Rheological Measurements and Models - Polymer Rheology - Engineering Sciences Previous Year Questions

1

2008 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2008

For a polymer, viscosity at 50 °C and at 80 °C was found to be 2.00 Pa s and 1.00 Pa s respectively. The value of viscosity at 60 °C is

A

1.65 Pa s

B

1.55 Pa s

C

1.45 Pa s

D

1.35 Pa s

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2

2009 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2009

The shear stress exerted by the polymer on the wall of the mold is

A

2.5 MPa

B

10 MPa

C

5 MPa

D

1 MPa

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3

2010 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2010

The Rheological diagram depicting the relation between shear stress and strain rate for different types of fluids is shown in the figure below.
The most suitable relation for flow of tooth paste being squeezed out of the tube is given by the curve

A

P

B

Q

C

R

D

S

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4

2010 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2010

If η represents viscosity of polymer solution and η₀ represents viscosity of pure solvent, then the specific viscosity (η_sp) of the polymer solution is expressed as

A

η / η₀

B

η / η₀ - 1

C

η₀ / η - 1

D

η₀ / η

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5

2010 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2010

In shear deformation of a polymer melt, the unit of shear rate is

A

m²sec^-1

B

m²sec^-2

C

msec^-1

D

sec^-1

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6

2010 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2010

Liquid A obeys power law equation σ = k γ̇ⁿ (as shown in the attached figure) where σ is shear stress, γ̇ is shear rate, k is consistency index and n is flow behavior index.
The correct unit of consistency index and nature of liquid are

A

Pa·s and Shear thinning

B

Pa·sⁿ and Shear thickening

C

Pa·s and Shear thickening

D

Pa·sⁿ and Shear thinning

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7

2012 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2012

If the flow curves of two viscous fluids are represented by [image] then, the viscosity plots of the fluids will be

A

[image]

B

[image]

C

[image]

D

[image]

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8

2013 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2013

In a cone and plate viscometer, the rate of strain is related to the speed of rotation of the cone, \( \omega \) (radian/second), and the angle between the cone and the plate, \( \alpha \) (radian), by the following relation

A

\(\omega\alpha \)

B

\(\omega\cos\alpha \)

C

\(\frac{\alpha}{\omega} \)

D

\(\frac{\omega}{\alpha} \)

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9

2013 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2013

For a periodic stress \(\sigma = \sigma_0 e^{i\omega t}\), the strain is given by

A

\(\gamma = \sigma_0 \left[\frac{1}{G} + \frac{i}{\omega}\left(\frac{1}{\eta_1} + \frac{1}{\eta_2}\right)\right]e^{i\omega t}\)

B

\(\gamma = \sigma_0 \left[\frac{1}{G} - \frac{i}{\omega}\left(\frac{1}{\eta_1} + \frac{1}{\eta_2}\right)\right]e^{i\omega t}\)

C

\(\gamma = [\sigma_0 + (\eta_1+\eta_2)\omega i]\frac{e^{i\omega t}}{G}\)

D

\(\gamma = [\sigma_0 - (\eta_1+\eta_2)\omega i]\frac{e^{i\omega t}}{G}\)

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10

2014 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2014

The constitutive equation of a shear thinning polymeric fluid is given by \[ \sigma = \frac{\mu_0 \dot{\gamma}}{1 + (\dot{\gamma}/\dot{\gamma}_0)} \] where \(\sigma\) represents shear stress (Pa), and \(\dot{\gamma}\), the corresponding shear rate (s⁻¹). The quantities \(\mu_0\) = 20 Pas and \(\dot{\gamma}_0\) = 10 s⁻¹ are constants. Find the apparent viscosity of the sample (Pas) when the applied shear rate is 40 s⁻¹.

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11

2016 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2016

For a high molecular weight polymer sample with a viscosity of 6 x 10¹¹ Poise and a stress relaxation modulus of 3 x 10⁶ dyne cm^-2 at a given temperature, the relaxation time will be ______ hours.

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12

2017 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2017

The unit of viscosity of a polymer is expressed as

A

Pa.s

B

Pa.s⁻¹

C

Pa.s⁻²

D

Pa.s⁻³

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13

2019 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2019

A 3 mm thick layer of softened poly(methyl methacrylate) at 190 °C is sandwiched between two flat parallel plates. A shear stress of 100 kPa is applied to the softened polymer. Assuming the softened polymer as a Newtonian fluid with an apparent viscosity of 3.9 × 10⁴ Pa s, the relative sliding velocity between the two plates is ______ mm s⁻¹ (round off to one decimal place).

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14

2021 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2021

The plateau modulus of polystyrene has a value of 0.2 × 10⁶ Pa at 150 °C. Given, the density of polystyrene is 1.05 g/cm³, the universal gas constant, R = 8.3 J K⁻¹ mol⁻¹, and the monomer molecular weight is 104 g/mol. The molecular weight between entanglements (rounded off to the nearest integer) of polystyrene chains is __________ g/mol.

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15

2021 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2021

At 215 °C, the viscosity of a polystyrene of molecular weight 250 × 10³ g/mol is 8.0 × 10³ Pa.s. The critical molecular weight of polystyrene, M_c = 35 × 10³ g/mol. For a similar polystyrene of molecular weight 500 × 10³ g/mol, the viscosity (rounded off to nearest integer) will be __________ × 10³ Pa.s.

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16

2024 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2024

Melt flow index (MFI) of a polymer depends on its molecular weight (MW) and melt viscosity (η). Select the correct relation(s) from the following.

A

MFI ∝ \(\frac{1}{MW}\)

B

MFI ∝ MW

C

MFI ∝ \(\frac{1}{η}\)

D

MFI ∝ η

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17

2024 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2024

For a polymer solution, the dependence of viscosity (η) on shear rate (γ̇) is described by the three-parameter Carreau model given by \[ \eta = \eta_0 [1 + (\lambda \dot{\gamma})^2]^{(n-1)/2} \] where, η₀, λ, and n are the three parameters of the model. Here, all three parameters are positive quantities. As the shear rate increases from 1 s⁻¹ to 100 s⁻¹, the viscosity of the polymer solution decreases by a factor of 10. For a polymer solution with n = 0.4 and η₀ = 15 Pa s, the value of the parameter λ is ______ s (rounded off to two decimal places).

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18

2025 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2025

Which one of the following measures of viscosity is dimensionless?

A

Inherent viscosity

B

Reduced viscosity

C

Zero-shear viscosity

D

Specific viscosity

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19

2026 · Engineering Sciences · Polymer Rheology · Rheological Measurements and Models

Engineering Sciences (XE) 2026

Which one of the following is NOT a rotational rheometer?

A

Cone and plate rheometer

B

Parallel plate rheometer

C

Capillary rheometer

D

Cylindrical Couette rheometer

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