The Enskog-2σ model, a new viscosity model for simple fluids and alkanes

Abstract

This thesis describes the development of a new model for viscosity, the Enskog-2σ model. The model is based on Enskog theory in which the viscosity of a hard sphere fluid is computed from the hard sphere interactions on the molecular level. The idea of the Enskog-2σ model is to introduce two effective weakly temperature dependent diameters in Enskog's approach. One of the diameters is linked to the collision rate between the fluid molecules, the other diameter to the molecule size. The optimisation of the two effective temperature dependent diameters allows the Enskog-2σ model to reproduce the viscosity data of simple fluids, i.e. fluids with non-polar, fairly spherical molecules, very well over a wide range of pressures and temperatures. For argon, for example, the model covers a pressure range from 0 to 400 MPa and temperatures from 0.6Tc to 4:6Tc (Tc = critical temperature of argon) and correlates the experimental reference correlation within ±10%. Making use of the universal behavior of the diameters for various simple fluids, the number of free parameters can be reduced to one or two constant scaling parameters that can be predicted well from viscosity data along one isotherm. The Enskog-2σ approach has been extended to model n-alkanes from ethane to octane. The molecules of n-alkanes are described as chains of equally sized hard spheres and a collision between two chains is modelled as collision between two spherical segments of the colliding chains. The Enskog-2σ model for n-alkanes contains two effective weakly temperature dependent chain lengths. The number of free parameters can be reduced by relating the chain lengths to the carbon number or to the chain lengths of a reference n-alkane. The remaining free parameters can usually be determined satisfactorily from viscosity data along one isotherm.