Tensile viscosity, more formally known as elongational or extensional viscosity, is a fundamental rheological property that describes a material's resistance to stretching deformation and governs process performance in film blowing, fiber spinning, coating, and inkjet printing. Professional tensile viscosity testing employs specialized extensional rheometry techniques to quantify strain-hardening behavior, Trouton ratios, and relaxation times across polymer melts, solutions, and formulated fluids. Accredited third-party laboratories provide these measurements to support material development, process optimization, and quality control in accordance with recognized ISO and ASTM standards.
Technical Overview
Tensile viscosity, also referred to as elongational viscosity or extensional viscosity, characterizes the resistance of a fluid or soft solid to deformation under stretching, as opposed to shearing. It is defined as the ratio of the tensile (extensional) stress to the applied extension rate. While shear viscosity describes resistance to sliding between fluid layers, tensile viscosity describes resistance to continuous elongation, a deformation mode that dominates many industrial processes such as fiber drawing, film orientation, parison sag, droplet formation, and atomization.
For a Newtonian fluid in uniaxial extension, the tensile viscosity equals three times the shear viscosity, a relationship known as the Trouton ratio. However, most polymer melts and solutions exhibit Trouton ratios far greater than three, particularly at large stretch rates and high strains. Polymeric materials may display either strain hardening, where the tensile viscosity rises sharply with accumulated Hencky strain, or strain softening, where it decreases. Strain hardening is strongly correlated with long-chain branching and molecular weight distribution, and it is a critical predictor of process stability in stretching-dominated operations.
Quantitative tensile viscosity measurement is technically demanding because the material must be stretched uniformly while force, sample geometry, and time are simultaneously monitored. Modern extensional rheometers overcome this challenge using filament stretching, capillary breakup, counter-rotating drum fixtures, and converging-flow analysis, enabling reliable determination of tensile viscosity as a function of extension rate, strain, temperature, and time.
Testing Samples
Polymer Melts and Thermoplastics
Melt-state testing covers polyolefins such as LDPE, LLDPE, HDPE, and polypropylene, engineering resins such as PET, PA, PC, and PMMA, and biopolymers including PLA, PBAT, and PHA. Elastomers, thermoplastic polyurethanes, and adhesive hot-melt compounds are also frequently evaluated. Specimens are typically compression-molded into rectangular strips with controlled dimensions and thickness, and are tested at processing temperatures ranging from approximately 150 °C to 300 °C.
Polymer Solutions and Formulated Fluids
Dilute and semi-dilute solutions of flexible polymers, including polyethylene oxide, polyacrylamide, hyaluronic acid, xanthan gum, and associative thickeners, are tested to characterize extensional thickening and relaxation behavior. These measurements are essential for fluids used in spraying, atomization, dosing, and dispensing applications.
Inks, Coatings, and Adhesives
Inkjet inks, spray coatings, lubricants, and pressure-sensitive adhesive precursors are evaluated for filament breakup behavior, satellite droplet formation, and stringiness. Extensional properties often control printability and transfer performance even when shear viscosity appears adequate.
Food and Biomaterials
Wheat dough, gluten dispersions, protein solutions, molten cheese analogues, saliva substitutes, and mucus-like fluids are tested to assess extensibility, processability, and swallowing or textural performance. Typical specimen forms include:
- Compression-molded polymer strips for melt extensional fixtures
- Small liquid droplets or aliquots of 0.05 mL to 1 mL for capillary breakup testing
- Extruded or cast films and ribbons for high-temperature stretching
- Pellet or granule feedstock for capillary rheometer converging-flow analysis
Testing Items
Comprehensive tensile viscosity characterization typically includes the following measured and derived parameters:
- Uniaxial tensile viscosity as a function of extension rate and Hencky strain
- Trouton ratio (ratio of tensile viscosity to shear viscosity at matched deformation rates)
- Strain-hardening coefficient and departure from the linear viscoelastic envelope
- Maximum attainable Hencky strain before filament rupture or sample failure
- Extensional relaxation time and filament thinning or breakup time
- Apparent extensional viscosity from capillary thinning analysis
- Planar and equibiaxial extensional viscosity for specialized applications
- Temperature dependence of tensile viscosity, including activation energy for extensional flow
- Comparison of extensional behavior between resin grades, formulations, or lot-to-lot samples
Testing Methods
Filament Stretching Extensional Rheometry
Filament stretching rheometry applies a controlled exponential velocity profile to stretch a cylindrical liquid filament between two plates while a laser micrometer records the midpoint diameter and a micro-force transducer records the tensile force. This technique delivers the most rigorous transient tensile viscosity data for low-to-medium viscosity liquids and polymer solutions, with strain rates typically spanning 0.1 to 1000 s⁻¹.
Capillary Breakup Extensional Rheometry
In capillary breakup rheometry, a liquid bridge is formed between small plates and stretched rapidly to a set height. The filament then thins under the action of surface tension and viscoelastic stresses, and the decay of the midpoint diameter is monitored optically. Analysis of the diameter decay curve yields the apparent extensional viscosity, the extensional relaxation time, and the filament breakup time. This method requires only microliter-scale samples and is ideal for low-viscosity fluids, inks, and biological liquids.
Counter-Rotating Drum Extensional Fixtures for Polymer Melts
Dedicated extensional fixtures mounted on rotational rheometers stretch rectangular polymer melt strips using two counter-rotating drums. The fixed wind-up speed produces a constant Hencky strain rate, and torque on the drive shaft is converted into tensile stress. This approach covers melt testing from ambient temperature up to approximately 350 °C and is widely used for polyolefins and engineering thermoplastics. Baseline shear properties are measured in parallel on the same instrument in accordance with ISO 3219.
Entrance Pressure Loss (Converging Flow) Method
The entrance pressure drop measured during capillary rheometry, after Bagley correction, can be converted into an apparent extensional viscosity using converging-flow analysis. This method applies to viscous melts and compounds at high rates and is performed in accordance with ASTM D3835 and ISO 11443. It is particularly useful when direct stretching methods are impractical for highly filled or reinforced materials.
Rotating-Clamp Melt Extensometers
Rotating-clamp instruments grip a ribbon or film sample at multiple points and elongate it uniformly at constant strain rate or constant stress. They achieve very large total Hencky strains, exceeding seven strain units in some configurations, making them suitable for evaluating long-chain branched polyolefins and elastomers intended for oriented film and fiber applications.
Applications
Tensile viscosity data directly support material selection, formulation design, and process troubleshooting across many industries:
- Film blowing: strain-hardening behavior stabilizes the bubble, suppresses melt fracture, and permits higher draw-down ratios
- Fiber spinning and meltblown nonwovens: extensional properties control spinline stability, filament diameter uniformity, and resistance to draw resonance
- Blow molding: tensile viscosity governs parison sag, swell, and wall-thickness distribution
- Cast film and extrusion coating: extensional data predict neck-in, edge-bead formation, and coating speed limits
- Inkjet printing: filament thinning dynamics determine ligament breakup, satellite droplet suppression, and nozzle performance
- Spraying and atomization: extensional viscosity controls ligament formation and droplet size distribution of agricultural, cosmetic, and pharmaceutical sprays
- Food processing: dough extensibility, cheese stretchability, and texture engineering for sheeted and extruded products
- Polymer flooding and enhanced oil recovery: extensional resistance affects injectivity and mobility control of polymer solutions in porous media
FAQ
What is the difference between shear viscosity and tensile viscosity?
Shear viscosity measures resistance to sliding deformation between fluid layers, whereas tensile viscosity measures resistance to stretching deformation. Many processes dominated by acceleration, thinning, or drawing are controlled by tensile viscosity, which can be orders of magnitude higher than the shear viscosity of the same material. A formulation that looks acceptable in shear testing may still fail in stretching-dominated processes.
What is the Trouton ratio?
The Trouton ratio is the tensile viscosity divided by the shear viscosity at the same deformation rate. For Newtonian fluids the ratio is 3 in uniaxial extension. Values significantly above 3 indicate strong extensional thickening, which is typical of polymer melts and solutions at high strain.
Why is strain hardening important?
Strain hardening means the tensile viscosity increases with accumulated strain. It stabilizes stretching processes because locally thinner or faster-moving sections stiffen and distribute deformation more uniformly. Long-chain branched polymers such as LDPE are classic examples of strain-hardening materials used for stable film blowing.
How much sample is required for testing?
Capillary breakup methods require less than 1 mL of liquid. Melt extensional fixtures typically need several molded strips measuring roughly 10 to 20 mm in length with thicknesses between 0.3 and 1.5 mm. Capillary rheometer methods require a few grams of pellets or granules.
What temperatures and rates can be covered?
Melt testing is routinely performed from ambient temperature up to 350 °C, with extension rates from approximately 0.01 to 1000 s⁻¹ depending on the instrument. Solution and ink testing is typically conducted at ambient to moderate temperatures with rates up to several thousand s⁻¹ during filament thinning.
Which standards govern tensile viscosity measurement?
Capillary-based extensional determination follows ASTM D3835 and ISO 11443, while supporting shear characterization follows ISO 3219. Dedicated extensional rheometry methods are performed in line with established rheological practice and instrument-validated procedures, and testing is available through accredited third-party laboratories to support certification and regulatory submissions.
Can all fluids be tested for tensile viscosity?
Pure low-molecular-weight solvents with viscosities below roughly 1 mPa·s show Newtonian Trouton behavior and are generally below the sensitivity of current techniques. Aqueous polymer solutions, melts, gels, doughs, and most formulated fluids are all well within the measurable range.