Ree-Eyring equation

The Newtonian and non-Newtonian terms appearing in the Ree-Eyring equation were evaluated by applying this equation to experimental flow curves. The Newtonian viscosity number, obtained in the low range of shear rates i of an... 

There are two main streams in the study of rheological properties of suspensions and polymeric solutions. One is the hydrodynamic approach/ and the other is the molecular kinetic investigation. The so-called Ree-Eyring equation is a result from the latter category it is written as follows ... 

The value of K varies between 1.2 and 4.0 depending on the method of estimating / or in other words, K varies around 2.5. One may also notice that in a given method of estimation the K value is constant irrespective of the molecular weights and concentrations, in agreement with the theoretical requirement. Thus it is concluded that the flow unit for the Newtonian term in the Ree-Eyring equation behaves like a hard sphere. 

Next we show that Einstein s equation (7) can be derived from the Ree-Eyring (R-E) theory (1). Here we assume that type 2 flow units are absent in dilute solutions. Then the Ree-Eyring equation is written as... 

The power law, Herschel-Bulkley equation, and Casson model are simple and easy to use. However, these equations only work for modeling steady shear flows rather than transient or elongational flows. Thus, many other models have been proposed to fit experimental data more closely for food materials. Among these, it is worth mentioning the Ree-Eyring equation which has three constants... 

When the concentration of the system is considerably high, the Robinson equation (11) holds. Next we derive (11) from the Ree-Eyring model. Let us assume the following ... 

Equation 17m becomes Robinson s equation if 2.5 is replaced by a constant K which takes the values around 2.5 in general. Thus we have derived (11) from the Ree-Eyring theory. 

The basic concept of the EHL model is described in [1], i. e. the non-Newtonian Ree-Eyring fluid model according to Ai cr al. [7] and the implementation of the 2D Reynolds-, elasticity- and load equation according to Venner [8]. The lubricant properties are the viscosity-pressure relationship as proposed by Mihailidis et al. [9] and the density-pressure relationship as proposed by Dowson and Higginson. The non-dimensional parameters in this work can be seen in table 1. 

The film thickness for the ordinary shear-thinning response of lubricants which can be measured is now calculated. There are many generalized Newtonian fluid models that will describe the shear response displayed in Figures 1 and 2 [16]. The Ree-Eyring model utilizes a series in inverse hyperbolic sine to approximate power-law behavior at high shear rate. In others [16] the power-law exponent, , appears explicitly. Today the most widely used model outside of tribology is the Carreau equation [17] that was advanced to describe the results of molecular network theory. 

Modifying Mooney s equation (37) in terms of Ree and Eyring s theory used for particle doublets, Krieger and Dougherty [68] arrived at an equation similar in form to several phenomenological equations presented above (17, 20, 21), but, unlike those equations, containing parameter cpmai ... 

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