An Approach to α Unified Theory of the Flow Behavior of Time-Independent Non-Newtonian Suspensions

A theoretical study is presented on the rheological properties of suspensions showing time-independent non-Newtonian behavior. It is assumed that bonds are formed between particles and that they are broken gradually with increase in shear stress or shear rate. Based on such a model of suspensions, a differential equation is derived to determine the flow curve of suspensions. The differential equation contains a dimensionless parameter α which is less than or equal to unity. When α=1, the flow curve is reduced approximately to power equation, and when α=1/2, the flow curve is reduced approximately to Casson equation. For a suspension showing a measurable yield-value, Bingham equation is obtained when α=0, and the flow curve is reduced approximately to Herschel and Bulkley equation when α=1. The flow curve for arbitrary values of α is also obtained. Casson equation is further discussed in detail.