Rheological properties Deborah number

In non-Newtonian fluids K a also depends on their physical and rheoiogical properties. The contribution of the latter has been normally expressed in terms of the apparent viscosity, and there is general agreement that this dependence is of the form Kj a 0(11 ) % where z can take values between 0.4 to 0.7. In the case of viscoelastic materials, inclusion of the fluid rheology is less straightforward. Several authors have tried to include the effect of elasticity via the Deborah number, which for stirred tanks is defined as the product of a characteristic time of the fluid and impeller speed. However, determination of the former is not an easy task because it is not always possible to characterize experimentally the viscoelastic properties of the fluid. Determination of the characteristic time of the fluid from experimental shear viscosity vs. shear rate curves [29] and from interpolation of published experimental data on viscoelastic properties [30] has been tried in the past. However, values thus obtained are not necessarily representative of the actual behavior of the liquid. At present, inclusion of the Deborah number in dimensional or dimensionless correlations has not been completely successful. 

The relaxation period defines the behavior of the system, in accordance with the Maxwell model with respect to the timescale of the applied stress. If the time t during which stress is applied is greater than the relaxation period, that is, t > t the system has properties similar to those of a viscous liquid, while at t t the system behaves like an elastic solid. The flow of glaciers and other processes of strain development in mountains and cliffs are representative examples of such behavior. In rheology, the ratio of a material s characteristic relaxation time to the characteristic flow time is referred to as the Deborah number. This parameter plays an important role in describing the response of various materials to different stresses. 

---