Abstract
V iscoplastic fluids are materials of great interest both in industry and in our daily lives. These applications range from food and cosmetics products to industrial applications such as plastics in the industry of polymers and drilling muds the oil industry. This class of material is characterized by having a yield stress that must be exceeded to the material starts to flow. These fluids are classically predicted by purely viscous models with yield stress. In the last decade, however, there some experimental visualizations has reported that the unyielded regions exhibit elasticity inside. This work is an attempt to investigate the effect of elasticity and inertia in those materials. We will studied, therefore, inertia flow of elastic-viscoplastic materials with no thixotropic behavior, according to the material equation introduced in de Souza Mendes (2011). The mechanical model is approximated by a stabilized finite element method in terms of extra stress, pressure and velocity. Due to its fine convergence feature, the method allows the use of equal-order finite elements and generates stable solutions in high advective-dominated flows. In this study is considered the geometry of a biquadratic cavity, in which the top wall moves to the right at constant velocity. In all computations is used biquadratic Lagrangian (Q1) elements. Results focuses in determining the influence of elasticity and inertia on the position and shape of unyielded. These results proved to be physically meaningful, indicating a strong interlace between elasticity and inertia on determining of the topology of yield surfaces.
Highlights
Elasto-viscoplastic fluids are structured materials that exhibit a complex non-Newtonian behavior that is related to their structure state, which, in turn, depends on the level of stress applied to it
The results aim to study the effect of inertia on the flow pattern of viscoplastic materials subject to elasticity, by determining the morphology and position of their apparently unyielded regions, being that the evaluation of the effects caused by inertia is due to the advective term of the momentum equation
When the flow intensity reaches a high value, a strong displacement occurs of the apparently unyielded regions in the top of the cavity, this is due to the displacement of the central vortex, called the main flow vortex, since with a high velocity, the inertial effects become more evident and with a high velocity and high inertial effects, we will have an increase of the advection in the flow
Summary
Elasto-viscoplastic fluids are structured materials that exhibit a complex non-Newtonian behavior that is related to their structure state, which, in turn, depends on the level of stress applied to it. 10 Giovanni Minervino Furtado, Renato da Rosa Martins: Numerical Approximation of a Non-Newtonian Flow with Effect Inertial account the fields of velocity, pressure and extres-stress as prime variables [2]. This formulation can be seen as an extension - for the elasto-viscoplastic case subject to shearthinning of the relaxation and retardation times, and the viscoplastic SMD function - of the formulation proposed in the paper, for fluids of constant viscosity [11]. The numerical results of inertial flows of elasto-viscoplastic fluids are obtained within a lid-driven cavity and a discussion is presented on inertia, elastic and viscous contributions to the flow pattern
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