Elasto capillary number

The elasto-capillary number ( symbol :) is a dimensionless number that is used for capillary tapering ( surface tension-driven tapering of an unstable liquid bridge) of non-Newtonian fluids . It is defined as the ratio of two time scales: ${\displaystyle {\mathit {Ec}}}$

${\displaystyle {\mathit {Ec}}={\frac {t_{ve}}{t_{e}}}}$

With

• the time scale of viscoelastically controlled taper ${\displaystyle t_{ve}=\lambda _{s}}$
  • ${\displaystyle \lambda _{s}}$: Shear relaxation time
• the timescale of viscous controlled rejuvenation ${\displaystyle t_{v}={\frac {\eta _{0}D}{2\Gamma }}}$
  • ${\displaystyle \eta _{0}}$: dynamic viscosity of the liquid at low shear rates
  • ${\displaystyle D}$: Diameter of the liquid bridge
  • ${\displaystyle \Gamma }$: Surface tension .

The following applies to the Elasto capillary number:

${\displaystyle {\mathit {Ec}}={\frac {2\lambda _{s}\Gamma }{\eta _{0}D}}}$

Alternatively, the Elasto capillary number can be calculated as the ratio of the Deborah number to the capillary number : ${\displaystyle {\mathit {De}}}$ ${\displaystyle {\mathit {Ca}}}$

${\displaystyle {\mathit {Ec}}={\frac {\mathit {De}}{\mathit {Ca}}}}$

See also

• Capillary number

Individual evidence

1. ↑ Shelley L. Anna, Gareth H. McKinley: Elasto-capillary thinning and breakup of model elastic liquids . In: Journal of Rheology . tape 45 , no. 1 , 2001, p. 115-138 , doi : 10.1122 / 1.1332389 .
2. ↑ Christian Clasen: Capillary breakup extensional rheometry of semi-dilute polymer solutions . In: Korea-Australia Rheology Journal . tape 22 , no. 4 , June 11, 2010, p. 331-338 .
3. ↑ Dirk Sachsenheimer, Bernhard Hochstein, Norbert Willenbacher: Experimental study on the capillary thinning of entangled polymer solutions . In: Rheologica Acta . tape 53 , no. 9 , September 2014, p. 725-739 , doi : 10.1007 / s00397-014-0789-8 .