Rheology of dense granular suspension systems

The goal of my PhD project is to establish a multiscale continuum theory for the rheology of dense granular suspension systems, which has greater predictive capability for a wide range of engineering applications. I intend to construct a complete continuum theory of the rheology across flow regimes, including the transition between different flow regimes. Many industrial processes will surely become more efficient and safe once a reliable continuum theory is successfully constructed. In the former work of Ness and Sun , a constitutive model is proposed to capture the flow regime transitions as a function of solid volume fraction, shear rate, and material properties, which has been shown to be able to predict the divergent behavior of the suspension viscosity with respect to the solid volume fraction. However, the work was based on the homogeneous simple shear flow, resulting in two main limitations: more complex unsteady rheology of dense granular suspensions and the rheology in coexisting regimes were not taken into consideration during the construction of constitutive model. To overcome these limitations, we have to research on a representative phenomenon of both unsteady flow and regime coexistence. Based on preliminary investigations, I found that discontinuous shear thickening (DST) satisfies these requisitions perfectly since the real flow in DST regime is unsteady . Futhermore, DST corresponds to a fragile state , which is considered as a coexistence of two regimes. Therefore, DST of dense granular suspensions is employed as the basic case of this proposal. The research on DST will provide more macroscopic and microscopic characteristics of unsteady rheology, which contribute to the construction of a more consummate and reliable continuum model of dense granular suspension systems.
The discontinuous shear thickening behavior is that the suspension viscosity experiences a discontinuous orders-of-magnitude increase as the shear rate becomes higher. A very good example of DST is cornstarch, as shown in Figure 1, which is a common thickening agent used in cooking. Wyart and Cates have proposed a rheological model to predict DST in different suspension systems. They claim that DST happens at high volume fraction. The S-shaped flow curves could occur with multiple flow states existing at a given shear rate but at greatly differing stresses. Jaeger's experiment found that DST is a fragile state that exhibits intermittently flow, which can be considered as a precursor to shear jamming and exhibits behavior of marginal material that is neither freely flowing nor fully jammed . The critical stress is independent of packing fraction since it only depends on the microscopic breakdown of lubrication. Moreover, unsteady flow has been observed in a Couette Cell system by Hermes et al , which was not predicted by recent theories. There have been many experimental and computational work on DST. However, a widely accepted theory has not been proposed yet. In summary, DST is an interesting phenomenon in the rheology of dense granular suspension. The research on DST can serve as perfect supplement for limitations of the former continuum model proposed by Ness and Sun .