page_title: Capillary breakup rheometry
section_title: Theoretical framework
hierarchical_section_title: Capillary breakup rheometry / Theoretical framework
caption_attribution_description: English: Capillary instabiltiy create extensional flow within necked filament
context_page_description: Capillary Breakup Rheometry is an experimental technique used to assess the extensional rheological response of low viscous fluids. Unlike most shear and extensional rheometers, this technique does not involve active stretch or measurement of stress or strain but exploits only surface tension to create a uniaxial extensional flow. Hence, although it is common practice to use the name rheometer, capillary breakup techniques should be better addressed to as indexers.
  Capillary breakup rheometry is based on the observation of breakup dynamics of a thin fluid thread, governed by the interplay of capillary, viscous, inertial and elastic forces. Since no external forcing is exerted in these experiments, the fluid thread can spatially rearrange and select its own time scales. Quantitative observations about strain rate, along with an apparent extensional viscosity and the breakup time of the fluid, can be estimated from the evolution of the minimal diameter of the filament. Moreover, theoretical considerations based on the balance of the forces acting in the liquid filament, allow to derive information such as the extent of non-Newtonian behaviour and the relaxation time.
context_section_description: Capillary breakup rheometry and its recent development are based on the original experimental and theoretical work of Schümmer and Tebel and Entov and co-workers. Nonetheless, this technique found his origins at end of the 19th century with the pioneering work of Joseph Plateau and Lord Rayleigh. Their work entailed considerable progress in describing and understanding surface-tension-driven flows and the physics underlying the tendency of falling liquid streams to spontaneously break into droplets. This phenomenon is known as Plateau–Rayleigh instability.
  The linear stability analysis introduced by Plateau and Rayleigh can be employed to determine a wavelength for which a perturbation on a jet surface is unstable. In this case, the pressure gradient across the free-surface can cause the fluid in the thinnest region to be "squeezed" out towards the swollen bulges, thus creating a strong uniaxial extensional flow in the necked region.
  As the instability grows and strains become progressively larger, the thinning is governed by non-linear effects. Theoretical considerations on the fluid motion suggested that the behaviour approaching the breakup singularity can be captured using self-similarity. Depending on the relative intensity of inertial, elastic and viscous stresses, different scaling laws based on self-similar considerations have been established to describe the trend of the filament profile near breakup throughout the time.
caption: Uniaxial extensional flow created within necked filament by a capillary instability
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