## 3 Results and Discussion
### Temperature Correction of Shear Viscosity  
A flow chart detailing the approach for performing the correction of shear viscosity for fluid temperature rises is given in Figure 3a, where the Cross-WLF model is used to model the flow curve in both Newtonian and shear thinning regimes. As an illustration of the approach, we discuss the results for HIPS. The procedure for correcting the shear viscosity is as follows: (i) Apply, respectively, the Bagley correction and the Weissenberg-Rabinowitsch correction to the apparent viscosity data; (ii) Fit the uncorrected viscosity data determined from step (i) at the measurement temperatures (\(T_{0}=170,\ 180,\ 190,\ 200,\ 220,\ 220,\ \mathrm{and}\ 240\ \mathrm{ \SIUnitSymbolCelsius}\)) to obtain an initial guess for the Cross-WLF model parameters (\(n\), \(\tau^{*}\), \(\eta_{0,r}\), and \(A_{1}\)) in Equations (5) and (6) (see Figure 3b and the model parameters in Table 2); (iii) Perform the nonisothermal runs (\(i\)th iteration) at \(\dot{\gamma}_{\mathrm{a}}=50\)-\(5000\ \mathrm{s}^{-1}\) and \(T_{0}=200,\ 220,\ \mathrm{and}\ 240\ \mathrm{ \SIUnitSymbolCelsius}\) to obtain the respective average fluid temperatures and shear rates at the capillary wall, and then replace the values from the \((i-1)\)th iteration: with \(\overline{T}_{\mathrm{w}}^{(i-1)}\) replaced by \(\overline{T}_{\mathrm{w}}^{(i)}\) and \(\overline{\gamma}^{(i-1)}\) by \(\overline{\gamma}^{(i)}_{\mathrm{r}}\) for each \(\dot{\gamma}_{\mathrm{a}}\); (iv) Calculate the average viscosities \(\overline{\eta}\) using Equation (13) at fixed values of \(\overline{\tau}_{\mathrm{w}}\) (which are set equal to experimental values) and then fit \(\overline{\eta}\) at the corresponding new fluid temperatures and shear rates to optimize the four Cross-WLF model parameters. Repeat steps (iii) and (iv) with improved model parameters until \(\left|\overline{T}_{\mathrm{w}}^{(i)}-\overline{T}_{\mathrm{w}}^{(i-1)} \right|<e\) is satisfied, where the tolerance \(e\) is set equal to \(0.1\ \mathrm{\SIUnitSymbolCelsius}\) (usually \(4-6\) iterations suffice the purpose). Because the iterative process ensures self-consistency between the optimized Cross-WLF model parameters and the resultant temperature profiles, the approach ultimately yields a reliable equivalent shear viscosity (see Figure 4a and the corrected \(n\) value in Table 2). Considering that the viscosity curve is well into the power-law regime such as those shown in Figure 4a-e, one may need to correct the power-law index \(n\) only, due to the fact that the viscous heating occurring at high shear rates does not affect the onset of shear thinning (\(\tau^{*}\)), as well as the temperature dependence of the viscosity at low shear rates (\(\eta_{0,r}\) and \(A_{1}\)). For all the melts studied in Figure 4a-e, the equivalent shear viscosity at \(T_{0}\) has been obtained by shifting the corrected shear viscosity, according to the WLF temperature shifting factor \(a_{\mathrm{T}}\), via the relations: \(\eta(T_{0})=\eta\left(\overline{T}_{\mathrm{w}}\right)/a_{\mathrm{T}}\) and \(\dot{\gamma}(T_{0})=a_{\mathrm{T}}\dot{\gamma}\left(\overline{T}_{\mathrm{w}}\right)\). The equivalent shear viscosity data are found to superpose onto the Cross-WLF model fit based on the corrected \(n\). The temperature correction ultimately gives an equivalent viscosity that is more viscous (i.e., larger \(n\)) and will augment \(\Delta P_{\mathrm{cap}}\). This can be seen from Equation (13)  
Figure 3: (**a**) Flow chart illustrating the viscous heating correction of the shear viscosity \(\eta\) (\(\dot{\gamma}\)). (**b**) Uncorrected steady-state shear viscosity \(\eta\) (\(\dot{\gamma}\)) for HIPS. that \(\overline{\eta}\) is proportional to \(\Delta P_{\rm cap}\). Thus, as observed in Figure 4a-e, an enhancement of viscosity as large as \(\sim\)30% at high shear rates could result in a similar increase in \(\Delta P_{\rm cap}\), as discussed later in Figure 7.