The definition of rheology, as originally agreed is, “Rheology is the study of the deformation and flow of matter”. The term was coined by Professor E. C. Bingham, of Lafayette college, Easton (Pa.), in the United States of America, on the advice of his Professor of Classics and was accepted when the (American) Society of Rheology was founded in 1929. These two parameters, deformation and flow, are the properties of most importance in the commercial processing of most polymeric and indeed, most non-polymeric materials. Without an understanding of a given material’s flow characteristics or simply defined, Viscosity, it is difficult to achieve and more importantly, maintain, optimum process control, which is directly related to profit margins through achieving maximum production rates and quality reproducible product.

Rheology can also be a powerful quality control tool as it can discriminate changes in material properties at the molecular level caused by e.g. batch to batch variation in molecular weight / molecular weight distribution at the polymerisation stage, thermal & mechanical degradation caused during processing, and determination of failure in service of products from UV / chemical attack, mechanical / physical degradation, etc.


Viscosity is basically the resistance to flow of a material and is a product of applied stress and resultant (strain) rate and can be visualised by imagining the flow in a river (akin to the flow through a cross section of e.g. an extruder die or injection moulding machine runner system). As we know, the flow in a river is fastest at the centre and stationary at the bank. (Figure 1)
Figure 1
 

The velocity of the water is increasing from the bank of the river to the centre line and this causes material to be sheared at the laminar interfaces. The gradient of this increasing velocity is known as the Shear Rate:

Where V = velocity & H = radial position

The primary method for producing flow in a fluid body is by the application of a shearing force, or stress. If we were to look at the grey element of the fluid body in Figure 1a in 3D, we can see it is under this type of stress - the element is subjected to a shear force (F) on one of it's faces, area (A), causing it to move with a velocity (V) relative to the opposite face, a distance (H) away. (Figure 2).
The fluid body is therefore said to be under a Shear Stress:
And it's Viscosity is given by the ratio:
In simple (Newtonian) fluids, the shear stress is proportional to shear rate which results in a shear viscosity independent of shear rate (Figure 3a). However, in polymeric flow situations, this not the case. Most commercial polymeric materials have melt viscosity values that under process conditions, can fall within the range 1 to 100,000 Pa.s which, as can be appreciated, gives huge variations in material processing characteristics. To make matters more complex, the viscosity of polymer melts changes during the processing cycle as they exhibit Psuedoplastic behavior (Figure 3b). Psuedoplasicity or shear thinning behaviour appears as a decrease in viscosity as a function of increasing shear rate and is highly influenced by a material's structure.
   

The rheological behaviour of a material is the single most important property in the commercial processing of polymers. Fact: If the material cannot be deformed and made to flow, you can not process it! Many material generic types / grades have very similar flow behaviour at low shear rate but due to structural issues such as molecular weight / molecular weight distribution, chain branching, polymer / filler interaction, etc, have radically different flow characteristics at process relevant shear rates. Traditionally many processors have relied on the Melt Flow Indexer (MFI - or latterly known as the Melt Flow Rate, MFR) for quality control of material pre-process flow properties.

Unfortunately because the MFI is a low shear, single point test, it is woefully inadequate at providing the full picture in relation to process-range data. Due to the pseudoplastic behaviour of polymer melts it is important to determine the magnitude of viscosity across as wide a shear rate range as possible, as the material will experience changes in flow geometries and hence shear rate during the process. Taking a typical Polypropylene having a MFI value of 2.4 g/10 mins (determined using a 2.16 kg applied mass @ 230°C), assuming the density is known, an approximate shear rate of 6.7 1/s can be calculated.¥ (It is an approximation because another failing of the MFI is the fact that the rate is not controlled; there is an increase in velocity as the MFI barrel empties under the constant applied stress (load)). As most polymer processing techniques involve shear rates of ~100 1/s up to 100,000 1/s it can be seen that the MFI is a poor representation of the process. Figure 4 gives a visual comparison of the MFI to other polymer processing techniques:

To determine the shear viscosity behaviour of polymers under processing conditions, a capillary rheometer is a fast, accurate means of providing flow behaviour over a wide range of shear rates at a number of temperatures and enables processing problems such as melt fracture, die swell, etc, to be predicted or solved offline. The data sets derived from testing can also be modelled mathematically to provide the input coefficients required by Finite element flow simulation software packages such as Moldflow and Sigmasoft - to provide accurate simulations of mould filling and packing & cooling accurate materials data is absolutely critical.

¥Ref: Fleming, D.J, Melt Fracture and Elongational Viscosity via Convergent Flow Analysis , Procedings of PolymerTesting '96 , RAPRA (1996).
   

Processes such as blow moulding, fibre spinning, film & extrusion through complex, convergent / divergent dies lead to flow regimes where extensional (tensile) flow dominates over simple shear flow, Figure 5.
Polymers with wide molecular weight distributions are extremely sensitive to extensional flow as it is believed the longer chain lengths retain more of the applied stresses than the shorter chains which effects the relaxation times of the melt. A practical example of this problem was an injection moulder producing components which contained a central membrane with extremely narrow tolerances (a few microns) on the wall thickness. This membrane was designed to fracture under a specified pressure differential. Incoming batches of material were in-house characterised prior to processing via MFI, but batch changes of material were still leading to sudden increases in reject rate. MFI is primarily a single point shear flow test and therefore unable to differentiate batches with varying molecular weight distribution. These batches with varying molecular weight distributions were being introduced to the process with the consequence of, under the same processing conditions, varying relaxation times and hence out of tolerance wall thickness leading to non-fracture of the membrane. By changing to extensional viscosity analysis as the pre-process quality control tool, rejects due to membrane wall thickness variation were virtually eliminated as out of spec. batches were apprehended and returned to the supplier.
The extensional viscosity can also increase (strain hardening) or decrease (strain thinning) with extension rate, Figure 6. This effect is important in fibre spinning where polymers which exhibit strain hardening are preferred, as strain thinning would be detrimental to the stability of the fibre and lead to dimensional instabilities and fibre breakage.

Gammadot derive extensional viscosity data by capillary rheometer using convergent capillary dies with 45° half entry angles. The capillary rheometer control software has the facility to analyse experimental using several extensional flow models including those of Cogswell, Gibson, Rides and Binding.