Fluids kinematic history

Non-Newtonian fluids are generally those for which the viscosity is not constant even at constant temperature and pressure. The viscosity depends on the shear rate or, more accurately, on the previous kinematic history of the fluid. The linear relationship between the shear stress and the shear rate, noted in Equation (1), is no longer sufficient. Strictly speaking, the coefficient of viscosity is meaningful only for Newtonian fluids, in which case it is the slope of a plot of stress versus rate of shear, as shown in Figure 4.2. For non-Newtonian fluids, such a plot is generally nonlinear, so the slope varies from point to point. In actual practice, the data... 

A non-Newtonian fluid is one whose flow curve (shear stress versus shear rate) is non-linear or does not pass through the origin, i.e. where the apparent viscosity, shear stress divided by shear rate, is not constant at a given temperature and pressure but is dependent on flow conditions such as flow geometry, shear rate, etc. and sometimes even on the kinematic history of the fluid element under eonsideration. Such materials may be conveniently grouped into three general elasses ... 

For some fluids the relation between the shear rate and the shear stress depends on the duration of the flow, or, more precisely, on the kinematic history of the fluid. We can distinguish two categories thixotropy and rheopexy. 

When we consider non-Newtonian liquids, the viscosity is not constant, because of the influence of shear rate and time. So for non-Newtonian fluids we refer to their apparent viscosity (p ), or effective viscosity, and we have to specify the conditions of shear rate to which this applies. When we speak of time-dependent fluids, we must also specify the shear history or kinematic history, at the point that their apparent viscosity is quoted. As long as we keep these restrictions in mind for a non-Newtonian fluid, we can still think of the apparent viscosity as ... 

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