Stability and nonlinear dynamics of multidimensional viscoelastic flows

In comparison to viscoelastic unidirectional viscometric flows, the literature on stability analysis of multi-dimensional flows is limited. Several bulk flows of interest in polymer processing, and flows through porous medium of interest to composites manufacturing and enhanced oil recovery are multi-dimensional. In polymer processing operations, the maximum attainable throughput and product quality are typically limited by the onset of flow instabilities. Moreover, experimental observations of the abrupt increase in the friction factor in creeping flows of viscoelastic polymer solutions through porous media have not been explained by first principle steady state simulations. Researchers have suggested that flow instability (that causes a transition to a secondary flow) could be a plausible reason. However dynamical simulations are required to verify this conjecture.; Numerical stability analysis of non-viscometric flows is a formidable task due to huge computational requirements and the difficulties associated with the differentiation of the physical dynamics of the system from numerical instabilities. In this study, we attempt to overcome these limitations by the development of computationally efficient numerical techniques and by systematic mesh-refinement studies. We specifically focus on the flow in benchmark geometries such as the periodically constricted channel (PCC). Our studies in the PCC geometry reveal the existence of a purely elastic instability that is absent in limiting case of the plane channel flow. Computationally efficient time-dependent simulations are performed to investigate the post-critical dynamics and the structure of the secondary flow. We observe that the coupling between velocity gradients in the base flow and disturbances in the polymer chain conformation is the key mechanism that triggers the transition to a secondary flow in which the polymer chain stretch is significantly higher. In a representative case considered, a 13% increase in shear rate resulted in a 100% increase in chain stretch as the flow transitioned into the post-critical regime. Models that incorporate finite chain stiffness predict an increase (∼0.1%) in the friction factor in the post-critical regime. This is the first study that has predicted this phenomenon using first-principle models.