Energy spectrum density distribution function of non-Newtonian liquid

6 Energy spectrum density distribution function of non-Newtonian liquid 

Until now, we have focused on Newtonian fluids. However, there are many kinds of non-Newtonian fluids in chemical industries, and the turbulent flow structure of non-Newtonian fluids has remained unknown. It is very important to solve this problem. In this section, the power law fluid is considered to discuss the turbulent flow structure because the power law fluid is a representative non-Newtonian fluid and it is easy to treat it mathematically. 

The rheological equation of the state of the power law fluid is expressed as 

The relationship shown in the above equation can be rewritten as follows for the respective fluids  

The density p and viscosity p, are physical properties whose values are fixed. Additionally, the eddy diameter i can be considered to be proportional to ML Therefore, Eqs (4.16) and (4.17) can be rewritten as  

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