Table 1 Robustness of the model with respect to parameter variations

	\(\dot \gamma _{{\mathrm{c}}_1}\)	\(\dot \gamma _{{\mathrm{c}}_2}\)	\(\dot \gamma _{{\mathrm{c}}_3}\)	\(\dot \gamma _{\mathrm{u}}\)	ψ_u
Basis	1.53	24.4	44.2	16.4	10.8°
ν_W = 0.5 s⁻¹	1.70	2.4	13.5	3.6	51°
ν_W = 10 s⁻¹	1.52	65	88	36	5.9°
θ₀ = −20°	1.23	43	81	29	6.4°
θ₀ = 0°	4.2	6.8	19	9.4	71°
ν_C = 0.2 s⁻¹	0.31	26	34	13	4.1°
ν_C = 10 s⁻¹	17.5	21	127	34	58°
Γ = 1	1.73	3.5	9.1	3.1	48°
Γ = 8	1.52	89	348	49	5.8°
\(\bar \nu _{\mathrm{H}} = 0.002\)	1.55	25	36	18	8.4°
\(\bar \nu _{\mathrm{H}} = 0.1\)	1.52	16	235	13	29°
\(\bar \nu _{\mathrm{V}} = 0.1\)	3.9	23	38	17	32°
\(\bar \nu _{\mathrm{V}} = 1.0\)	0.88	25	52	17	6.1°
θ_V = 0.57°	1.54	23	38	19	8.4°
θ_V = 5.7°	1.59	27	56	17	13°

Columns give the three critical shear rates, \((\dot \gamma _{{\mathrm{c}}_1},\dot \gamma _{{\mathrm{c}}_2},\dot \gamma _{{\mathrm{c}}_3})\) (s⁻¹), the optimal shear rate for upstream orientation, \(\dot \gamma _{\mathrm{u}}\) (s⁻¹), and the corresponding in-plane angle at the right fixed point, \(\psi _{\mathrm{u}} = \psi _{\mathrm{R}}^ \ast (\dot \gamma _{\mathrm{u}})\). The first row corresponds to the basis parameter set, and subsequent rows vary one parameter at a time, as indicated in the first column, keeping the other parameters from the basis set: ν_W = 4 s⁻¹, θ₀ = −10°, ν_C = 1 s⁻¹, Γ = 4, \(\bar \nu _{\mathrm{H}} = 0.02\), \(\bar \nu _{\mathrm{V}} = 0.5\), θ_V = 2.3°

Quick links

Search