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2003 Course Advanced Polymer Rheology

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Total No. of Questions : 12] P1358 [Total No. of Pages : 7 [3864]-388 B.E. (Polymer) ADVANCED POLYMER RHEOLOGY (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates : 1) All questions from Section-I and II are compulsory. 2) Marks are given on Right hand side. 3) Use of calculator is allowed. 4) Assume suitable data very necessary. SECTION - I Q1) a) Find the state of stress at a point A in fig. 1. Also, find the magnitude of stress vector acting on a surface whose normal is n= 1 (x1 + x2 ). 2 b) Derive the equation of conservation of momentum. c) [6] [6] Write down the deformation tensor for uniaxial extension and simple shear for a block of material in the fig. 2. [4] P.T.O. OR Q2) a) Forces measurements were made around 1 mm2 test surfaces around a point in a fluid. The vectors normal to the test surfaces correspond to co-ordinate directions x1 , x2 and x3 . The measured force vectors on these surfaces are f1 = 1N in x1 direction; f2 = 2N in x3 direction and f3 = 2N in x2 direction. Find (i) The state of stress at the point. (ii) Calculate invariants of the stress tensor. (iii) Calculate net force on 1 mm2 surface whose normal is x1 + x2 . [9] b) Write a note on different flow phenomena attributed to the first normal stress difference and second normal stress difference. [4] c) Write down the rate of deformation tensor for steady uniaxial extensional flow and steady simple shear flow. Also mention the invariants of the tensor. [3] Q3) a) Polypropylene melt obeying power law model gave the following rheological data. Calculate the value of = r/r0 at which Ryan Johnson stability parameter is maximum. Also calculate reynolds number for the transition between laminar & turbulent flow. [10] Rate of Shear S 1 Shear Stress kPa 3.67 22.4 7.73 32.7 22.8 53.6 51.4 61.8 114.0 87.1 306.0 111.0 682.0 148.0 1380.0 173.0 3340.0 202.0 6390.0 221.0 b) Write a note on Hank s criteria used to study transition between laminar and turbulent flow. [6] [3864]-388 -2- Q4) a) Explain TOM s effect. OR [4] b) Write down expression for pressure drop due to shear and extensional flow through a wedge shaped die. [6] c) Derive an expression for swelling ratio due to tensile stresses for flow through a short capillary (zero length). [6] Q5) a) The behaviour of a plastic in consideration is according to the KelvinVoight model. It is subjected to stress history as shown in fig. 3. Use Boltzman s superposition principle to calculate strain in the material after (i) 90 seconds (ii) 150 seconds. The spring constant is 12 GN/m2 & dash pot constant is 360 GN-s/m2. [8] b) Derive an expression for creep stress relaxation and recovery for a Maxwell model. [6] c) Write a short note on Rouse theory. [3864]-388 -3- [4] OR Q6) a) A plastic is subjected to stress history as shown in fig.4 The behaviour of the material is as per the Maxwell model with elastic constant E = 25 GN/m2 and viscous component = 1200 GNs/m2. Determine strain in the material (i) after u1 seconds and (ii) after u2 seconds. [6] b) Write a note on Boltzman s superposition principle. [6] c) Derive an expression for creep, stress relaxation and recovery for standard linear solid model. [6] [3864]-388 -4- SECTION - II Q7) a) Discuss the effect of melt temperature and molecular branching on polymer melt viscosity. [8] b) Discuss activation energy of flow and factors on which it depends. [4] c) Write a note on storage modulus and storage compliance. [4] OR Q8) a) Derive an expression for flow behaviour index n in terms of activation energy at constant shear stress and activation energy at constant shear rate. [10] b) Discuss the effect of molecular weight on melt rheology of polymers.[6] Q9) a) Explain how Bagley s correction factor is estimated using a capillary rheometer. A rubber based compound gave the following pressure dropvolumetric flow rate data when extruded through a capillary rheometer through a capillary diameter of 1.5 mm. The pressure drop for different L/D ratio capillaries for flow rate of 330 10 9 m3/s are as follows: [8] L/D ratio 20.0 10 5.0 1.0 p.r. drop P (MPa) 64.3 37.0 24.8 14.5 b) Derive an expression for apparent viscosity for a Brookfield viscometer. [8] OR Q10) a) Explain the effect of wall slip phenomena on rheological measurements using a capillary rheometer. [7] b) For a cone and plate rheometer with plate diameter of 12 cm and cone angle 2 , the frequency of rotation and the torque data as recorded is given below. Determine the rheological behaviour of the melt. Assuming that power law model applies. Frequency of rotation rad/mt 6 30 54 90 180 360 600 Torque 9 14.5 17.1 20.0 24.2 30.6 34.4 Find the power law constants. [3864]-388 -5- [9] Q11) a) The runner layout given in the figure 5 is to be balanced by finding dimensions x and y. The polymer follows the power law form = 1,75,000 r 0.3 where z is in N/m2 and r in S 1. The mass flow rate of the polymer is 75 g/s and melt density is 0.7 g/cm3. Calculate the total pressure drop across the runners and the gates. [10] [3864]-388 -6- b) Derive an expression for pressure drop through a wire coating die. [8] OR Q12) a) Plot the thickness distribution along the wall of a 150 mm diameter, 480 mm deep cylindrical container thermoformed out of a polystyrene sheet initially 2.5 mm thick. [6] b) Derive an expression for compaction force for compression molding of a disc with radius R and thickness H. [7] c) A power law fluid with constants 0 = 1.5 104 N s/m2 and n = 0.35 is injected through a centre gate into a disc 3 mm in depth and 220 mm in diameter. If injection rate is constant at 6.5 10 5 m3/s, find the time taken to fill the cavity and minimum injection pressure for non-isothermal condition. [5] rrr [3864]-388 -7-

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