For a viscoelastic fluid, the characteristics of normal stress and normal stress difference in a converging channel was analyzed. In a constrained converging flow, the stress equation was obtained by perturbation method and Coleman-Noll and connected Maxwell models were used as a constitutive equation. An extensional stress, $-\tau$rr, shows a same increasing-decreasing phenomena along the centerline in above two models. But in the profiles of normal stares difference, -($\tau$rr-$\tau$,θ,θ), two models show difference. -($\tau$ rr-$\tau$,θ,θ) has a maximum peak in Coleman-Noll model but this value increases monotonously in Maxwell model.
In a free converging flow, computer simulation was used with Coleman-Noll model. A normal stress difference, $\tau$xx-$\tau$yy, represents increasing-decreasing phenomena along the centerline in this geometry as same as in the constrained converging geometry. But an extra stress, Sxx, is increasing-decreasing, thereafter, decreasing-increasing whereas the extra stress is increasing monotonously in case of constrained converging flow.
The temperature distribution in a free converging channel was obtained considering heat dissipation. Coleman-Noll model, which have a temperature-dependent constant, was used. At the vicinity of abrupt contraction, temperature-rise is high and has a maximum value. Temperature -rise is strongly affected by Brinkman number and Pechlet number. At high heat dissipation, the normal stress difference is affected by heat dissipation and the value of this is decreased.
With an introduction of molecular dynamics, the constitutive equation was developed. We extended Doi's theory by proposing a new process of equilibrium across slip-links of polymer. The stress equation developed allows a smooth transition from Doi's process A to B at the initial stage of stress relaxation in the simple shear deformation. The relaxation spectrum of normal stress difference was obtained for different strain value. The spectrum shows smooth transition also.
수축챈넬에서 점탄성유체의 연신응력 분포 및 법선응력차(normal stress differnce)를 수학적으로 구해 보았다. 섭동법을 이용하여 경사수축에서 의 응력 분포를 구하였고 자유수축흐름에서는 수치해석을 사용하였다. 두 시스템을 비교한 결과, 수축흐름에서 나타나는 법선응력의 증가 감소현상의 원인은 차이가 있었다. 경사수축에서는 비-뉴우튼 점도가 이 현상의 원인이지만 자유수축흐름에서는 비뉴우튼 점도와 수축흐름계의 구조때문으로 볼 수 있으며 후자가 오히려 큰 역할을 한다. 짧은 시간 영역에서의 응력완화를 설명할 수 있는 점도식을 분자역학의 원리를 이용하여 구하였다. 짧은 시간 영역에서의 고분자의 응력완화를 설명할 수 있는 새로운 과정을 설정하여 점도식을 구했으며, 이를 타 모델과 비교해 보고 연신 흐름에 적용하여 법선응력차를 구해 보았다. 제시된 모델은 짧은 영역에서의 응력변화를 잘 설명해 주었다. 수축챈넬에서 온도분포를 heat dissipation을 고려하여 구해 보았다. 수축챈넬에서 수축부근의 온도는 heat dissipation을 고려하지 않은 온도와 상당한 차이가 있었으며, Br 수와 Pe 수에 크게 영향을 받았다. Heat dissipation이 클 때에 법선응력차는 줄어드는 경향을 보였다.
