Many particle suspensions behave as thixotropic-viscous materials and they are present in different industrial processes, including coating applications. Specifically, the production of battery electrodes involves slot coating of a thixotropic liquid. In most cases, the flow of slurries and other particle suspensions is described by using a time-independent model that assumes the viscosity to be solely a function of the local deformation rate. However, the viscosity of thixotropic fluids is associated to the evolution of its microstructuring level, which does not change instantaneously with the shear stress (or deformation rate). In the case of imposing constant shear stress (or shear rate), the microstructure evolves until reaching an equilibrium state; but this process takes time. Even in a steady-state flow, the liquid flows through regions where there are significant changes in the levels of shear stress and the flow is transient in a Lagrangian point of view. Therefore, assuming that the viscosity at each point of the flow is the steady-state viscosity described by a time-independent model may lead to an inaccurate flow description. The relative magnitude of the characteristic response time of the liquid and the residence time of the flow becomes an important parameter. This is particularly relevant in small scale flows with very small residence time. Flows of a thixotropic-viscous liquid through a constricted microcapillary and in a slot coating process were analyzed here using two rheological models: a time-independent model (TIM) and a thixotropic model that takes into account the liquid time-dependent response. The resulting set of fully coupled, non-linear equations was solved by the Galerkin and SUPG Finite Element Method. The results show that the use of a TIM to describe thixotropic viscous materials, such as some particle suspensions, can lead to very large errors on the predicted flow behavior. Furthermore, time-independent models are not able to predict complex flow phenomena, like hysteresis, which could lead to unstable flows. These inaccuracies highlight the need for a more complete model that takes into account time-dependency of the flowing liquid in a certain range of flow parameters.