When we did King Kong in the 70s, one minute you'd have a shot of Rick Baker in this big suit and then you'd cut to this 80ft stiff model, and they looked nothing alike.
But Robertson stiff model has better agreement with the experimental values of shear stress and shear rate data of the developed polymer gel system than the other models tested.
Conventional continuum mechanistic models for polymer degradation typically involve thousands of coupled differential-algebraic equations, requiring an efficient solver to solve the complex set of stiff model equations.
This steady state is in practice often simulated by chemical engineers using a series of CSTRs type model due to its stable behavior with respect to spatial discretization and smooth convergence for the underlying stiff model equations.
For a stiff model, the uniformization rate λ ≥ max x ∈ S λ x will correspond to the fastest time scale.
In a stiff model the components of the underlying system act on time scales that differ by several orders of magnitude and this arises in various application domains, especially in systems biology.
The Bingham plastic, Herschel-Bulkley, Mizrahi-Berk, and Robertson-Stiff models give an excellent ability to describe the flow behavior of polymer gel solution.
The nonlinear rheological models like Herschel-Bulkley, Mizrahi-Berk, and Robertson-Stiff models are found to be more suitable compared to the linear rheological model like the Bingham plastic flow model.
In order to determine the polymer gel solution parameters of each model, a linear regression analysis was used for the Bingham model, while a nonlinear regression analysis method was used for the Herschel-Bulkley, Mizrahi-Berk, and Robertson-Stiff models.
We present a procedure for deriving reduced-order, non-stiff models for the fast and slow dynamics, and a framework for rational control system design that accounts for the time scale separation exhibited by the system dynamics.
