Classification of non-Newtonian fluids

Classification of non-Newtonian fluids

• Many mathematical models are available to describe the nonlinear "shear-stress vs deformation-rate" relationship of non­ Newtonian fluids. But no general model can describe the constitutive equation ("shear stress vs rate of deformation" relationship) of all kinds of non-Newtonian fluids. However, the mathematical model for describing the mechanistic behaviour of a variety of commonly used non-Newtonian fluids is the Power-Law model which is also known as Ostwald-de Waele model (the name is after the scientist who proposed it).According to Ostwald-de Waele model

(2.1)

where m is known as the flow consistency index and n is the flow behavior index.
Hence viscosity for the Power-law fluids (as per Power Law model) can be described as:

μ =

(2.2)

It can be observed from above that the viscosity of non-Newtonian fluid is function of deformation rate and is often termed as apparent or effective viscosity.

 

• When n = 1, m equals  , the model identically satisfies Newtonian model as a special case.
  When n < 1, the model is valid for pseudoplastic fluids, such as gelatine, blood, milk etc.
  
  When n > 1, the model is valid for dilatant fluids, such as sugar in water, aqueous suspension of rice starch etc.
  
• There are some substances which require a yield stress for the deformation rate (i.e. the flow) to be established, and hence their constitutive equations do not pass through the origin thusviolating the basic definition of a fluid. They are termed as Bingham plastic. For an ideal Bingham plastic, the shear stress- deformation rate relationship is linear.