The Processing of Polymers

1. The Processing of Polymers Spring 2001

2. Introduction • Three types of polymers of importance • Thermoplastics • Thermosets • Elastomers • As a group, polymers (plastics) possess • Light weight • Corrosion resistance • Electrical insulating resistance • Thermal insulating resistance Dr. Ken Lewis ISAT 430

3. Introduction2 • Applications • Automobile parts • Packaging materials • Electrical and electronic components • Household articles • Utensils • Tubing • Foamed products • Fibers • Films • Paints, varnishes • Fiber matrix composites Dr. Ken Lewis ISAT 430

4. Introduction3 • Polymer usage is surpassing most other materials, at least in volume (low density!) • Plastics are replacing • Metals • Glasses • Woods Dr. Ken Lewis ISAT 430

5. Introduction4 – why plastics are important. • Polymers are easily shaped into unlimited designs • Many plastics are molded which is net shaping so little further processing is necessary • Heating is needed, but far less than for most metal processes. • Many times finishing or painting is not necessary. Dr. Ken Lewis ISAT 430

6. Properties Used in Processing • Enthalpy (Specific Heat) • Thermal Conductivity • Viscosity • Most of these materials are all processed under similar constraints Both of these affect the initial plastification and the final cooling Affects the flow through the dies and spinnerets and mold cavities Dr. Ken Lewis ISAT 430

7. Polymer Characteristics of importance • High viscosity Dr. Ken Lewis ISAT 430

8. In order to understand Polymer processing… We need some grounding in viscosity and viscous flow Dr. Ken Lewis ISAT 430

9. Fluid Mechanics 201 Dr. Ken Lewis ISAT 430

10. Viscosity and Shear Rate • Consider two large parallel plates separated by a fluid. • At time t = 0 the upper plate is set in motion with a velocity v0. • As time proceeds, the fluid gains momentum and we arrive at the final steady state velocity distribution Dr. Ken Lewis ISAT 430

11. Dr. Ken Lewis ISAT 430

12. Viscosity and Shear Rate Consider two very long and wide parallel plates. One is at rest and one is moving with velocity v0. Dr. Ken Lewis ISAT 430

13. Shear Rate • The fluid adheres to both walls so the velocity of the fluid • Is zero at the bottom plate • Is v0 at the top plate • Is proportional to the distance from the bottom plate Dr. Ken Lewis ISAT 430

14. Shear Rate We may rewrite this as: The proportionality constant is just the slope of the line, or: Dr. Ken Lewis ISAT 430

15. Shear Rate • The slope, or the rate of change of the x-velocity in the y direction is called the shear rate. • Shear rates have unit of sec-1. • The faster the plate moves, or the closer they are together… the more stress is imposed on the fluid Dr. Ken Lewis ISAT 430

16. To support this motion, There must be a tangential force on the upper plate  v0  1/Y F/A, the force per unit area  is called stress. We may rewrite this as: Shear Stress yx & Viscosity  Dr. Ken Lewis ISAT 430

17. Newton’s Law of Viscosity • The shear force per unit area is proportional to the local velocity gradient. • The constant of proportionality is called the viscosity Dr. Ken Lewis ISAT 430

18. Newton’s Law of Viscosity • In the neighborhood of the moving surface, the fluid acquires a certain amount of x-momentum. • This fluid in turn, imparts some of its momentum to the adjacent ‘layer’ of liquid causing it to remain in motion in the x direction. • Hence, x-momentum is transmitted through fluid in the y direction. • Thus, yx may be interpreted as the viscous flux of x-momentum in the y direction Dr. Ken Lewis ISAT 430

19. Flux is the “rate of flow per unit area” Dr. Ken Lewis ISAT 430

20. Shear Flow in a Cylinder • Let’s go from plates to cylindrical flow • Flow exhibited by fluid in pipes, capillaries, etc. • The flow is purely axial • No radial components Dr. Ken Lewis ISAT 430

21. Shear Flow in a Cylinder • Fluid velocity is zero at the wall. • Fluid velocity remains constant on concentric cylindrical surfaces. • The flow is purely axial • The fluid velocity reaches a maximum at the center. • This is called: Laminar Flow Dr. Ken Lewis ISAT 430

22. Velocity Distribution in a Cylindrical Tube • The fluid moves under the influence of a pressure gradient. • There is friction, both • at the wall of the tube • Within the fluid itself • Thus, the fluid is: • Accelerated by the pressure gradient • Retarded by the frictional shearing stress Pressure gradient Dr. Ken Lewis ISAT 430

23. Shear Rate The Driving Force is: The Resisting Force is: At equilibrium, they must balance: Dr. Ken Lewis ISAT 430

24. Shear Rate2 So, Stress is greatest At the wall And zero at the center At equilibrium, they must balance: Solving for the shear stress: Dr. Ken Lewis ISAT 430

25. Shear Rate3 If we insert Newton’s Law: Dr. Ken Lewis ISAT 430

26. Shear Rates4 • Shear rate • 0 at the center (r = 0) • Max at the wall (r = R) • Shear rate is an indication of the stress being seen by the fluid, and how fast it sees it! • The shear rate at the wall for a Newtonian fluid is: Q = volumetric flow rate D = diameter Dr. Ken Lewis ISAT 430

27. Viscosities Dr. Ken Lewis ISAT 430

28. Volumetric Newtonian Flow in a Tube The laminar flow of a Newtonian fluid in a pipe or tube may be expressed: Where: Q = the volumetric flow rate [=] m3/s or gal/min P = the pressure drop or driving force [=] kg/m2 or Pa R = the radius of the tube [=] m or cm L = the length of the pipe [=] m or cm  = the Newtonian viscosity [=] Pa s Dr. Ken Lewis ISAT 430

29. The effect of viscosity on Pressure Drop • The Pressure drop across a pipe is a measure of the energy necessary to drive a fluid through the pipe. • Assume a Newtonian Fluid • Two cases: • A viscosity of 0.001 Pa s (like water) • A viscosity of 500 Pa s (like many polymers) Dr. Ken Lewis ISAT 430

30. The effect of viscosity on Pressure Drop Let: Then: Dr. Ken Lewis ISAT 430

31. So the effect of viscosity on fluid transport can be IMPORTANT Dr. Ken Lewis ISAT 430

32. Viscosity • For a Newtonian fluid, the viscosity  is constant. • This holds for simple fluids like water, all gases. • However • For almost all polymeric fluids, the viscosity is NOT constant. • Many times it is a function of the shear rate! Dr. Ken Lewis ISAT 430

33. Newton’s Law of Viscosity or Dr. Ken Lewis ISAT 430

34. Power Law Fluids • The Ostwald-de Waele Model • Known as the Power Law Model Note that for n=1, this reduces to Newton’s Law of viscosity with m =  Dr. Ken Lewis ISAT 430

35. Power Law Fluids • The deviation of n from unity indicates the degree of Non-Newtonian behavior. • If n < 1, material behavior is pseudoplastic • If n> 1, material behavior is dilatant. Dr. Ken Lewis ISAT 430

36. Power Law Viscosity • For most polymers, the isothermal viscosity decreases with increasing shear rate. • Effect of shear on the entangled polymer chains • Usually, in the literature, the viscosity is not shown as “”, but rather “” • So: Dr. Ken Lewis ISAT 430

38. Viscosity • Newtonian Fluid • Viscosity (slope) constant • Non-Newtonian Fluid • Viscosity is not constant • Profound affect on processing Dr. Ken Lewis ISAT 430

39. Remember for a Newtonian fluid n=1  is constant Power Law Viscosity • For a power law fluid: The effect of shear rate on viscosity can be enormous! Dr. Ken Lewis ISAT 430

40. The Effect of Shear Rate on Viscosity

41. The Effect of Shear Rate on Viscosity • The effect can be enormous • In this case the zero shear viscosity is about 1000 Pa s. • At a shear rate of 1000 sec-1, the viscosity has dropped to about 5 Pa s Dr. Ken Lewis ISAT 430

42. The Effect of Shear Rate on Viscosity • The effect can be enormous Dr. Ken Lewis ISAT 430

43. Power Law Shear Rates. • It can be shown that for the flow of a power law fluid through a cylindrical pipe, the maximum shear rate is; Note If n = 1, This reduces to The Newtonian Shear rate Dr. Ken Lewis ISAT 430

44. Power Law Shear Rates2 • And the volumetric flow rate Q for a Power Law fluid through a pipe can be shown to be: Note If n = 1, This reduces to The Newtonian Flow rate Dr. Ken Lewis ISAT 430

45. Properties Dr. Ken Lewis ISAT 430

46. The effect of shear rate on viscosity which affects pressure drop. • Remember the problem of finding the pressure drop necessary to push a fluid through a pipe at a desired flow rate. • Two cases • The Newtonian fluid (water) with a viscosity of 0.001 Pa s. • The polymer with a zero shear viscosity of 500 Pa s. • Let the power law exponent n = 0.55 • And remember the conditions: Dr. Ken Lewis ISAT 430

47. The effect of shear rate on viscosity which affects pressure drop. • Remember the problem of finding the pressure drop necessary to push a fluid through a pipe at a desired flow rate. • In the first case, the results are the same since the fluid is Newtonian and the viscosity is constant…. Dr. Ken Lewis ISAT 430

48. The effect of shear rate on viscosity which affects pressure drop. • Remember the problem of finding the pressure drop necessary to push a fluid through a pipe at a desired flow rate. • In the second case • The fluid is non-Newtonian • This means that the apparent viscosity will be a function of the shear rate • Thus, we must first find the shear rate at the above conditions, • Then using our power law relationships find the apparent viscosity at that shear rate • Finally using the power law equation, calculate the pressure drop that will occur. Dr. Ken Lewis ISAT 430

49. The effect of shear rate on viscosity which affects pressure drop. We know: Dr. Ken Lewis ISAT 430

50. The effect of shear rate on viscosity which affects pressure drop Remember: m is the zero shear viscosity 500 Pa s And n = 0.55 And from the equation for a power law viscosity Look at the Difference! Dr. Ken Lewis ISAT 430