*a* | constant in Carreau–Yasuda model |

*A*_{d} | aspect ratio *w*/*d* |

*A*_{h} | aspect ratio *w*/*h* |

*d* | duct height at inlet (m) |

*D* | downstream duct height (m) |

*De* | Deborah number (≡*λ*/*T*_{CH}) |

*D*_{MID} | mid-point filament diameter in extensional viscosity measurements at any instant in time (m) |

*D*_{0} | diameter of extensional rheometer end platens (m) |

*D*_{1} | value of *D*_{MID} (at time=0) (m) |

*G* | elastic modulus (Pa) |

*G*′ | storage modulus (Pa) |

*G*″ | loss modulus (Pa) |

*h* | step height (m) |

*h*_{0} | initial platen separation in extensional rheometer (m) |

*n* | power-law index |

*N*_{1} | first normal stress difference (Pa) |

| apparent flow rate determined by numerical integration of velocity profiles (m^{3} s^{−1}) |

| flow rate from flow meter (m^{3} s^{−1}) |

*R* | expansion ratio *D*/*d* |

*R*_{i} | radius of curvature of concave section of gradual contraction (m) |

Re_{CR} | critical Reynolds number at which switch to asymmetric flow occurs |

Re_{d} | Reynolds number (≡*ρdU*_{B}/*μ*_{CH}) |

Re_{h} | Reynolds number (≡*ρhU*_{B}/*μ*_{CH}) |

*t* | time (s) |

*T*_{CH} | characteristic time of deformation process *h*/*U*_{B} (s) |

*U* | streamwise velocity (m s^{−1}) |

*U*_{B} | bulk velocity (m s^{−1}) |

*U*_{SD} | bulk velocity within square duct (m s^{−1}) |

*w* | channel width (also duct height upstream of gradual contraction) (m) |

*x* | streamwise distance from expansion (m) |

*x*_{R} | reattachment length (m) |

*X*_{R} | non-dimensional reattachment length (*x*_{R}/*h*) |

*y* | transverse distance from downstream duct floor (m) |

*z* | spanwise distance from sidewall (m) |

| strain rate (s^{−1}) |

*Λ* | initial aspect ratio of sample in extensional rheometer *h*_{0}/*D*_{0} |

*η*_{app} | apparent extensional viscosity (Pa s) |

*λ* | relaxation time of fluid (s) |

*λ*_{CY} | constant which represents onset of shear thinning in Carreau–Yasuda model (s) |

*λ*_{EX} | characteristic relaxation time from extensional viscosity measurements (s) |

*λ*_{i} | relaxation time in Maxwell model (s) |

*μ*_{CH} | Carreau–Yasuda viscosity corresponding to characteristic shear rate (Pa s) |

*μ*_{CY} | Carreau–Yasuda viscosity (Pa s) |

*μ*_{0} | zero-shear-rate viscosity (Pa s) |

*μ*_{∞} | infinite-shear-rate viscosity (Pa s) |

| shear rate (s^{−1}) |

| characteristic shear rate (s^{−1}) |

*η*_{i} | viscosity constant in Maxwell model (Pa s) |

*σ* | surface tension (N m^{−1}) |

*τ* | shear stress (Pa) |

*ω* | angular frequency (rad s^{−1}) |