Table 5 Overview of fluid dynamic...

Table 5

Overview of fluid dynamic numbers for the characterization of non-Newtonian fluids according to Clasen et al. (2012) with u_jet: velocity of the jet, d: nozzle diameter, λ: relaxation time, σ: surface tension, η: dynamic viscosity and ρ: density

Fluid dynamic no.	Target range	Material property-based no.	Range
Ohnesorge number $O h = \frac{η}{\sqrt{ρσd}}$	0.1 – 1 (Clasen et al., 2012)	Capillary number $C a = \frac{η U_{j e t}}{σ}$	0.007–2 (Nallan et al., 2014)
Deborah number $D e_{0} = \sqrt{\frac{λ^{2} σ}{{ρd}^{3}}}$	> 1 (Clasen et al., 2012)	Weber number $W e = \frac{p U_{j e t}^{2} d}{σ}$	2–25 (Clasen et al., 2012)
Elasto-capillary number $E_{c} = \frac{λ σ}{ηd}$	> > 4.7 (Clasen et al., 2012)	Weissenberg number $W i = \frac{λ U_{j e t}}{d}$	< 0.5 (Haque et al., 2015; McIlroy et al., 2013)

Fluid dynamic no.	Target range	Material property-based no.	Range
Ohnesorge number $O h = \frac{η}{\sqrt{ρσd}}$	0.1 – 1 (Clasen et al., 2012)	Capillary number $C a = \frac{η U_{j e t}}{σ}$	0.007–2 (Nallan et al., 2014)
Deborah number $D e_{0} = \sqrt{\frac{λ^{2} σ}{{ρd}^{3}}}$	> 1 (Clasen et al., 2012)	Weber number $W e = \frac{p U_{j e t}^{2} d}{σ}$	2–25 (Clasen et al., 2012)
Elasto-capillary number $E_{c} = \frac{λ σ}{ηd}$	> > 4.7 (Clasen et al., 2012)	Weissenberg number $W i = \frac{λ U_{j e t}}{d}$	< 0.5 (Haque et al., 2015; McIlroy et al., 2013)

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