Find the viscosity for a LDPE with the following constants$a_T=b_1$exp$(\frac{b_2}{(T)})$

$log{a}_T=\frac{-C_1((T)-T_0)}{C_2+(T-T_0)}$

$log{}_a=log{a}_T+A_0+A_{1}log(a_T({}_a))+A_2[log(a_T({}_a)){]}^2+A_3[log(a_T({}_a)){]}^3+A_4[log(a_T({}_a)){]}^4$

Crystalline polymer shift factor: influence of temperature on viscosity

Amorphous polymer shift factor: influence of temperature on viscosity

Viscosity considering effect of

both temperature and shear rate

$\frac{1}{n}=1+A_1+2A_{2}log(a_T({}_a))+3A_3[log(a_T({}_a)){]}^2+4A_4[log(a_T({}_a)){]}^3$

Power law index considering effect of both

temperature and shear rate

Example: Find the viscosity for a LDPE with the following constants

$A_o=4\mathrm{.}2541$

$A_1=-0\mathrm{.}4978$

$A_2=-0\mathrm{.}0731$

$A_3=0\mathrm{.}0133$

$A_4=-0\mathrm{.}0011$

$b_1=5\mathrm{.}13{10}^{-6}$

$b_2=5640K$

$at{}_a^o=500s^{-1}$ and $T=200C$