# Spriggs Power Law Model

This is a three-paramter model described by the following equation.

This model describes the viscosity using a power-law relationship. The exponent n determines the nature of the relationship. Unlike the power-law model where the Consistency A has complex units Pa-s^n, here the consistency is identical to viscosity. This is because the effective shear rate is normalized with zero shear rate limit. This makes the data easily understandable.

## Syntax

Polymer | PolymerName | { |

ConstituveModel = | "SpriggsPowerLaw" | |

Density = | ρ | |

SpecificHeat = | Cp (T) | |

Conductivity = | K (T) | |

CoeffOfThermalExpansion = | βT | |

VolumetricHeatSource = | Qvol | |

Consistency = | A | |

Exponent = | n | |

ZeroShearRate = | γ0 | |

TemperatureDependence = | "None" } |

## Explanation of Parameters

Parameter | Description | Units | Data Type | Condition | Typical Value |
---|---|---|---|---|---|

ConstitutiveModel | Describes the model used | None | String | Required | "SpriggsPowerLaw" |

Density | Density fo the polymer | kg/m^3 | Constant | Required | 995.0 |

SpecificHeat | Specific heat at constant pressure | J/kg/K | Constant/F(T) | Required | 2000.0 |

Conductivity | Thermal conductivity | W/m/K | Constant/ F(T) | Required | 0.167 |

CoeffOfThermalExpansion | Indicates the change in volume with change in temperature | 1/K | Constant | Required | 1.0e-05 |

VolumetricHeatSource | Heat generated/removed in the volume by methods like electrical heating | W/m^3 | Constant | Required | 0.0 |

Consistency | One of the parameters of the power law model. When n=1 it is the same as viscosisty. | pa s^n | Constant | Required | 1.0e+04 |

Exponent | Power law index, defines the dependency of viscosity on shear rate. | None | Constant | Required | 0.66 |

ZeroShearRateLimit | See above | 1/s | Constant | Required | 0.01 |

TemperatureDependence | See Temperature Dependence | None | String | Required | "Exp(-Beta(DeltaT))" |

ReferenceTemperature | Temperature at which data is calculated for the intialization step. | K | Constant | Required only if TD is not "None" | 533 |

FreezeTemeprature | This ist eh no flow temperature. Below this temperature, material ceases to flow. | K | Constant | Required only if TD is not "none" | 350 |

ActivationEnergy | A parameter required by Arrhenius model. | J/mol | Constant | Required only if TD is Exp(Q/RT) | 16628 |

UniversalGasConstant | A parameter from state equation PV=nRT, R is universal gas constant. | J/mol/K | Constant | Required only if TD is Exp (Q/RT) | 8.314 |

TemperatureSensitivity | A derived parameter which has the same physical meaning as Q/R. | K | Constant | Required only if TD is Exp(Tb/T) | 2000 K |

WLFConstant 1 | Constant C1 of WLF model | None | Constant | Required only if TD is WLF | 17.44 |

WLFConstant2 | Constant C2 of WLF model. This is like DeltaT, hence the value is same in K and Celsius. | K | Constant | Required only if TD is WLF | 51.6 |

GlassTransitionTemperature | Temperature below with polymer molecules ceases to move (frozen). There are few definitions of this term | K | Constant | Required only if TD is WLF | 320 |

Beta | Parameter in the relationship Exp(-BetaDeltaT)) | None | Constant | Required only if TD is Exp(-Beta(DeltaT)) | 0.005 |

F(T) - Function of Temperature. Can be specified as a TABLE1 or TCL function.

TD - TemperatureDependence