GATE Overflow for GATE XE - Recent activity in Polymer Rheology

Edited: GATE XE 2026 | Question: 120

Thu, 02 Apr 2026 08:32:29 +0000

A viscoelastic polymer is subjected to a constant strain of $0.3$. The behaviour of the polymer follows Maxwell model of linear viscoelasticity. Elastic modulus of the polymer is $5$ $\text{MPa}$ and the relaxation time is $200$ days. The stress in the polymer after $100$ days from the initial application of the strain is $\_\_\_\_\_\_$ $\text{MPa}$ (rounded off to two decimal places).

Edited: GATE XE 2026 | Question: 113

Thu, 02 Apr 2026 08:10:18 +0000

The variation of steady shear viscosity $(\eta)$ of a polymer melt with shear rate $(\dot{\gamma})$ is shown in the figure, where $\dot{\gamma}_{s}$ is the upper limit of the applied shear rate.

Which one of the following figures, labeled $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$, shows the most appropriate variation of shear stress $(\tau)$ with shear rate for the same polymer melt?

$\mathrm{P}$
$\mathrm{Q}$
$\mathrm{R}$
$\mathrm{S}$

Edited: GATE XE 2026 | Question: 104

Thu, 02 Apr 2026 07:37:49 +0000

Which one of the following is NOT a rotational rheometer?

Cone and plate rheometer
Parallel plate rheometer
Capillary rheometer
Cylindrical Couette rheometer

Edited: GATE XE 2026 | Question: 102

Thu, 02 Apr 2026 07:35:41 +0000

Norrish-Smith effect or Trommsdorff effect during free radical bulk polymerization at high conversion is characterized by $\_\_\_\_$.

increase in rate of polymerization with time due to increase in viscosity
decrease in rate of polymerization with time due to increase in viscosity
decrease in rate of polymerization with time due to reduction in viscosity
increase in rate of polymerization with time due to reduction in viscosity

Edited: GATE XE 2025 | Question: 110

Mon, 30 Jun 2025 15:05:07 +0000

Which one of the following measures of viscosity is dimensionless?

Inherent viscosity
Reduced viscosity
Zero-shear viscosity
Specific viscosity

A certain polymer synthesized in the laboratory shows that all the chains have the same number

Tue, 03 Jun 2025 02:42:55 +0000

Recategorized: GATE XE 2023 | Question: 113

Mon, 05 May 2025 12:16:29 +0000

\begin{tabular}{|c|c|c|c|c|}
\hline \multirow[t]{2}{*}{ Q. 123} & \multicolumn{4}{|c|}{\begin{tabular}{l}
Mechanical stress is applied on a polymer. Identify the correct match(es) \\
between the statements $(1,2,3,4,5)$ that describe the deformations and \\
the regimes (P, Q, R).
\end{tabular}} \\
\hline & $P$ & Rubbery regime & 1 & \begin{tabular}{l}
Stress-relaxation takes place and the excess \\
free energy is dissipated
\end{tabular} \\
\hline & Q & \begin{tabular}{l}
Region around \\
glass transition \\
temperature $\left(T_{g}\right)$
\end{tabular} & 2 & \begin{tabular}{l}
The motions of the molecules are long- \\
range
\end{tabular} \\
\hline & $\mathrm{R}$ & \begin{tabular}{l}
Sample under \\
deformed state
\end{tabular} & 3 & \begin{tabular}{l}
Segmental motion of the molecules is \\
important
\end{tabular} \\
\hline & & & 4 & \begin{tabular}{l}
The maximum relaxation time is strongly \\
dependent on the molecular weight
\end{tabular} \\
\hline & & & 5 & \begin{tabular}{l}
The deformations are independent of the \\
molecular wcight and primarily depend on \\
the local structure
\end{tabular} \\
\hline

& \multicolumn{4}{|c|}{ P-2; Q-5; R-1 } \\
\hline
& \multicolumn{4}{|c|}{ P-1; Q-5; R-1 } \\
\hline
& \multicolumn{4}{|c|}{ P-2; Q-3; R-4 } \\
\hline
& \multicolumn{4}{|c|}{ P-4; Q-3; R-1 } \\
\hline
\end{tabular}

Recategorized: GATE XE 2024 | Question: 105

Mon, 05 May 2025 10:54:41 +0000

The 'die swell' phenomenon exhibited by a polymer melt is due to

viscous deformation
plastic deformation
viscous and elastic deformation
elastic recovery

Recategorized: GATE XE 2024 | Question: 112

Mon, 05 May 2025 10:54:20 +0000

Melt flow index $\text{(MFI)}$ of a polymer depends on its molecular weight $(M W)$ and melt viscosity $(\eta)$. Select the correct relation(s) from the following.

$\text{M F I} \propto \frac{1}{M W}$
$\text{M F I} \propto M W$
$\text{M F I} \propto \frac{1}{\eta}$
$\text{M F I} \propto \eta$

Recategorized: GATE XE 2024 | Question: 119

Mon, 05 May 2025 10:53:55 +0000

For a polymer solution, the dependence of viscosity $(\eta)$ on shear rate $(\dot{\gamma})$ is described by the three-parameter Carreau model given by
\[
\eta=\eta_{0}\left[1+(\lambda \dot{\gamma})^{2}\right]^{(n-1) / 2}
\]
where, $\eta_{0}, \lambda$, and $n$ are the three parameters of the model. Here, all three parameters are positive quantities. As the shear rate increases from $1 \mathrm{~s}^{-1}$ to $100 \mathrm{~s}^{-1}$, the viscosity of the polymer solution decreases by a factor of $10$. For a polymer solution with $n=0.4$ and $\eta_{0}=15 \mathrm{~Pa} \mathrm{~s}$, the value of the parameter $\lambda$ is __________ s $\text{(rounded off to two decimal places)}$.

Recategorized: GATE XE 2024 | Question: 121

Mon, 05 May 2025 10:53:46 +0000

The linear viscoelastic behaviour of a polymer is described by the Kelvin-Voigt model consisting of a spring element of elastic modulus $10$ MPa in parallel with a dashpot of viscosity $3.6 \times 10^{11} \mathrm{~Pa} \mathrm{~s}$. A fixed stress of $40$ MPa is suddenly applied to the polymer and maintained thereafter. The value of the strain after one hour from the sudden application of the stress is _________ $\text{(rounded off to two decimal places)}$.