Table 1 Overview over composite reference values used for non-dimensionalization of the uni-axial fiber dry spinning model and the resulting dimensionless numbers. Here, the scales \(\varrho _{M,0}\), \(v_{0}\), \(r_{0}\), \(d_{0}\), \(\mu _{0}\), \(q_{0}\), \(T_{0}\), \(\alpha _{0}\), \(\gamma _{0}\), \(C_{0}\), \(D_{0}\), \(u_{\mathrm{out},0}\), \(\rho _{\star ,0}\), \(p_{\star ,0}\), \(q_{\star ,0}\), \(\nu _{\star ,0}\), \(\lambda _{\star ,0}\), \(D_{d,\star ,0}\) are assumed to be given from the considered setup

Length scale

\(s_{0}=r_{0}\)

m

Fiber length

\(L_{0}=r_{0}\)

m

Cross-sectional radius

\(R_{0}=d_{0}\)

m

Mass density

\(\rho _{0}=\varrho _{M,0}/d_{0}^{2}\)

kg/m³

Scalar velocity

\(u_{0}=v_{0}\)

m/s

Stress

\(\sigma _{0}=\varrho _{M,0}v_{0}^{2}\)

N

Outer force

\(f_{0}=\varrho _{M,0}v_{0}^{2}/r_{0}\)

N/m

Enthalpy

\(h_{0}=q_{0}T_{0}\)

J/kg

Evaporation enthalpy

\(\delta _{0}=h_{0}\)

J/kg

Mass transfer coefficient

\(\beta _{0}=\gamma _{0}/\rho _{\star ,0}\)

m/s

Air temperature

\(T_{\star ,0}=T_{0}\)

K

Air velocity

\(v_{\star ,0}=v_{0}\)

m/s

Slenderness

\(\varepsilon =d_{0}/r_{0}\)

Reynolds

\(\mathrm{Re}=\varrho _{M,0}v_{0}r_{0}/(d_{0}^{2}\mu _{0})\)

Froude

\(\mathrm{Fr}=v_{0}/\sqrt{gr_{0}}\)

Drawing

\(\mathrm{Dr}=u_{\mathrm{out},0}/u_{0}\)

Mass Peclet

\(\mathrm{Pe}_{c}=v_{0}d_{0}/D_{0}\)

Temperature Peclet

\(\mathrm{Pe}_{T}=\varrho _{M,0}v_{0}q_{0}/(C_{0}d_{0})\)

Mass Stanton

\(\mathrm{St}_{c}=\gamma _{0}d_{0}^{2}/(v_{0}\varrho _{M,0})\)

Temperature Stanton

\(\mathrm{St}_{T}=\alpha _{0}d_{0}^{2}/(v_{0}\varrho _{M,0}q_{0})\)

Air-fiber Reynolds

\(\mathrm{Re}_{\star }=d_{0}v_{0}/\nu _{\star ,0}\)

Nusselt

\(\mathrm{Nu}_{\star }=\alpha _{0}d_{0}/\lambda _{\star ,0}\)

Prandtl

\(\mathrm{Pr}_{\star }=q_{\star ,0}\rho _{\star ,0}\nu _{\star ,0}/\lambda _{\star ,0}\)

Sherwood

\(\mathrm{Sh}_{\star }=\gamma _{0}d_{0}/(\rho _{\star ,0}D_{d,\star ,0})\)

Schmidt

\(\mathrm{Sc}_{\star }=\nu _{\star ,0}/D_{d,\star ,0}\)