﻿ Spriggs Power Law Model
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# Spriggs Power Law Model

This is a three-parameter 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

Syntax of the data packet Polymer is as follows:

 Polymer PolymerName { ConstitutuveModel = "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 of 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 same as viscosity. Pa s Constant Required 1.0e+04 Exponent Power law index, defines the dependency of viscosity on shear rate. None Constant Required 0.66 ZeroShearRateLimit Parameter of the model to define a zero shear rate limit. This over comes the chief limitation of the traditional power-law model. 1/s Constant Required 0.01 TemperatureDependence None String Required "Exp(-Beta(DeltaT))" ReferenceTemperature Temperature at which data is calculated for the initialization step. K Constant Required only if TD is not "None" 533 FreezeTemperature This is the 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 WLFConstant1 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(-Beta(DeltaT)) 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