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# Polymer melt rheology

Every Plastic thermoplastic object manufactured in the world will have gone through the melt stage during its processing. Normally solid plastic polymer pellets will be feed into an extruder or injection moulding machine, where the polymer is melted and then shape formed to create a fibre, film, tube or injection moulded article. Thermoplastic shape forming is a highly developed technology with a huge economic turnover; however a deep scientific and engineering understanding of how thermoplastics behave whilst being processed has only recently started to emerge. With the aid of sophisticated numerical modelling and the choice of a correct viscoelastic constitutive equation it is now possible for engineers to model the way thermoplastic can be processed. This in turn means that existing processes can be improved and new processes discovered not by just trial and error, but by engineering design.

The polymer melt rheology story is one that has been with me all my academic life. It has involved **first** observing, using **flow birefrengence** techniques, the **processing flow behaviour** of molten polymer. N.Checker, M.R. Mackley and D.W. Mead. *On the flow of molten polymer into within and out of ducts Part 1 , Part 2 *Phil. Trans. Roy. Soc. (Lond.). A308, 451-477 (1983).

**Then, **the polymer had to be **characterised **in the correct way. M.R.Mackley, R.T.J.Marshall, J.B.A.F.Smeulders and F.D.Zhao. The rheological characterization of polymeric and colloidal fluids. Chem Eng Sci. 49,16, 2551-2565 (1994).

**Then** systematic experiments were carried out using the **Multipass Rheometer (MPR)** that was specifically developed for the task of following polymer processing flow.

**Below is a Powerpoint presentation given about the MPR in 2006 at Yamagata Japan**

Others developed numerical code that was able to **model ** the processing behaviour of molten polymer. T.D.Lord, L. Scelsi, D.G. Hassell, M.R. Mackley, J. Embery, D Auhl and O.G.Harlen The matching of 3D Rolie-Poly viscoelastic numerical simulations with experimental polymer melt flow within a slit and a cross-slot geometry*. *Journal of Rheology 54, 2. 355-373 (2010)

The** final part** of the MPR story is told in a seminar presentation given in 2009 at The University of Science abd Technology, Hong Kong.

There are two movie sequences relevant to the Hong Kong presentation

The MPR movie below shows the flow birefringence processing behaviour of **molten polyethylene flowing within a slit**. Each dark retardation band measures a certain level of stress within the polymer

The movie below shows the flow birefringence processing behaviour of **molten polyethylene flowing within a Cross Slot geometry**. Each dark retardation band measures a certain level of stress within the polymer.

**Papers relevant to polymer melt rheology are given below**

- V.Kamath and M.R. Mackley.
*The determination of polymer relaxation moduli and memory functions using integral transforms*Journal of Non-Newtonian Fluid Mechanics. 32, 119-144 (1989). - M.R.Mackley, R.T.J.Marshall, J.B.A.F.Smeulders and F.D.Zhao. The rheological characterization of polymeric and colloidal fluids. Chem Eng Sci. 49,16, 2551-2565 (1994).
- R. Liang and M.R. Mackley. Rheological characterisation of the time and strain dependence of polyisbutylene melts. Journal of Non-Newtonian Fluid Mech. 52, 387-405 (1994).
- R. Ahmed and M.R.Mackley. Experimental centreline planar extension of polyethylene. Journal of Non-Newtonian Fluid Mechanics. 56, 2, 127-149 (1995).
- R Ahmed, R Liang and M.R.Mackley. The experimental observation and numerical prediction of planaar entry flow and die swell for molten polyethylene. Journal Non Newtonian Fluid Mech. 59, 2-3, 129-153 (1995).
- M.R.Mackley and R Rutgers.
- M Ranganthan, M.R.Mackley and P.H.J.Spittler. Experimental observations and modelling of time dependent capillary flow for a high density polyethylene using a multipass rheometer J Rheology ,43(2) 443-451 (1999).
- K. Lee and M.R.Mackley The importance of slip in matching polyethylene processing data with numerical simulation J Non Newtonian Fluid Mech 94 159-177 (2000)
- R.Rutgers and M.R.Mackley The correlation of experimental surface extrusion instabilities with numerically predicted exit surface stress concentrations and melt strength for linear low density polyethylene Journal of Rheology 44(6) 1319-1334 (2000)
- R.F Liang and M.R.Mackley The gas-assisted extrusion of molten polyethylene Journal of Rheology. 45 (1) 211-226 (2001)
- K Lee and M.R.Mackley The application of the Multi-Pass rheometer for precise rheo-optic characterisation of polyethylene melts Chemical Engineering Science 56, 5653-5661 (2001)
- K Lee, M.R.Mackley, T.C.B. Mcleish, T.M.Nicholson, and O.Harlen

Experimental observation and numerical simulation of transient stress fangs within flowing molten polyethylene Journal of Rheology. 45(6) 1261-1277 (2001) - R.P.G.Rutgers and M.R.Mackley The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE J Non Newtonian Fluid Mech 98, 185-199 (2001)
- J.F.Agassant , F. Baaijens , H. Bastian, A. Bernnat, A.C.B.Bogaerds T.Coupez, B. Debbaut, A.L.Gavrus, A.Goublomme , M. van Gurp, R.J. KoopmansG, H.M.Laun, K.Lee, O.H. Nouatin, M.R.Mackley, G.W.M.Peters , G. Rekers W.M.H.Verbeeten , B.Vergnes M.H. Wagner, E.Wassner and W.F. Zoetelief. The matching of experimental polymer processing flows to numerical simulation
- D.R.Arda and M.R.Mackley, The Effect of Die Exit Curvature, Die Surface Roughness and a Fluoropolymer Additive on Sharkskin Extrusion Instabilities in Polyethylene Processing. Journal of Non Newtonian Fluid Mechanics 126, 47-61 (2005)
- D.R. Arda and M.R. Mackley, Sharkskin instabilities and the effect of slip from gas-assisted extrusion. Rheol. Acta 44, 4, 352-359 (2005)
- M.W. Collis, M.R. Mackley. The melt processing of monodisperse and polydisperse polystyrene melts within a slit entry and exit flow. J. Non-Newtonian Fluid Mech. 128 ,29–41 (2005)
- M.W.Collis, A.K.Lele, M.R.Mackley, R.S.Graham, D.J.Groves, A.E.Likhtman, T.M.Nicholson, O.G. Harlen, T.C.B.Mcleish, L.R.Hutchings, C.M. Fernyhough, and R.N.Young Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization. Journal of Rheology 49 (2) 501-522 (2005)
- R Valette, M R. Mackley and G Hernandez Fernandez del Castillo Matching time dependent pressure driven flows with a Rolie Poly numerical simulation. Journal of Non-Newtonian Fluid Mechanics Volume 136, Issues 2-3 , 15 July, 118-125 (2006)
- J-F. Agassant, D.R. Arda, C. Combeaud, A. Merten, H. Muenstedt ,M.R. Mackley, L. Robert and B. Vergnes,Polymer processing extrusion instabilities and methods for their elimination or minimisation
*.*Journal of International Polymer Processing. V3, 239-255 (2006) - K. D. Coventry and M. R. Mackley Cross-slot extensional flow birefringence observations of polymer melts using a multi-pass rheometer Journal of Rheology 52, 2, 401-415 (2008)
- D.G.Hassell and M.R.Mackley. Localised flow-induced crystallisation of a polyethylene melt. Rheologica Acta. 47, Nos 9 435-446 (2008)
- D.G. Hassell, D. Auhl, T. C. B. McLeish and M.R.Mackley. The effect of viscoelasticity on stress fields within polyethylene melt flow for a cross-slot and contraction–expansion slit geometry. Rheologica Acta 47, Nos 7 821-834 (2008)
- L. Scelsi
*&*M. R. Mackley Rheo-optic flow-induced crystallisation of polypropylene and polyethylene within confined entry–exit flow geometries Rheologica Acta 47. 895–908 (2008) - L. Scelsi, M. R. Mackley, H. Klein, P. D. Olmsted, R. S. Graham, O. G. Harlen, and T. C. B. McLeish. Experimental observations and matching viscoelastic specific work predictions of flow-induced crystallization for molten polyethylene within two flow geometries Journal of Rheology 53,4, 859-876 (2009)
- D. G. Hassell, J. Embery, T.C.B. McLeish and M.R Mackley An experimental evaluation of the formation of an instability in monodisperse and polydisperse polystyrenes. Journal of Non Newtonian Fluid Mechanics, 157,1. 1-14 (2009)
- D.G. Hassell and M.R Mackley An experimental evaluation of the behaviour of mono and polydisperse polystyrenes in Cross-Slot flow.
- D.G. Hassell, D. Hoyle, D. Auhl, O. Harlen, M.R. Mackley and T. C. B. McLeish Effect of branching in cross-slot flow: the formation of “W cusps”. Rheol Acta 48. 551–561 (2009)
- T.D.Lord, L. Scelsi, D.G. Hassell, M.R. Mackley, J. Embery, D Auhl and O.G.Harlen The matching of 3D Rolie-Poly viscoelastic numerical simulations with experimental polymer melt flow within a slit and a cross-slot geometry
*.*Journal of Rheology 54, 2. 355-373 (2010) - M.R.Mackley and D.G.Hassell The Multipass rheometer; a review Part 1 , Part 2 Journal of Non Newtonian Fluid Mechanics, 166, 9-10, 421-456 (2011)
- D.Auhl, D.M.Hoyle, D.Hassell, T.D.Lord, M.R.Mackley, O.G.Harleen, T.C.B.Mcleish Cross-slot extensional rheometry and steady state extensional response of long chain branched polymer melts. J. Rheology. 55, 875- 901 (2011)
- D. G. Hassell • T. D. Lord , L. Scelsi , D. H. Klein , D. Auhl , O. G. Harlen , T. C. B. McLeish and M. R. Mackley The effect of boundary curvature on the stress response of linear and branched polyethylenes in a contraction–expansion flow Rheologica Acta. 50, 675–689 (2011)
- V. Ganvir, B.P.G Harshawardhan P. M. S. Bhamla, L.Sclesi, R.Thaokarb, A. Lele, M.R. Mackley Extrudate swell of linear and branched polyethylenes: ALE simulations and comparison with experiments J. Non-Newtonian Fluid Mech. 166 12–24 (2011)