The mechanism of elastic instability in viscoelastic Taylor-Couette flow
- Dilute polymer solution: the property of viscoelasticity means that the stress field in the polymeric liquid is not defined directly by the current rate of strain, but instead the history of the liquid deformation.
- Rate of strain tensor (D): describe how fluid element deforms over time (stretching/compressing/shearing). It is the symmetric part of the velocity gradient
- Stress tensor: describe the internal force in the fluid to resist deformation.
- Viscosity is a proportionality constant linking the deformation to the resulting stress.
- Polymer molecules are stretched by the flow and takes some characteristic relaxation time to adjust to the change in flow condition.
- Large elastic energy stored in the polymer chains stretched by the primary flow is released by a secondary flow.
- This is typically occurs at curved streamline, such as the famous Weissenberg effect, where is a rotating rod is inserted in the polymeric flow, we see the liquid start climbing, instead of pushing away due to centrifugal force.