Measuring maximum tensile strength of liquids at low stressing rates A.S. Lubansky a,b,⇑ , R. Brad a , P.R. Williams a , D. Deganello c , T.C. Claypole c a Multidisciplinary Nanotechnology Centre, Swansea University, Swansea SA2 8PP, United Kingdom b Department of Engineering Science, University of Oxford, Parks Rd., Oxford OX1 3PJ, United Kingdom c Welsh Centre for Printing and Coating, Swansea University, Swansea SA2 8PP, United Kingdom article info Article history: Available online 12 April 2011 Keywords: Extensional rheology Tensile strength Cavitation Bullet-piston abstract A technique is presented for determining the maximum tensile strength of a given fluid through the anal- ysis of the break-up at the end of a capillary-thinning experiment. This technique allows the character- isation of the tensile strength, an important parameter for understanding cavitation, of a fluid at lower stressing rates than previous methods, such as bullet-piston apparatus. The method was validated by tests on a range of concentrations and molecular weights of polyethylene glycol, comparing the results with the values and behaviours observed from the bullet piston apparatus. Excellent agreement was observed between the two techniques, with quantitative differences corresponding to the differences in stressing rates. The results from the capillary break-up experiments were also used to investigate the effect of concentration and molecular-weight on tensile strength. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Knowledge of the tensile strength of a fluid at appropriate stressing rates is important for determining the onset of cavitation. For Newtonian fluids, cavitation phenomena have been dealt with in many instances, whereas non-Newtonian fluids have only been considered in a small number of studies [1]. Behaviour of non- Newtonian fluids could be influenced by various stressing rates; an accurate analysis of the tensile strength for non-Newtonian flu- ids requires therefore the ability to study a given fluid at various stressing rates. An established technique for determining the tensile strength of fluids is by using the bullet-piston apparatus [2,3]. This apparatus enables the determination of the tensile strength of mobile liquids only at high stressing rates of the order of 10 10 Pa=s [4]. These stressing rates are of the same order as found in lubrication of jour- nal bearings, where the cavitation caused by the stresses exceeding the tensile strength is important for the load bearing capacity of the journal bearing. Lower stressing rates are not possible using the bullet-piston apparatus. Lower stressing rates are characteristic of a range of important applications such as in industrial printing or food pro- cessing, where fluid splitting phenomena occur. The ability to mea- sure the tensile strength of a fluid at lower stressing rates would have, therefore, not only a physical importance but also valuable practical applications. The technique presented in this work will cover this range, allowing the measurement of the maximum ten- sile strength for stressing rates of order 10 4 —10 5 Pa=s through analysis of the break-up in a capillary thinning experiment. Recently, capillary thinning and filament stretching techniques have been gaining in popularity for determining the apparent extensional viscosity of fluids [5]. These techniques take advantage of a tensile field being applied over a slender filament to elongate and thin the filament. Capillary thinning is commonly used in an extensional rheometer called a CaBER – a capillary break-up exten- sional rheometer. Despite its name, however, the rheometric infor- mation given by the CaBER derives from capillary thinning, rather than capillary break-up. To the authors’ knowledge, no previous researchers have taken advantage of the information available at break-up in a capillary thinning experiment, and the rupture of fil- aments of non-concentrated solutions has not been the subject of previous investigations. Its application for the calculation of the maximum strength of a fluid will therefore be a novel breakthrough. Malkin and Petrie [6] gave a detailed description of conditions for failure and rupture of polymer melts in extension in stretching experiments, concluding that several modes of break-up were available and giving a master-curve for rupture in and above the transition to the rubbery zone. For liquid regime flow, however, they proposed that a filament would be stable. Hassager et al. [7] proved that an idealised Newtonian filament would not undergo ductile failure in the absence of surface tension. Their work, how- ever, also made the assumption that there is no limiting stress a Newtonian fluid can withstand, independent of rheological and geometric considerations. 0377-0257/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnnfm.2011.04.004 ⇑ Corresponding author at: Multidisciplinary Nanotechnology Centre, Swansea University, Swansea SA2 8PP, United Kingdom. E-mail address: alex.lubansky@eng.ox.ac.uk (A.S. Lubansky). Journal of Non-Newtonian Fluid Mechanics 166 (2011) 896–899 Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: http://www.elsevier.com/locate/jnnfm