• 한국안전학회지
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• 제3권1호
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• pp.15-19
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• 1988

The falling ball viscometer has been widely used for measuring the viscosity of the Newtonian fluids because of its simple theory and low cost. The use of the falling ball viscometer for measuring the non-Newtonian viscosity has been of interest to rheologists for some years. The analysis of the experimental results in a falling ball viscometer rest on Stokes law which yields the terminal velocity for a sphere moving through an infinite medium of fluids. An attempt to use the falling ball viscometer to measure the non-Newtonian viscosity in the intermediate shear rate ranEe was sucessfully accomplished by combining the direct experimental obserbations with a simple analytical model for the average shear-stress and shear rate at, the surface of a sphere. In the experiments with highly viscoelastic polyacrylamide solutions the terminal velocity was observed to be dependent on the time interval between the dropping of successive balls. The time-dependent phenomenon was used to determine characteristic diffusion times of the concentrated solutions of polyacrylamide.

• Korea-Australia Rheology Journal
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• 제14권1호
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• pp.33-45
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• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.

• Korea-Australia Rheology Journal
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• 제12권3_4호
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• pp.165-173
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• 2000

Three-dimensional numerical simulation of isothermal/nonisothermal coextrusion process of two immiscible polymers through a rectangular channel has been done using the finite element method. The encapsulation phenomenon with the less viscous layer encapsulating the more viscous layer was investigated with the generalized Newtonian fluids. The interface position around the symmetric plane obtained by numerical simulation nearly coincided with the one observed in experiments, but the degree of encapsulation was less than the one observed experimentally. Open boundary condition method was found to be applied to the simulation of nonisothermal coextrusion process, however, the results are not far from those using the fully developed boundary condition, because the temperature development along the downstream direction is very slow in the case of convection dominated flow. When the inlet velocity is increased, the interface profile does not change in isothermal flow, while it moves upward in nonisothermal situation. The degree of encapsulation decreases along the downstream direction in nonisothermal flow. When the inlet temperature increases compared to the wall temperature, the outlet interface moves downward and the degree of encapsulation increases. The difference of degree of encapsulation between the simulation and the experiments seems to arise from the viscoelastic effect of the materials. It was concluded that the nonisothermal effect alone does not explain the complex coextrusion process and the viscoelastic effect needs to be considered.

• 유변학
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• 제10권4호
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• pp.234-246
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• 1998

본 연구의 목적은 고분자 농후용액의 정상유동특성(비선형 거동)과 소진폭 전단변형하에서의 동적 점탄성(선형 거동) 간에 존재하는 상관관계를 파악함에 있다. 이를 위해 Advanced Rheometric Expansion System(ARES)과 Rheometrics Fluids Spectrometer (RFS II)를 사용하여 폴리에틸렌 옥사이드, 폴리이소부틸렌 및 폴리아크릴 아마이드 농후용액의 정상류점도 및 동적 선형 점탄성을 광범위한 전단속도와 각주파수 영역에서 측정하였다. 이들 측정결과로부터 정상류점도와 동적점도 또는 동적 유동성간의 상관관계를 제시한 몇 가지 관계식의 적용성을 비교.검토하였다. 그리고 정상류점도와 복소점도의 절대치를 비교하여 양자간의 등가관계를 나타내는 Cox-Merz 법칙의 적용성에 대한 농도의 영향을 실험적으로 검증하였다. 나아가서 대변형하에서의 비선형성의 정도를 나타내는 비선형 스트레인 척도의 개념을 도입하여 Cox-Merz 법칙의 적용성에 미치는 영향을 이론적 관점에서 고찰하였다. 이상의 연구를 통해 얻어진 결과를 요약하면 다음과 같다. (1) 정상류점도의 전단속도 의존성과 동적 점탄성의 각주파수 의존성간에 제시된 여러 관계식들 중에서 정상류점도와 복소점도 절대치간의 등가관계를 나타내는 Cox-Merz법칙이 가장 우수한 적용성을 갖는다. (2) 높은 전단속도 또는 각주파수 영역에서는 정상류점도와 복소점도의 관계가 용액 농도에 따라 서로 상이하게 나타난다. 즉 낮은 농도의 용액에서는 정상류점도가 복소점도에 비해 다소 큰 값을 나타내며, 농도가 증가할수록 이러한 경향은 역전되어 높은 농도의 용액에서는 복소점도가 정상류점도에 비해 큰 값을 갖는다. (3) 비선형 스트레인 척도는 작은 크기의 변형량에서는 직선적으로 증가하다가 점차적으로 그 증가율이 감소하여 최대치에 도달한 후 그 이상의 변형량 영역에서는 변형량이 증가함에 따라 점차 감소하는 거동을 나타낸다. 이러한 거동은 스트레인 증가에 따라 진폭이 점차로 감소하는 감쇠진동함수의 형태를 갖는 이론적 예측과는 상당한 차이를 나타낸다. (4) 대변형하에서 비선형 스트레인 척도의 기울기 (고분자 용액의 비선형성의 정도)는 Cox-Merz 법칙의 적용성에 영향을 미치며, 이 값이 감소할수록 Cox-Merz 법칙은 더욱 잘 성립한다.

• International Journal of Precision Engineering and Manufacturing
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• 제8권1호
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• pp.66-72
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• 2007

A computer code was developed to simulate the filling stage of an injection/compression molding process using a finite element method. The constitutive equation was the compressible Leonov model and the PVT relationship was assumed to follow the Tait equation. The flow-induced birefringence was related to the calculated flow stresses through the linear stress-optical law. Simulations of a disk under different processing conditions, including variations of the compression stroke and compression speed, were performed to determine their effects on the flow-induced birefringence. Simulated pressure traces were also compared to those obtained in conventional injection molding and with experimental data from the literature.

• Korea-Australia Rheology Journal
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• 제14권1호
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• pp.25-32
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• 2002

We report the first steps of a collaborative project between the University of Queensland, Polyflow, Michelin, SK Chemicals, and RMIT University, on simulation, validation and application of a recently introduced constitutive model designed to describe branched polymers. Whereas much progress has been made on predicting the complex flow behaviour of many - in particular linear - polymers, it sometimes appears difficult to predict simultaneously shear thinning and extensional strain hardening behaviour using traditional constitutive models. Recently a new viscoelastic model based on molecular topology, was proposed by McLeish and carson (1998). We explore the predictive power of a differential multi-mode version of the porn-pom model for the flow behaviour of two commercial polymer melts: a (long-chain branched) low-density polyethylene (LDPE) and a (linear) high-density polyethylene (HDPE). The model responses are compared to elongational recovery experiments published by Langouche and Debbaut (19c99), and start-up of simple shear flow, stress relaxation after simple and reverse step strain experiments carried out in our laboratory.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2004년도 추계학술대회논문집
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• pp.65-69
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• 2004

A computer code was developed to simulate the filling stage of the injection/compression molding process by a finite element method. The constitutive equation used here was the compressible Leonov model. The PVT relationship was assumed to follow the Tait equation. The flow-induced birefringence was related to the calculated flow stresses through the linear stress-optical law. Simulations of a disk part under different processing conditions including the variation of compression stroke and compression speed were carried out to understand their effects on flow-induced birefringence. The simulated results were also compared with those by conventional injection molding and with experimental data from literature.

• 설비공학논문집
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• 제11권6호
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• pp.733-739
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• 1999

A modified low-Re $k-\varepsilon$ model is used for the calculation of drag-reducing turbulent flow by polymer injection in a pipe. With the viscoelastic model, molecular viscosity in the definition of turbulent viscosity is related to elongations viscosity of the solution to account for the effects of drag reduction. Finite volume method is used for the discretization, and power-law scheme is used as a numerical scheme. Computed dimensionless velocity profiles are in good agreements with the experimental data in case of low drag reductions. However, in case of high drag reductions, they deviate largely from the measurements in the central zone of the flow field.

• Korea-Australia Rheology Journal
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• 제15권3호
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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.

• Korea-Australia Rheology Journal
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• 제21권1호
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• pp.59-69
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• 2009

The prediction of pressure drop for a droplet flow in a confined micro channel is presented using FE-FTM (Finite Element - Front Tracking Method). A single droplet is passing through 5:1:5 contraction - straight narrow channel - expansion flow domain. The pressure drop is investigated especially when the droplet flows in the straight narrow channel. We explore the effects of droplet size, capillary number (Ca), viscosity ratio ($\chi$) between droplet and medium, and fluid elasticity represented by the Oldroyd-B constitutive model on the excess pressure drop (${\Delta}p^+$) against single phase flow. The tightly fitted droplets in the narrow channel are mainly considered in the range of $0.001{\leq}Ca{\leq}1$ and $0.01{\leq}{\chi}{\leq}100$. In Newtonian droplet/Newtonian medium, two characteristic features are observed. First, an approximate relation ${\Delta}p^+{\sim}{\chi}$ observed for ${\chi}{\geq}1$. The excess pressure drop necessary for droplet flow is roughly proportional to $\chi$. Second, ${\Delta}p^+$ seems inversely proportional to Ca, which is represented as ${\Delta}p^+{\sim}Ca^m$ with negative m irrespective of $\chi$. In addition, we observe that the film thickness (${\delta}_f$) between droplet interface and channel wall decreases with decreasing Ca, showing ${\delta}_f{\sim}Ca^n$ Can with positive n independent of $\chi$. Consequently, the excess pressure drop (${\Delta}p^+$) is strongly dependent on the film thickness (${\delta}_f$). The droplets larger than the channel width show enhancement of ${\Delta}p^+$, whereas the smaller droplets show no significant change in ${\Delta}p^+$. Also, the droplet deformation in the narrow channel is affected by the flow history of the contraction flow at the entrance region, but rather surprisingly ${\Delta}p^+$ is not affected by this flow history. Instead, ${\Delta}p^+$ is more dependent on ${\delta}_f$ irrespective of the droplet shape. As for the effect of fluid elasticity, an increase in ${\delta}_f$ induced by the normal stress difference in viscoelastic medium results in a drastic reduction of ${\Delta}p^+$.