an instability criterion for the flow problem is proposed based on the analysis on the pressure gradient and some supporting numerical simulations. The critical De number for various model fluids is given. It increases with the geometrical aspect ratio h/R (half channel width/cylinder radius) and depends on a viscosity ratio ${\beta}$(polymer viscosity/total viscosity) of the model. A shear thinning first normal stress coefficient will delay the instability. An excellent agreement between the predicted critical Deborah number and reported experiments is obtained.

• The Korean Journal of Rheology
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• v.1 no.1
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• pp.71-79
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• 1989

임계연신비로 특징지어지는 비등온 방사공정에서의 Draw Resonance 발생을, White 의 변형속도에 따라 변하는 물질의 이완시간 모델에 의한 convected Maxwell 유체의 방사 모형을 사용해서 연구했다. 임계연신비의 계산에는 다른 연구자들이 이용하는 통상의 복잡 한 수치계산인 eigenvalue 방법을 쓰지 않고 전파하는 동적 waves 에 근거한 간단한 Hyun 의 이론을 사용했다. 그 결과 Staton Number와 냉각 공기온도로서 나타내지는 방사공정의 냉각이 공정을 안정시킨다는 것이 밝혀졌다. 다시 말해서 연신점도가 변형후화인 유체이거 나 변형박화인 유체이거난 상관없이 항상 Stanton Number가 켜지거나 또는 냉각공기온도 가 낮아질수록(즉냉각효과가 커질 때) 임계연신비가 커지는 것이다(단변형박화 dvcp의 빌부 구간을 제외하고) 한편 Draw Resonacnce 에 미치는 냉각의 효과는 무차원 이완시간(a Weissenberg Number 혹은 a Deborah number)이 커질수록 작아진다는 것도 발견됐다. 이 것은 process Time 이 작아지면 열전달이 작아지기 때문이다. 이러한 내용들은 다른 연구 자들의 결과와도 잘 부합된다.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.219-226
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• 2004

In this study the deformation of liquid-air interface of Newtonian or Boger fluids filled between two par­allel-plates geometry was investigated when two surfaces were separated at a constant speed. The interface between the fluid and air showed either stable or unstable deformation depending on experimental con­ditions. Repeated experiments for a wide range of experimental conditions revealed that the deformation mode could be classified into three types: 'stable region', 'fingering' and 'cavitation'. The experimental condition for the mode of deformation was plotted in a capillary number vs. Deborah number phase plane. It has been found that the elasticity of Boger fluids destabilize the interface deformation. On the other hand, the elasticity suppresses the formation and growth of cavities.

• Korea-Australia Rheology Journal
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• v.16 no.1
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• pp.35-45
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• 2004

Rates of chemical absorption of $CO_2$ in water-in-oil (w/o) emulsion were measured in a flat-stirred vessel at $25^{\circ}C$. The w/o emulsion was composed of aqueous monoethanolamine (MEA) droplets as a dispersed phase and non-Newtonian viscoelastic benzene solutions of polybutene (PB) and polyisobutylene (PIB) as a continuous phase. The liquid-side-mass transfer coefficient ($k_L$) was obtained from the dimensionless empirical equation containing Deborah number expressed as the properties of pseudoplasticity of the non-Newtonian liquid. $k_L$ was used to estimate the enhancement factor due to chemical reaction between $CO_2$ and MEA in the aqueous phase. PIB with elastic property of non-Newtonian liquid made the rate of chemical absorption of $CO_2$ accelerate compared with Newtonian liquid.

• Fire Science and Engineering
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• v.5 no.2
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• pp.21-35
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• 1991

As a part of studies of drag reduction phenomenon, at the entrance flow region of abrupt contraction tube flowing water, dilute and concentrated drag reducing polymer solutions contraction losses are estimated experimentally. Futher more, entrance lengths are considered theoretically and are measured experimentally. In the present experiment, fluid temperature is fixed l$0^{\circ}C$ and flow rates are 3,000

• Journal of Pharmaceutical Investigation
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• v.29 no.4
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• pp.295-307
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• 1999

Using a Rheometries Fluids Spectrometer (RFS II), the dynamic viscoelastic properties of aqueous poly(ethylene oxide) (PEO) solutions in small amplitude oscillatory shear flow fields have been measured over a wide range of angular frequencies. The angular frequency dependence of the storage and loss moduli at various molecular weights and concentrations was reported in detail, and the result was interpreted using the concept of a Deborah number De. In addition, the experimentally determined critical angular frequency at which the storage and loss moduli become equivalent was compared with the calculated characteristic time (or its inverse value), and their physical significance in analyzing the dynamic viscoelastic behavior was discussed. Finally, the relationship between steady shear flow and dynamic viscoelstic properties was examined by evaluating the applicability of some proposed models that describe the correlations between steady flow viscosity and dynamic viscosity, dynamic fluidity, and complex viscosity. Main results obtained from this study can be summarized as follows: (1) At lower angular frequencies where De<1, the loss modulus is larger than the storage modulus. However, such a relation between the two moduli is reversed at higher angular frequencies where De>l, indicating that the elastic behavior becomes dominant to the viscous behavior at frequency range higher than a critical angular frequency. (2) A critical angular frequency is decreased as an increase in concentration and/or molecular weight. Both the viscous and elastic properties show a stronger dependence on the molecular weight than on the concentration. (3) A characteristic time is increased with increasing concentration and/or molecular weight. The power-law relationship holds between the inverse value of a characteristic time and a critical angular frequency. (4) Among the previously proposed models, the Cox-Merz rule implying the equivalence between the steady flow viscosity and the magnitude of the complex viscosity has the best validity. The Osaki relation can be regarded to some extent as a suitable model. However, the DeWitt, Pao and HusebyBlyler models are not applicable to describe the correlations between steady shear flow and dynamic viscoelastic properties.