The displacement of a thixotropic fluid by an immiscible Newtonian fluid is investigated theoretically in a rectangular Hele-Shaw cell. Assuming that the thixotropic fluid of interest obeys the purely-viscous Moore model, use is made of the generalized Darcy’s law for finding the basic-flow. Having imposed infinitesimally-small normal-mode perturbations to the basic-flow, an analytical solution is found for calculating the growth rate and wavenumber of unstable modes. The analytical solution enables us to easily investigate the effects of the Moore’s model thixotropy parameters on the viscous fingering phenomenon in the Hele-Shaw cell. Based on the results obtained in the present work, it is concluded that thixotropy has a stabilizing effect on the Saffman-Taylor instability.
The occurrence condition of a temporal shear stress oscillation phenomenon of wormlike micellar solutions is experimentally investigated. The two samples that have different surfactant and salt concentrations but have a same relaxation time are examined. The salt rich sample forms network micelles structure and does not exhibit the temporal shear stress oscillation, but the other sample that forms wormlike micelles shows the stress oscillation phenomenon. This sample has a stress plateau region in its flow curve and the stress oscillation phenomenon occurs in the higher shear rate regime of this plateau region. This shear rate regime coincides with the shear-induced structure (SIS) generation regime, and the flow birefringence measured near the inner and outer wall shows different value at the phenomenon. The phenomenon is not caused by secondary flow or shear-banding to the vorticity direction but it is closely related with the generation of the velocity gradient shear-banding and the SIS.